Valuing unit linked life insurance
contracts with a guaranteed return
under IFRS 17
Master’s Thesis to obtain the degree in Actuarial Science and Mathematical Finance University of Amsterdam
Faculty of Economics and Business Amsterdam School of Economics
Author: B. R. Sinchico Arias
Student nr: 10009353
Email: rayusinchico@live.nl
Date: December 16, 2017
Supervisor: Drs. R. Bruning AAG
Statement of Originality
This document is written by Student Benjamin Rayu Sinchico Arias who declares to take full responsibility for the contents of this document.
I declare that the text and the work presented in this document are original and that no sources other than those mentioned in the text and its references have been used in creating it.
The Faculty of Economics and Business is responsible solely for the supervision of completion of the work, not for the contents.
Valuing unit linked insurances with a guarantee under IFRS 17 — iii
Abstract
This thesis studies the effects of the IFRS 17 standard on reporting unit linked life insurance contracts that have a guaranteed return for the policyholder and a variable fee for the entity embedded in the contract. The lack of ability to compare listed companies internationally within IFRS 4 led to the introduction of IFRS 17, which will be effective from January 1st 2021.
Under IFRS 17 the liabilities are build out of building blocks. The estimated future cash flows, the time value of money, the risk ad-justment and the contractual service margin together form the building blocks. The way the liabilities are measured depends on the approach that is used. IFRS 17 describes 3 different approaches, namely the Building Block Approach, the Premium Allocation Ap-proach and the Variable Fee ApAp-proach. This thesis focuses on the Variable Fee Approach since the unit linked life insurance contracts with a guarantee and a variable fee meet the requirements of the Variable Fee Approach.
This thesis also studies option valuation techniques for determining the time value of options and guarantees because a guarantee is embedded in the unit linked life insurance contract, which needs to be assessed under IFRS 17. By presenting the time value of options and guarantees, the contractual service margin and the profit and loss statement for different created scenarios, the effects of the IFRS 17 standard are studied. Because IFRS 17 leaves a lot of freedom for the entity in choosing valuation methods, discussion about these choices will arise the coming years and further research on these topics are needed.
Keywords IFRS 17, Variable Fee Approach, Unit linked life insurance contract, Options and guarantees, Valuation of options, Closed-form solution, Stochastic processes
Preface vi
1 Introduction 1
2 Standards 3
2.1 IFRS 17 . . . 3
2.1.1 Building Block Approach . . . 4
2.1.2 Profit and Loss Statement and Other Comprehensive Income 7 2.1.3 Premium Allocation Approach . . . 9
2.1.4 Reinsurance contracts . . . 9
2.1.5 Variable Fee Approach . . . 10
2.2 IFRS 9 . . . 15
3 Valuation of options 17 3.1 The Black-Scholes-Merton model . . . 18
3.1.1 Model properties . . . 19
3.1.2 Discrete form . . . 20
3.1.3 Disadvantages of the model . . . 20
3.2 Time value of options and guarantees . . . 21
4 The Models 23 4.1 IFRS 17 . . . 23
4.2 Defining the P&L and OCI . . . 28
4.2.1 Underwriting result . . . 29
4.2.2 Investment result . . . 29
4.2.3 OCI . . . 30
4.3 TVOG . . . 30
Valuing unit linked insurances with a guarantee under IFRS 17 — v
5 Assumptions and scenarios 32
5.1 Specifications of the insurance contracts . . . 32
5.2 Rates assumptions . . . 35 5.3 Scenarios . . . 36 5.3.1 Scenario 1 . . . 36 5.3.2 Scenario 2 . . . 37 5.3.3 Scenario 3 and 4 . . . 37 5.3.4 Scenario 5 and 6 . . . 37 5.3.5 Scenario 7 and 8 . . . 38 5.3.6 Scenario 9 . . . 38 5.3.7 Scenario 10 . . . 39
6 Results and discussion 40 6.1 UL1 . . . 40
6.1.1 Results scenario 1 . . . 40
6.1.2 Results scenario 2 . . . 44
6.1.3 Results scenario 3 and 4 . . . 45
6.1.4 Results scenario 5 and 6 . . . 47
6.1.5 Results scenario 7 and 8 . . . 48
6.1.6 Results scenario 9 . . . 50 6.1.7 Results scenario 10 . . . 51 6.2 UL2 . . . 53 6.2.1 Results scenario 1 . . . 53 6.2.2 Results scenario 2 . . . 55 6.2.3 Results scenario 3 . . . 56 6.2.4 Results scenario 5 . . . 57 6.2.5 Results scenario 9 . . . 58
6.3 Summary and discussion . . . 59
7 Conclusion 63
This master’s thesis brings an end to my well enjoyed student life and initiates my working career. I would like to take this oppor-tunity to thank a number of people who have made it possible for me to write my master’s thesis successfully.
First, I would like to show my gratitude to Rob Bruning for his great support and guidance during the past three months. During our meetings, which took place at a.s.r., Triple A - Risk Finance and the UvA, he provided great feedback on the concept versions of my master’s thesis and sent me in the right direction when i was struggling with my research. And for that, I am very grateful.
Furthermore, I would like to thank my in-company supervisor Tim Delen at Triple A - Risk Finance for introducing me and guiding me through the subject of this master’s thesis. His expertise on IFRS 17 has helped me broaden my scope on the subject. I also would like to thank Carlo Jonk and Enno Veerman for our meetings and their effort during this project.
Last but not least, I would like to thank my family, and especially my mother, for all their support during my student years. They always believe in me which encourages me to create the best version of myself. Obtaining my bachelor’s and master’s degree was only possible because they supported me at all time.
Chapter 1
Introduction
International Financial Reporting Standards (hereinafter IFRS) are accounting standards for annual reports of listed companies. They are issued by the IFRS Foundation and the International Accounting Standards Board (hereinafter IASB) to provide a clear overview of the financial condition of the listed companies in such a way that they are understandable and can be compared across international boundaries.
At this moment IFRS counts 16 standards (IFRS 1 up to and including IFRS 16) of which IFRS 4 covers the subject insurance contracts. IFRS 4 leaves a lot of freedom for the entity to choose a method of reporting the financial statements of in-surers, which leads to a lot of different methods of reporting. For example, liabilities can still be determined using local accounting rules. Within IFRS 4 there barely are international standards which makes it difficult to compare listed companies across international boundaries.
The lack of comparability within IFRS 4 should be solved by IFRS 17. IFRS 17 has been published in may 2017 by the IASB after it had released several draft versions. IFRS 17 will be effective from 1 January 2021 but can be implemented earlier provided that IFRS 9 is applied. IFRS 17 introduces two main changes. On the one hand, there is the valuation based on fair value, on the other hand, there is the way of presenting the results on the reported profit or loss. Both parts of the standard are expected to have a huge impact on the systems and the processes at insurance companies. The liabilities of insurance contracts will be valued as the present value of future cash flows with a provision for risk. The IASB differentiates between three different methods to value these liabilities where each of them are applied to different kind of insurance contracts. One of them is the Variable Fee Approach (hereinafter VFA). The VFA values the liabilities of insurance contracts
that are so called ’direct participating contracts’. Many insurers issue these type of contracts, such as unit linked life insurance contracts with a guarantee, that share returns on the underlying items with the policyholders.
IFRS 17 will bring the most significant change to European insurance report-ing standard ever and the size of change will vary significantly between insurance companies. Also, the ways of interpreting and comparing the listed companies in-ternationally will change for analysts and investors. Given the anticipated scale of changes, insurers should start assessing the impacts and effects of IFRS 17. This thesis will therefore address the following central research question:
”How should insurers value unit linked life insurance contracts with a guarantee under IFRS 17 and what are the effects of the guidelines of IFRS 17 on the profit and loss statement for these kind of insurances?”
To find out what the effects of the guidelines of IFRS 17 will be like, the new standard will be studied in several simulated situations by creating a cash flow model and a model that produces the annual report of the contracts according to the IFRS 17 standard.
As mentioned, many insurers issue unit linked life insurance contracts with a guarantee on the return of the investment. Under IFRS 17, it is important to mea-sure the value of uncertainty caused by promising future guaranteed returns on the investment. This uncertainty is captured in the time value of options and guarantees under IFRS 17. For this reason, valuation of options will also be discussed.
The remainder of the research is organized as follows. The IFRS 17 standard and the components of the new standard are discussed in Chapter 2. Next, Chapter 3 provides a detailed description of methods used to value options. Then the model that reports the annual report according to the IFRS 17 standard is presented in Chapter 4. Chapter 5 contains the assumptions made for the calculations and describes the different scenarios that are used to study the new standard. The results and analysis are discussed in Chapter 6. Finally, a summary and conclusions are presented in the last chapter of this thesis
Chapter 2
Standards
In order to investigate the effects of the new standard, several methods and tech-niques for accounting are needed. This chapter will discuss them individually in separate subsections. The first step is to evaluate the new insurance standard by showing how the insurance liabilities should be measured and presented on the bal-ance sheet which results in different reported profits and losses. Section 2.2 describes the IFRS 9 standard. The assets that are associated with the insurance contracts should also be measured and reported according to a standard. IFRS 9 introduces the way the assets should be measured such that it matches the measurement ac-cording to the IFRS 17 standard of the insurance liability.
2.1
IFRS 17
In this section the new standard for insurance contracts will be thoroughly dis-cussed and summarized. This will be done by considering the guidelines of IFRS 17 standard published by IFRS Foundation (2017b), the Insurance Contracts First Impressions IFRS 17 published by KPMG (2017), the IFRS 17 Implications for Eu-ropean insurers published by EY (2017) and the Illustrative example of the Variable Fee Approach published by EFRAG (2017). Just like IFRS 4, the new standard puts the focus on the type of contracts rather than the type of entities. It applies to in-surance contracts and to all reinin-surance contracts that are issued by the entity. It also applies for reinsurance contracts the entity holds and investment contracts with discretionary participating features if an entity issues these insurance contracts. In this research all will be referred to as insurance contracts. This research will not list the exact conditions a contract should meet in order to be within the scope of IFRS 17.
With the introduction of IFRS 17, updated systems, processes and models will be needed. Next to that, new data should be acquired. As many insurers operate over a long time horizon, this could be quite challenging for the insurers (KPMG, 2017). These issues will not be discussed in this research and since the purpose of this study is to find out what happens if a portfolio is measured according to the IFRS 17 standard, the insurance contracts considered are assumed to be recognized already.
The transition from IFRS 4 to IFRS 17 will bring many differences in the mea-surement and presentation of the insurance contract liabilities. The liabilities will be measured at fair value through 3 different approaches. The General Approach, also called the Building Block Approach (hereinafter BBA), is the general measurement approach for general insurance contracts. Insurance contracts with a short dura-tion can be measured with a simplified approach called the Premium Allocadura-tion Approach (hereinafter PAA). The PPA can also be used if the insurance liabilities produced by the PPA do not differ materially from the insurance liabilities pro-duced by the BBA. Certain unit linked and participating contracts are measured through the Variable Fee Approach (hereinafter VFA). These three approaches will be discussed, though this research will primarily focus on the measurement of unit linked life insurance contracts with a guarantee which are measured using the VFA.
2.1.1 Building Block Approach
The new standard requires an entity on initial recognition to measure a group of insurance contracts at the total of the fulfilment cash flows and the contractual service margin. The BBA, which is used to measure the general insurance and reinsurance contracts, measures the group of insurance contracts on the basis of four building blocks (IFRS Foundation, 2017b, p. 15-20):
• The expected value of future cash flows
• The adjustment to reflect the time value of money and the financial risks related to the future cash flows
• The risk adjustment for non-financial risk
• The contractual service margin
Together they form the fulfillment cash flows and the contractual service margin. The first building block is the estimation of future cash flows. The entity should base these estimates on all reasonable and supportable information that is available
Valuing unit linked insurances with a guarantee under IFRS 17 — 5
at that time, and should not leave out any available information about amount, timing and uncertainty. Every reporting period, the estimations of the future cash flows need to be updated and reflect the perspective of the entity while being, when relevant, market consistent. Expenses that are not directly assigned to the insurance contract should not be included in the expected future cash flows, but will be recognized directly in the profit and loss statement (IFRS Foundation, 2017b, p. 15).
The second building block is the discounting of the expected cash flows. The expected future cash flows will be discounted to reflect the time value of money, the liquidity characteristics and the financial risks of the insurance contracts. The discount rates that are used should be consistent with observable market prices of financial instruments such that the discount rates reflect the timing, currency and liquidity of the cash flows. The new standard does not prescribe a single technique to estimate the discount rates but does specify that a ’top-down’ approach (IFRS Foundation, 2017b, p. 62-63 B81-B85) or ’bottom-up’ approach (IFRS Foundation, 2017b, p. 62 B80) could be used. Using the top-down approach, an entity determines the discount rates by taking the returns of a reference portfolio and adjust the returns for credit risk by subtracting a credit risk spread. Using the bottom-up approach, an entity will take the risk free rates based on highly liquid bonds and adjust the rates by adding an illiquidity premium (IFRS Foundation, 2017b, p. 57 BC196). The determined yield curve on initial recognition is called the ’locked in rate’.
The third building block is the risk adjustment for non-financial risk. The risk adjustment should be measured such that an entity would be indifferent between fulfilling the liabilities of an insurance contract that has different possible outcomes caused by the non-financial risk involved or paying a fixed cash flow with the same expected present value as the liabilities (IFRS Foundation, 2017, p. 64 B87). From an entity’s perspective the risk adjustment reflects the diversification of the entity and the entity’s risk aversion. The risk adjustment fulfills the same role as the risk margin under Solvency II. Under Solvency II the ’cost of capital’ method is prescribed for determining the risk margin. IFRS 17 does not prescribe methods for determining the risk adjustment. Different methods are allowed but they should meet the following characteristics (IFRS Foundation, 2017b, p. 65 B91):
• Risks with low probabilities and high severity result in a higher risk adjust-ment
adjustment
• Risks with a higher variance will result in a higher adjustment
• If the estimation of the best estimate parameters are less accurate, the risk adjustment will be higher
• If emerging experience reduces uncertainty, the risk adjustment will be lower.
In terms of presentation there is the obligation to publish the confidence level and the used method. The IFRS Board proposed to use the Confidence level (Value at Risk) method, Conditional Tail Expectation (or Tail Value at Risk) method or Cost of Capital approach (IASB Insurance Working Group, 2010). The applicability of a method follows from the nature of the risks (the skewness of distribution, the duration of the liabilities, etc.).
The fourth and last building block is the contractual service margin (hereinafter CSM). The CSM is the expected unearned profit in an insurance contract. The initial measurement of the CSM at inception will be given by the value that is equal and opposite of the net amount of the sum of the fulfillment cash flows and possibly any cash flows that existed before the start of coverage, provided that the contract is profitable. If the insurance contract is profitable, the CSM will be positive, if not, the CSM will be 0 and the contract is loss-making, which is called ’onerous’.
Generally at the end of each reporting period the CSM is adjusted. The esti-mated future cash flows and the risk adjustment are updated and changes in the estimated future cash flows and risk adjustment that arise from a change in non-financial assumptions will be processed within the CSM to the extent that the CSM remains non-negative. Changes in the CSM can be divided into (IFRS Foundation, 2017b, p. 18):
• Interest accreted on the CSM using the locked in rate
• Experience adjustments arising from the received premiums that relate to to future services
• Change in estimates of the present value future cash flows caused by non-financial assumption changes
• Change in value of the risk adjustment for non-financial risk that relate to future services
Valuing unit linked insurances with a guarantee under IFRS 17 — 7
• Allocation of CSM in Profit & Loss due to earned profit as services are pro-vided
• Allocation of CSM in Profit & Loss due to a negative CSM
Each reporting period a part of the remaining CSM will be released in the Profit and Loss statement. The amount that will be released is related to the provided services during the period since the CSM reflects the unearned profit of future service to be provided for a group insurance contracts. The provided services of each reporting period will be measured by identifying the coverage units in the group. The coverage units are based on the quantity of the benefits provided and the expected duration of these benefits. Once the number of coverage units in a group is determined, allocation of the CSM will be done equally to each coverage unit provided in the current period and expected to be provided in the future. Finally, the amount allocated to the coverage units provided in the period will be recognized in the Profit and Loss statement (IFRS Foundation, 2017b, p. 70-71 BB119).
2.1.2 Profit and Loss Statement and Other Comprehensive Income
The new standard describes which amounts should be taken into the Profit and Loss Statement (hereinafter P&L) or into the Other Comprehensive Income (hereinafter OCI). Together they form the Total Comprehensive Income. The OCI is a separate component on the balance sheet, where amounts that have an effect on the equity on the balance sheet but not on the P&L are reported, such that there are no accounting mismatches.
The new standard also requires an entity to make an accounting policy choice as to whether to disaggregate the effect of changes in assumptions that relate to financial risk for the period between P&L and OCI (IFRS Foundation, 2017b, p. 29). This means that the changes in fair value of the portfolio of insurance contract caused by the change in discount rates could be reported in the P&L (hereinafter FVPL) and in the OCI (hereinafter FVOCI).
As described in the previous section, each reporting period a part of the re-maining CSM will be released in the P&L. The new standard prescribes that the following results are recognized in the P&L:
• Losses caused by the insurance portfolio being onerous at initial recognition
• Changes in estimated cash flows related to past and current services that do not adjust the CSM.
• Release of the CSM due to earned profit as services are provided
• Release of risk adjustment related to past and current services and changes in the risk adjustment for non-financial risk
• The expected claims and expenses incurred this period
• Difference between the claims and expenses that incurred this period and the latest expectation of them
• The interest rate expenses on the fulfillment cash flows and the CSM excluding the amount that is reported in the OCI
• Other results that are not processed in the CSM or reported in the OCI
To show how this results in the reported P&L, an example of the reported output in the statement of comprehensive income is shown in figure 2.1
Figure 2.1: Created example of the statement of comprehensive income
The insurance revenue consists of the amortization of the CSM, the expected incurred claims and other expenses and the release of the risk adjustment. Together
Valuing unit linked insurances with a guarantee under IFRS 17 — 9
with the insurance contract expense, which includes the incurred claims, the amorti-zation of insurance acquisition cash flows, losses of onerous contracts and recoveries of onerous contracts, they form the underwriting result. Chapter 4 will go into more detail about each of the components since Figure 2.1 is just an example to picture the results of the new standard.
2.1.3 Premium Allocation Approach
Under the Premium Allocation Approach (hereinafter PAA) the BBA may be sim-plified for certain insurance contracts to measure the liabilities for remaining cov-erage. The PAA uses the same method as existing European non-life insurance accounting where two components are used to measure the liability of the contract (KPMG, 2017):
• a liability for the remaining coverage, which measures the fulfilment cash flows relating to future services that will be provided to the policyholders
• a liability for incurred claims, which measures the fulfilment cash flows for claims and expenses that are already incurred
The PPA can be used if the insurance liabilities produced by the PPA do not differ materially from the insurance liabilities produced by the BBA or if the contracts of the insurance portfolio have a coverage period of one year or less. Many non-life insurance contracts meet the criteria since they have a coverage period of one year or less at initial recognition. Since the PPA goes beyond the scope of the research, this thesis will not discuss the PPA more extensively.
2.1.4 Reinsurance contracts
Although reinsurance contracts are not of interest within this research, measurement of these contracts under the new standard is discussed shortly since it is part of IFRS 17. Reinsurance contracts that are issued are measured by the same method as typical insurance contracts. The BBA is used to measure these contracts. The modifications introduced to the BBA by the new standard are relevant for the reinsurance contracts that are held. Usually reinsurance contracts held are assets rather than liabilities (KPMG, 2017). They need to be measured separately from the underlying insurance contract, which is done by the BBA with certain modifications. One of the most important modifications is that the CSM is not restricted to being non-negative. Also, it is important to note that the reinsurance contracts can not offset the original contracts.
2.1.5 Variable Fee Approach
This thesis will primarily focus on the measurement of unit linked life insurance contracts with a guarantee and a variable fee which are measured under IFRS 17 using the Variable Fee Approach (hereinafter VFA). This approach is called the VFA because the CSM will be adjusted to reflect the variability of the insurer’s fee. The VFA is a modification of the BBA, and is applied to insurance contracts with direct participating features. Insurance contracts with direct participation features are insurance contracts that are investment-related service contracts. The entity promises an investment return based on underlying items. These contracts contain the following conditions at initial recognition (IFRS Foundation, 2017b, p. 67 B101):
• the policyholder participates in a share of a clearly identified pool of under-lying items
• the entity expects to pay an amount equal to a substantial share of the fair value returns on the underlying items to the policyholder
• a substantial part of the cash flows the insurer expects to pay to the pol-icyholder should be expected to vary with cash flows from the underlying items
An insurance contract would need to meet all three conditions for it to be mea-sured by the VFA. At initial recognition, the entity will determine whether these conditions are met using its expectations of the insurance contract and will not reevaluate the contract afterwards to see if the conditions are still met, unless the specifications of the insurance contract are changed.
The policyholder should participate in a share of a clearly identified pool of underlying items. With it a variable fee for the entity can be expressed as an amount or percentage of the portfolio returns. The pool of underlying items can contain any items, but it has to be clearly identified in the insurance contract.
The new standard prescribes that the entity shall determine the variability in the cash outflows to the policyholders. Consider for example an insurance contract with a guarantee embedded. If the entity expects the cash outflows to be based on the fair value returns on underlying items, there will be scenarios in which the cash outflows to the policyholders fluctuate with the fair value returns of the underlying items because the guaranteed amount does not exceed the fair value returns on the underlying items. But there will also be scenarios in which the expected cash outflows to the policyholder do not fluctuate due to the changes in the fair value of
Valuing unit linked insurances with a guarantee under IFRS 17 — 11
the underlying items because the guaranteed amount exceeds the fair value return on the underlying items (IFRS Foundation, 2017b, p. 69 B108).
This thesis will asses this variability in the cash outflows to the policyholders by measuring the time value of options and guarantees (hereinafter TVOG). This means that when an unit linked life insurance contract with a guarantee is mea-sured under the new standard, the TVOG needs to be determined too. The new standard will require entities to implement stochastic modeling of financial options and guarantees which may cause extra implementation difficulties for entities that are not using stochastic modeling under IFRS 4. The TVOG should be measured and recognized on current, market consistent basis and will involve stochastic mod-eling. Another approach could be to use a deterministic model and run it for a number of times such that they reflect different scenarios and asses the variability in the cash outflows to the policyholders caused by the guarantee embedded in the contract. For example, the Black & Scholes (1973) formula could be used for certain simple options and guarantees, which could be equivalent to stochastic modeling. Chapter 3 will discuss extensively the valuation techniques that could be used for valuing the unit linked insurance contracts with a guarantee and the TVOG.
As mentioned before, the VFA is a modification of the BBA. The VFA uses about the same method as the BBA for measuring insurance contracts with just a few crucial differences. One of the differences is the accretion of interest on the CSM. For the BBA the interest accreted on the CSM is based on the locked in rate. However, under the VFA there is no interest accretion on the CSM required since the CSM is effectively remeasured when it is adjusted for changes in financial risk. Under the BBA the changes in market variables including options and guaran-tees are recognized immediately in either the P&L or in the P&L and OCI. The VFA regards these changes as part of the variability of the fee for future services. As a result, the changes in shareholders’ share of underlying items, which include the options and guarantees, are processed in the CSM1 (EFRAG, 2017, p.5).
The CSM under the VFA is adjusted each reporting year for the following changes (IFRS Foundation, 2017b, p.19):
• Changes relating to the fair value of the underlying items
• Interest accreted on the present value of the future cash flows
• Change in the present value of the estimated future cash flows due to a change
1
Unless the CSM reaches zero. At that moment, it will be recognized the same way as under the BBA.
in the discount rate
• Change in the present value of estimated future cash flows caused by assump-tion changes
• Change in value of the risk adjustment for non-financial risk that relate to future services
• Change in value of the time value of options and guarantees
• Allocation of CSM in Profit & Loss due to Earned profit as services are pro-vided
• Allocation of CSM in Profit & Loss due to a negative CSM
Actually, the IFRS 17 standard prescribes that the CSM should be adjusted for the entity’s share of the change in the fair value of the underlying items. The entity is not required to identify each separate component that adjusts the CSM, instead a combined amount, like the total change in the fair value of the entity’s share of the underlying items, can be identified (IFRS Foundation, 2017b, p.70).
To describe the adjustments of the CSM more clearly, each component that form the amount of the change in the fair value of the entity’s share of the underlying items is described above. The changes in the fair value of the underlying items, the interest accretion on the present value of the estimated future cash flows, the interest accretion on the risk adjustment and the changes in the present value of the estimated future cash flows due to changes in the discount rates together compose the amount of the change in the fair value of the entity’s share of the underlying items (EFRAG, 2017, p.22). Whether this change is a positive or negative amount depends on the value of each of the components. The results of this thesis described in Chapter 6 will display numerical values for each of the components.
The risk adjustment changes each period due to the interest accretion, a change in the non-financial risk assumptions and the release to the P&L. The changes in risk adjustment caused by the interest accretion and by changes in the non-financial risk assumptions will be processed in the CSM.
The IFRS 17 standard does not prescribe clearly that the total change in value of the TVOG should be processed in the CSM. Also, it does not prescribe whether each period a part of the TVOG should be released to the P&L. The example of EFRAG (2017) and the Illustrative Example of IFRS Foundation (2017a) process changes in the TVOG caused by assumption changes through the CSM, because the effect of the time value of money and financial risk and changes therein are
Valuing unit linked insurances with a guarantee under IFRS 17 — 13
processed in the CSM (IFRS Foundation, 2017b, p. 70). Because both the examples adjust the CSM for changes in the TVOG, this method is also used in the model described in Chapter 4. Each year the TVOG is measured and the CSM is adjusted for the change in TVOG. This way, any profit or loss caused by a change in TVOG is not directly recognized, but will be recognized through the CSM, resulting in a less volatile P&L.
The effect of any new contracts added to the group and the effect of any currency exchange differences that arise on the CSM are not discussed since they will not be used in the created portfolio of insurance contracts in this research. Chapter 5 will discuss the assumptions made for the portfolios of insurance contracts that are used in this research.
The CSM can be seen as the profit that has not yet been realized. With a vari-able fee, the profit changes each reporting period as the underlying items change. Excluding the allocation of CSM to the P&L, all components described above cap-ture the change in the variable fee of the entity. For example, a good market year will result in a positive fair value change of the underlying items. But as the fair value of the underlying items increases, the other components could decrease and cancel out the positive change in the CSM due to an increase in fair value of the underlying items.
To illustrate the discussed differences between the BBA and the VFA, table 2.1 shows a numerical example of the treatment of changes in the financial risk (here the discount rate). A portfolio of insurance contracts with a coverage period of 5 years is considered, where at maturity the policyholder will receive 95% of the fair value of the underlying items. The total premium received at inception is 50.000, within the first 4 years no policyholder dies and for simplicity the risk adjustment is set at zero. The discount rate is assumed to be 8% but is exposed to a market shock at the end of year 3. Due to this shock, the interest rate changes to 4%. The CSM at inception is 2500 and is accreted with the locked in rate for the BBA.
As table 2.1 shows, the CSM is not accreted separately for the VFA. The CSM is remeasured when it is adjusted for changes in financial risk. This way, the CSM is accreted indirectly through other components (in this case the interest expense). If a guarantee is embedded in the insurance contract, the change in discount rate will change the time value of options and guarantee. The example shows how this change is accounted for. As mentioned, changes in the value of options and guar-antee are accounted in the P&L or P&L and OCI under the BBA. Under the VFA the changes are accounted in the CSM (EFRAG, 2017, p.5).
BBA
Statement of comprehensive income Year 1 Year 2 Year 3 Year 4 Changes in FV of Assets 4000 4320 4666 2519
Interest expense -3800 -4104 -4432 -4787
Accretion on CSM -200 -216 -233 -252
Investment result 0 0 0 - 2519
Change in TVOG due to shock - - - in P&L or P&L/OCI
VFA
Statement of comprehensive income Year 1 Year 2 Year 3 Year 4 Changes in FV of Assets 4000 4320 4666 2519
Interest expense -4000 -4320 -4666 -2519
Accretion on CSM - - -
-Investment result 0 0 0 0
Change in TVOG due to shock - - - in CSM
Table 2.1: Numerical example of the BBA versus the VFA
The second building block of the VFA discounts the expected cash flows that vary based on the returns of any financial underlying items. These cash flows shall be discounted by one of the following methods (IFRS Foundation, 2017b, p. 61 B74):
• discounting the cash flows using rates that reflect the variability of the cash flows
• After the cash flows are adjusted for the effect of the variability, discounting the cash flows at a rate that reflects the adjustment made
Using the first method, the expected future cash flows are determined using the expected returns of the underlying items. Using a deterministic real-world projection rate, which means that a risk premium is included, the expected future cash flows could be determined. The discount rates that are used for discounting should also
Valuing unit linked insurances with a guarantee under IFRS 17 — 15
include a risk premium in order to match that variability. Using the second method, the expected future cash flows are adjusted for the effect of that variability. The expected future cash flows are not determined using the expected returns of the underlying items but are estimated using a deterministic risk-free rate. The discount rates that are used for discounting will also be on a risk-free basis .
It holds for both methods that the discount rates are consistent with the rates that are used to determine the future cash flows. As a result, any valuation mismatch and double counting are avoided, which means that theoretically both methods should obtain the same results.
As mentioned before, if there is a minimum guarantee on return embedded in an insurance contract, the cash flows that change based on the returns on underlying items do not change solely based on the returns on the underlying items. In some cases where the guarantees are in-the-money (i.e. the guaranteed return is greater than the return on the underlying items), the cash flows will not change based on the underlying items. An entity needs to adjust the rate that is used to reflect the variability of the returns on the underlying items for the effect of the guaran-tee (IFRS Foundation, 2017, p. 61 B76). Notice that the standard does not give a mandatory and clear method for determining the discount rates, only a few re-strictions the discount rates must meet are presented. This could lead to discussion about the discount rates that should be used.
This thesis does not adjust the rate that is used to reflect the variability of the returns on the underlying items for the effect of the guarantee embedded in the insurance contract. Instead, it is assumed that the TVOG already captures the effect of the guarantee embedded in the insurance contract.
2.2
IFRS 9
When IFRS 17 will be implemented, IFRS 9 already has to be applied. The assets that are associated with the insurance contracts should also be measured and re-ported according to a standard. IFRS 9 introduces the way the assets should be measured such that it matches the measurement according to IFRS 17 standard of the insurance liability. IFRS 9 is not the main subject this research, that is why only the most relevant sections of the standard that connect with the reporting of insurance contracts will be discussed.
IFRS 9 measures interest accretion and fair value of the assets through the P&L or the OCI. This determines what kind of effect shocks in the interest rates will
have on the P&L, which connects with the way these shocks are measured under IFRS 17. IFRS 9 uses three different models to measure (IFRS Foundation, 2014):
• Amortised cost based (AC): Both of the following conditions should be met for the asset to be measured through AC: the asset is held with the purpose to collect contractual cash flows; and the contractual cash flows are solely payments of principal and interest on the principal amount outstanding.
• Fair value through other comprehensive income (FVOCI): financial assets are classified and measured at FVOCI if they are solely and principal and held to both collect contractual cash flows and sell financial assets.
• Fair value through profit or loss (FVPL): the financial assets that are not held in one of the two models discussed are measured at FVPL.
Interest accretion of assets measured at AC or FVOCI that are newly obtained go through the P&L. The value that is recognized in the OCI will be set to zero if these assets are sold and is recognized through the P&L.
Under the FVPL model all changes in the fair value that are caused by changes in the discount rates or interest accretion are recognized through the P&L. The amount that recognized already in P&L and the fair value are the same, which means that if assets are sold, no extra amounts will be processed.
Now that IFRS 17 and the relevant sections of IFRS 9 are discussed, it is clear how insurance contracts should be measured under IFRS 17. As mentioned, this thesis focuses on measuring unit linked life insurance contracts with a guarantee embedded. Chapter 4 will discuss the model that is created for measuring these types of contracts under IFRS 17, but since there is a guarantee embedded in the contract, valuation techniques for valuing the time value of options and guarantees that should be reported under IFRS 17 are first discussed in the next chapter.
Chapter 3
Valuation of options
The previous chapter discussed and summarized IFRS 17. As mentioned, under the VFA the time value of options and guarantee (hereinafter TVOG) of a unit linked insurance contract with a guarantee on return should be valued since it provides valuable information for an entity’s balance sheet. The purpose of the TVOG is to measure the value of the uncertainty of future cash outflows of the entity, which is caused by promising future guaranteed amounts to the policyholders. These guarantees create an option value due to the asymmetry in the contracts. Entities are required to assess the TVOG using stochastic techniques. Closed-form solutions could be used but only if they lead to sufficiently accurate results. They may not be suitable in valuing more complex guarantees, stochastic simulation is needed to establish a realistic estimate of their value.
The TVOG should be measured and recognized on current, market consistent basis. Simply explained the stochastic model is market consistent if, after the stochastic model is specified and parametrized, the market prices of the deriva-tives are obtained with the use of the simulations created by the model. Not only are stochastic models needed that create market scenarios well, they should also include fast simulation techniques. Many academics have contributed to the devel-opment of stochastic models and many models have been build in the last decade. For example, different methods for option pricing using the Fast Fourier Transforms were suggested by Carr & Madan (1999) and exact simulation frameworks using stochastic volatility models are introduced by Broadie & Kaya (2004).
This chapter aims to find a stochastic model that is most suitable for valuing options and guarantees embedded in insurance products. This is done by discussing relevant literature for measuring these options and guarantees. For simplicity rea-sons, fixed volatility of stock prices is assumed. Well known models that assume a
fixed volatility of the underlying item are the binomial tree model (Cox, Ross, & Rubinstein, 1979) and the Monte Carlo simulation model of Boyle (1977). Since the results of the models will eventually converge to the Black-Scholes-Merton model (Black & Scholes, 1973), only the Black-Scholes-Merton model is extensively dis-cussed.
This chapter is constructed as follows. First, an overview of the well known Black-Scholes-Merton model is explained. The specifications, the benefits and the important drawbacks of the model are discussed. Next, the method for measuring the TVOG is presented by discussing the intrinsic value and the market value of an option
3.1
The Black-Scholes-Merton model
For over a long period of time, different academics have contributed to the creation of the Black-Scholes-Merton model. It initiated with the idea to use a stochastic process for measuring stock prices. Bachelier (1900) assumed that the price of the underlying stock (item) is normally distributed. He made that assumption based on the Central Limit Theorem and the stochastic process for measurement of stock prices. Bachelier’s research created the stochastic process that is known as the arithmetic Brownian motion.
In the 60’s multiple mathematicians began to study option and warrant pricing. One of them was C.M. Sprenkle. Where Bachelier (1900) assumed a normal distri-bution for the price of the underlying stock, Sprenkle (1961) assumed a log normal distribution. The growth rate of the price of the underlying stock was also added to the pricing formula. Another mathematician who studied option and warrant pricing was A.J. Boness. In his research, Boness (1964) recognized the value of the time value of money (Kritzman, 2002). In order to measure the present value of the underlying stock, the underlying stock should be discounted, which he did by using the expected return of the underlying stock.
Samuelson (1965) allowed the expected return on the underlying stock to vary with the expected return on the option where he assumed both of the expected returns to be constant and known Kritzman (2002). He based his research on the results of Bachelier’s research.
Samuelson wrote his next published research together with his student R. Mer-ton. In this research, the option price is measured by a function of the price of the
Valuing unit linked insurances with a guarantee under IFRS 17 — 19
underlying stock (Samuelson & Merton, 1969). Researchers F. Black and M. Scholes were also researching option pricing and got inspired by this published research. A few years later Black and Scholes published their own work (Black & Scholes, 1973). They assume that when a hedge position is created, the expected return on such a hedged position must be equal to the return on a risk free asset (Black & Scholes, 1973, p. 640). Black and Scholes used this risk free condition to create the Black-Scholes Option Pricing Model. It is also called the Black-Black-Scholes-Merton Option Pricing Model, because of the fact that the valuation method of Black and Scholes is partly inspired by and based on the research of Merton.
3.1.1 Model properties
The Black-Scholes-Merton option pricing framework was a huge breakthrough in the financial markets. Under certain strong and ideal conditions (see appendix A) the closed-form formulas created to measure call and put options can be used (Black & Scholes, 1973). The framework is based on a normal distribution of the under-lying stock returns, which means that the underunder-lying stock price is log-normally distributed. Under risk measure P, the stock price is assumed to follow a Geometric Brownian motion:
dSt= µStdt + σStdWt (3.1)
where µ is the continuously compounded expected rate of return, σ is the volatility of the stock price and Wta Wiener process, with dWt∼ N (0, dt). Black and Scholes
assume a risk neutral world where the market is complete and there are no arbitrage possible. In a risk neutral world the assets are risk-less and as a result, the expected return of the asset is equal to the risk-free rate r (µ = r) such that there are no arbitrage opportunities (Cox & Ross, 1976).
The most famous solutions to the differential equation are the Black-Scholes-Merton closed-formulas for the prices of European call and put options. These formulas are: c = S0N (d1) − Ke−rTN (d2) (3.2) p = Ke−rTN (−d2) − S0N (−d1) (3.3) where d1 = ln(S0 K) + ( r+σ2 2 )T σ√T , d2 = ln(S0 K) + ( r−σ2 2 )T σ√T = d1− σ √ T
The function N (x) is the probability that a variable with a standard normal dis-tribution, φ(0, 1), will be less than x, which is called the cumulative probability distribution function for a standardized normal distribution. As seen in (3.2) and (3.3), the expected return on the stock does not enter into the Black-Scholes-Merton closed-formula. The volatility of the stock price is critically important for estimat-ing the derivatives. To estimate it empirically, the stock price should be taken at fixed periods of time. For each of the periods, the natural logarithm of the ratio of the stock price at the end of the period to the stock price at the beginning of the period is calculated. Next, the volatility can be estimated as the standard deviation of these results divided by the square root of the length of the period expressed in years (Hull, 2006).
3.1.2 Discrete form
The discrete form of the Black-Scholes-Merton model with a constant return is obtained by integrating the differential equation (3.1). This will result in:
∆St= µSt∆t + σSt
√
∆t (3.4)
Where the variable ∆S is the change in stock price S for the time period and σ is the volatility of the stock price. The variable has a standard normal distribution. √∆ can be written as ∆W such that variable W follows a Wiener process in the limit for ∆t is zero. As mentioned, under risk neutral valuation, the expected rate of return of the stock µ can be seen as the risk free rate r.
3.1.3 Disadvantages of the model
Using the Black-Scholes-Merton model, there is a closed-form formula to calculate the option price, which is a great advantage regarding calculation time. The only parameter that is needed is the stock volatility. However, since the volatility is assumed to be constant, the Black-Scholes-Merton model usually does not give an accurate representation of the real-world financial markets. These are the drawbacks attached to the use of the model:
• The stock volatility is assumed to be constant. Using constant volatility, all implied volatilities of options with the same underlying single stock are equal, which usually does not hold. Since the implied volatility increases as the option becomes more in-the-money or out-of-the-money in the market of options, the real market shows that the Black-Scholes-Merton model does not hold.
Valuing unit linked insurances with a guarantee under IFRS 17 — 21
• The prices of a stock are assumed not to jump. Historical data of stock prices show that stock prices can jump from time to time1.
These shortcomings could be corrected by using more complex models. Volatility could be assumed stochastic instead of constant. There are many models avail-able that incorporate stochastic volatility. If the volatility is assumed to follow a stochastic process, an extra random component is added to the model. For the ex-tra random component in the volatility process, there are no fully correlated assets that can be traded. This means that the market is incomplete, i.e. the option can not be perfectly hedged using an underlying asset and a bank account.
The Heston (1993) model, which is probably the most well known and most flexible stochastic volatility model, proposed to assume that the risk premium of volatility risk is consistent with variance. But there are other examples of stochastic volatility models. The Hull & White (1987) model proposed the stock and vari-ance processes to be two geometric Brownian motions that correlate to each other. The Stein & Stein (1991) model assumes that the stock prices follow a geometric Brownian motion and that the process of the variance of these stock prices is a mean-reverting geometric Brownian motion, where these two processes should be independent of each other.
An extensive economic scenario generator would use a model with stochastic volatility and stochastic interest rates. Creating such an economic scenario generator is out of the scope of this thesis, which is why only the model of Black & Scholes (1973) is used.
3.2
Time value of options and guarantees
When there is an option or guarantee embedded in an insurance contract, the TVOG should be reported on the yearly report. The TVOG is meant to value the risks of the options and guarantees embedded in the insurance contract. To measure the TVOG, two components should be measured first, namely the market value and the intrinsic value. The TVOG will then be defined by the difference between the market value and the intrinsic value of the option.
Since the market values are not available for insurance contracts, the market values should be measured using stochastic risk neutral valuation techniques. The closed formula solution created by Black & Scholes (1973) can be used for relative
1
If small market crashes occur or when companies make profit and loss announcements, the stock prices tend to jump.
simple options and guarantees embedded in insurance contracts, but the common approach would be to use a stochastic analysis. Using the Black-Scholes-Merton closed formula to determine the TVOG, the market price is measured by the closed formula. Next, the intrinsic value can be measured by removing the volatility, which means that the investment will increase with the risk free rate. Subtracting the guaranteed amount K from the investment at maturity, will give the intrinsic value of the option.
Using the stochastic analysis approach, the present value of the expected future cash outflows are calculated for a set of different stochastic risk neutral scenarios created using Monte Carlo simulations. Averaging the calculated present values of the expected future cash flows for the different stochastic scenario’s and subtracting the value of future cash flows calculated from a deterministic scenario, where the return follows the risk free rate without any volatility and the guarantee is removed, will result in the TVOG.
Now that the methods used for valuing the TVOG are presented, the model for valuing unit linked life insurance contracts with a guarantee under IFRS 17 is discussed in the next chapter.
Chapter 4
The Models
In this chapter, the modeling of the new standard and the assumptions made for modeling are discussed. The modeling of the new standard is performed in Microsoft Excel 2016. The model is created to test the performance of the new standard, and is relatively simplified by making certain assumptions. Table 4.1 shows a complete overview of all the assumptions that are made.
The account for profit and loss, the statement of comprehensive income and the balance sheet are created by the model. As the starting point, two different portfolios of each 200 same unit linked life insurance contracts with a guarantee, initiated at the beginning of year 1, are taken. Two different types of unit linked life insurance contracts are considered, namely one with a yearly guarantee embedded which is inspired by the insurance contract used in the example of the VFA of EFRAG (2017) and one with a guarantee embedded at maturity. The different specifications of these insurance contracts and the scenarios that are used to study the effects of IFRS 17 are discussed in the Chapter 5. It is assumed that there are no expenses for the insurer concerning the insurance portfolio, except those of the incurred claims. Furthermore, all cash flows are processed at the end or at the beginning of the year. The results are projected at each year until maturity of the contract. This way, all effects on the P&L can be analyzed over the years to see if they are lasting or just temporary.
4.1
IFRS 17
As mentioned before, this research focuses on measuring unit linked life insurance contracts with a guarantee under IFRS 17. The VFA is used in this thesis for measuring these type of contracts as they meet the criteria described in Section
A portfolio of 200 unit linked life insurance contracts is considered Maturity of the contracts n is 10 years
Cash flows and changes occur at the beginning and end of the year Risk adjustment is simplified
All costs are due to claims, no other expenses are taken into account
Stocks at FVPL under IFRS 9 and Bonds are measured at FVOCI or FVPL under IFRS 9 Dividend payments are ignored
Table 4.1: Overview of the assumptions made for the VFA model
2.1.5, which means that only the VFA is modeled. First, the best estimates of the future cash flows of the portfolio of insurance contracts are determined. The cash flows contain the premiums, the claims that depend on the scenarios, the income and the expenses of the portfolio. This means that the cash flows depend on the mortality assumptions, the lapse assumptions, the return on the underlying items assumptions, the discount rate assumptions, the type of unit linked insurance contract and the created scenarios discussed in Chapter 5. The premium payments are paid at the beginning of the year, the rest of the payments will be at the end of the year. All premiums are paid at inception1of the insurance contract. EF CFt,0:end
is a vector which contains all estimated future cash flows from point of view year t of year t + 0 until maturity. The estimated future cash flow in year t + i from point of view year t is defined as follows:
EF CFt,i = −Activet,iP remiumt,i+ CF Gt,i+ Activet,iqt,iM ortality
+Activet,ilt,iLapse − F eet,i
(4.1)
with t = {0, . . . , n} and i = {0, . . . , n − t}
Where t denotes the point of view year and i indicates the years after point of view year t. In the formula, Activet,i is the amount of active policyholders at the
beginning of year t+i from point of view year t, P remiumt,iis the premium received
of each active policyholder at year t + i from point of view year t. CF Gt,i is the cash
flow of the guarantee at year t + i from point of view year t, which is defined by the kind of guarantee that is embedded in the insurance contract. Also, the fee of the entity defined by F eet,i depends on the kind of option embedded in the insurance
1
Inception is the start of the contract. IFRS Foundation (2017b) uses t = 0 as the time of initial recognition of a contract, which can be understood as the end of year 0.
Valuing unit linked insurances with a guarantee under IFRS 17 — 25
contract. qt,i and lt,i are the expected mortality and lapse rates of year t + i from
point of view year t. Mortality is the mortality payout and Lapse is the lapse payout of the insurance contract. Once the best estimates of all cash flows are measured, the first building block is obtained.
Each reporting year the estimates of the future cash flows should be corrected for their time value by discounting using the appropriate discount rates. Dt,i is
defined as the discount rate of year t + i from point of view year t. It follows that Dt
is the vector of discount rates from point of view year t. With the discount rates, the present value of the estimated future cash flows for point of view year t can be obtained by: P V EF CFt= n−t X k=0 EF CFt,k(Dt,k)k (4.2) with t = {0, . . . , n}
To determine the CSM, the risk adjustment is needed. For simplicity reasons, and since exploring the risk adjustment is not within the scope of this research, the risk adjustment is not determined using any of the proposed methods of section 2.1.1. Instead, the risk adjustment at inception RA0 is determined by 0,4% times the
received premiums at inception. Each year the risk adjustment is, as a simplification, partly allocated to the P&L. The amortization pattern that is used, has the same methodology of the one used for the allocation of CSM to the P&L. The rational for choosing this method is that as the amount of contract decreases each year, the amount of non financial risks also decreases. The method is based on the amount of contracts in the portfolio for which coverage is expected to be provided in each reporting period and the amount of contracts for which coverage has been provided current year:
Allocation of RA in P&L year t = RAendt ∗PnCUt,0
i=0CUt,i
(4.3)
with t = {1, . . . , n} and i = {0, . . . , n − t}
Where RAendt is the risk adjustment at the end of current projection year t before a part of it is allocated to the P&L. CUt,i is the amount of coverage units (contracts
for which service is provided) in year t + i where t denotes the current projection year, i the years after the current projection year t and n the year of maturity of the contracts. For example, CU1,2 is the amount of coverage units expected in year
3 from point of view year 1. After the allocation of the risk adjustment to the P&L, the risk adjustment of year t RAt is obtained.
The last building block is the CSM. The CSM is the profit the entity expects to recognize by providing services in the future. The initial measurement of the CSM at date of entry of the contracts is given by the value that is equal and opposed to the fulfillment cash flows:
CSM0 = max{0, −(P V EF CF0+ RA0+ T V OG0)} (4.4)
Where P V EF CF0 contains the present value of estimated future cash flows at
in-ception, RA0the risk adjustment at inception and T V OG0the TVOG at inception.
Reporting takes place the end of each point of view year t. This means that each year the CSM is remeasured and adjusted for changes as follows:
CSMt= CSMtend− Recoveryt− CSMtP &L (4.5)
with t = {1, . . . , n}
Where CSMtend is the CSM after all adjustments have been made except for the allocation of it to the P&L for year t. Recoveryt is a recovery made of the losses
created in the past by a negative CSM. CSMtP &L is the allocation of the CSM to the P&L in year t. Each of these components are described below, starting with the adjusted CSM before a part of it is allocated to the P&L:
CSMtend= max{CSMt−1+ (F Vt− F Vt−1) − rt∗ RAt−1 −T V OGincreaset − rt∗ n−(t−1) X k=1 EF CFt−1,k(Dt−1,k)k − n−t X k=1 (EF CFt,k− EF CFt−1,k+1)(Dt−1,k+1)k − n−t X k=1 (EF CFt,k) ∗ ((Dt,k)k− (Dt−1,k+1)k), 0}, (4.6)
With F Vt the fair value of the assets at the end of year t, which means that
(F Vt− F Vt−1) is the change in fair value of the underlying items. RAt−1 is the
risk adjustment at the end of year t − 1 and rt the interest rate of year t, such
that rt∗ RAt−1 is the interest accretion of the risk adjustment. Due to the market
performance and the presence of a guaranteed return, the uncertainty of the amount of loss the entity will make can increase or decrease. Each year the estimated future
Valuing unit linked insurances with a guarantee under IFRS 17 — 27
market performance changes and because of this the TVOG will increase or decrease. The change is debited to the CSM under the VFA and given by T V OGincreaset .
rt∗Pn−(t−1)k=1 EF CFt−1,k(Dt−1,k)kcaptures the interest accretion on the present
value of the estimated future cash flows at the beginning of year t (which can be seen as the end of year t − 1). Pn−t
k=1(EF CFt,k− EF CFt−1,k+1)(Dt−1,k+1)k is the
change in the present value of future estimated cash flows caused by assumptions changes and Pn−t
k=1(EF CFt,k) ∗ ((Dt,k)k− (Dt−1,k+1)k) captures the change in the
present value of the future estimated cash flows caused by a changes in the discount rates. Now that the CSMtend is described, the allocation of the CSM to the P&L and the recovery component Recoverytwill be described.
The recognition of the CSM in profit or loss CSMP &L uses coverage units to
determine the amortization pattern of the CSM. Each insurance contract is taken as a coverage unit because all contracts in the portfolio are the same2. First, the amount of coverage units still remaining in the portfolio should be identified. The CSM at the end of the period, before a part of the CSM is recognized in the the P&L, will be allocated equally to each coverage unit for which service has been provided this period, or will be provided in future periods. The amount that will be recognized in the P&L is the amount allocated to the coverage units provided in the period (IFRS Foundation, 2017, p. 70-71):
CSMtP &L = (CSMtend− Recoveryt) ∗
CUt,0 Pn i=0CUt,i (4.7) with t = {1, . . . , n} and i = {0, . . . , n − t} Where CSMend
t is the CSM at the end of point of view year t before a part of it is
allocated to the P&L. CUt,i is the amount of coverage units in year t + i where t
denotes the point of view year, i the years after point of view year t and n the year of maturity of the contracts.
The Recoveryt is the part of CSMtend that recovers previous losses made by a
negative CSM. Given that losses have been made and have not fully recovered, i.e. N CSMt−1≤ 0, the recovery component in year t will be:
Recoveryt= ( −N CSMt−1, if CSMtend≥ −N CSMt−1≥ 0 CSMtend, −N CSMt−1≥ CSMend t ≥ 0 (4.8) 2
If the contracts in the group wouldn’t be the same, a better choice for the coverage units would be to take the amount of cash flows as coverage units. For example, a total cash flow in year 1 of 4.000 would mean that service is provided to 4000 coverage units in year 1.
with t = {1, . . . , n} and i = {0, . . . , n − t}
If losses have not been made or have been recovered already, i.e. N CSMt≥ 0 the
recovery component at time t will be 0. Here the variable N CSMt is the tracked
CSM without the restriction of being positive.
Even though the CSM can not be negative, it is important to track the same CSM but without the restriction of being positive. At initial recognition of the portfolio of the contracts the CSM could be negative (’onerous’). Also, the portfolio could become loss-making during the duration of the portfolio. By a positive change in the estimated future cash flows, the portfolio could become profitable again, and the CSM will rise. In that case the recovery component arises which is taken into the P&L insofar losses have been made in the past due to a negative CSM. If after the settlement a positive result remains, the CSM becomes positive again. This means that an entity should keep track off losses from the CSM to the P&L in their administration. The NCSM keeps track of these losses and will be remeasured each year as follows: N CSMt= N CSMt−1+ (F Vt− F Vt−1) − rt∗ RAt−1− T V OGincreaset −CSMP &L t − rt∗ n−(t−1) X k=1 EF CFt−1,k(Dt−1,k)k − n−t X k=1 (EF CFt,k− EF CFt−1,k+1)(Dt−1,k+1)k − n−t X k=1 (EF CFt,k) ∗ ((Dt,k)k− (Dt−1,k+1)k), (4.9) with t = {1, . . . , n} and N CSM0 = −(P V EF CF0+ RA0+ T V OG0)
4.2
Defining the P&L and OCI
As shown in figure 2.1, the P&L consists of two parts, namely the underwriting result and the investment result. First the underwriting result is defined. Next, the investment result and the assumptions made for reporting the investments are discussed. Last, the OCI and the assumptions made for reporting changes in the fair value of the portfolio due to the change in discount rates will be defined. Together, these three components form the total comprehensive income.
Valuing unit linked insurances with a guarantee under IFRS 17 — 29
4.2.1 Underwriting result
The formula for the underwriting result contains two components:
Underwriting resultt= Insurance revenuet+ Insurance expenset (4.10)
Insurance revenuet= CSMtP &L+ RAP &Lt + P rovisionP &Lt (4.11)
Insurance expenset= −ExpectedClaimt+ min{min{N CSMt, 0}−
min{N CSMt−1, 0}, 0} + Recoveryt− Exp.Adj.t
(4.12)
Provision is released to the P&L on the basis of the expected death benefit. The expected claim in year t ExpectedClaimt, which is not investment related (for
ex-ample a mortality payment paid from the entity’s bank account), is settled in the insurance expense. Next to that, the entity keeps track off losses from the CSM to the P&L. This is done by the min{min{N CSMt, 0} − min{N CSMt−1, 0}, 0} part.
Recovers from previous losses are tracked by Recoveryt. The last part of the
in-surance expense are the experience adjustments Exp.Adj.t. This part captures the
unexpected claims that are not investment related in year t. For example, unex-pected mortality will result in unexunex-pected claims.
4.2.2 Investment result
Before the investment result can be defined, assumptions have to be made about the measurement and modeling of the financial assets. The financial assets considered in this research are stocks which are, for simplicity reason, non-dividend paying and bonds . Directly after receiving the premiums of the policyholders, the entity invests a part of the amount received in a pool of stocks and a pool of fixed-rate bonds, and together they form the underlying items. This research considers bonds that are hold, which are allowed to be measured at FVOCI and FVPL under IFRS 9. All other changes in fair value of the financial assets are measured at P&L under IFRS 9. The investment outcomes will depend on the investment strategy the entity uses, which will be discussed in chapter 5.
To measure the investment result, the changes in fair value of the assets at P&L F V P Lt, the interest expense of the fulfillment cash flows IF CFt, payment of unit
linked investment claims U LClaimst, which are paid by the sales of stocks and the
returns on the underlying assets, and the released provision U LP rovisiont should
be measured as they relate to the investment result by:
4.2.3 OCI
The entity has to make an accounting policy choice about the disaggregation of the changes in fair value of the portfolio due to changes in the discount rates between the P&L and OCI. The accounting choice made in this research in the basis scenario, which will be discussed in Chapter 5, is a rather logical one, namely to allocate an amount of the change in fair value of the portfolio in the OCI equal to the amount of changes in the fair value of the bonds measured at FVOCI. As a result, the amounts cancel each other out and the OCI will be 0. For example, would the bonds fair value increase, a higher amount of changes in the future estimated cash flows caused by a change in the discount rate would be taken in the OCI, such that the amounts cancel each other out. The results of scenario 10 that is described in Chapter 6 show how this exactly works in numerical values.
4.3
TVOG
For the valuation of the option of guaranteed returns embedded in unit linked insurance contracts, the common approach is to use stochastic analysis. Stochastic risk neutral scenarios are needed and can be created using Monte Carlo simulations. The returns of a stock are simulated as follows. First, the values of the stock for each period are estimated:
St= St−1er−
σ2
2 +σ, for 0 ≤ t ≤ n + 1 (4.14)
Where ∼ N (0, 1), Stis the stock value at time t, r is the risk free rate and σ is the
volatility of the stock. Once the stock values are simulated, the simulated returns can be valued:
Rt=
St− St−1
St−1
, for 0 ≤ t ≤ n (4.15)
If the guarantee embedded in the unit linked life insurance contract is such that each year a minimum return is guaranteed to the active policyholders, the cash outflows of the guarantee for each active policyholder will be:
CF Gt= P remium ∗ max{G, (1 − f ee)(Rts + Ctb)} (4.16)
Valuing unit linked insurances with a guarantee under IFRS 17 — 31
Where G is the guaranteed return, Rtis the return of the stocks in year t, s is the
percentage of the received premium invested in stocks, Ct the return of the bonds
in year t, b is the percentage of the received premium invested in bonds, f ee is the percentage taken from the equity returns as a fee for the insurer and P remium is the amount of received premium per policyholder. It is assumed that the entity invest the premiums in a pool of stocks and a pool of bonds immediately after receiving them and receives a percentage of the equity returns as a fee.
Now that the approach for valuing the cash outflows related to the guarantee is discussed, the remaining components that influence the TVOG are mortality and lapse. The less policyholders are active, the less the risk there is for the insurer with respect to the guarantee embedded in the contract. The assumptions made for mortality and lapse will be discussed in Chapter 5.
As explained in Chapter 3, the TVOG can be calculated by the difference be-tween the market value of the option, which can be determined for simple options using the closed formula of Black & Scholes (1973) described in Chapter 3, and the intrinsic value of the option. Depending on the kind of guarantee embedded in the insurance contract, a choice of method for determining the TVOG has to be made. This thesis studies 2 types of options embedded in an unit linked life insurance con-tract. Specifications of both options will be discussed in the next chapter. One of the options will have a guarantee at maturity, which means that the closed formula method can be used for this plain vanilla option to determine the TVOG. A more complicated option is a yearly guarantee on returns of the underlying assets, for this type of option the stochastic analysis method is used.
The models and methods used for determining the results have been described in this chapter. Chapter 5 discusses the assumptions made for the model and describes the studied scenarios that are created to study the effects of IFRS 17 on unit linked life insurance contracts with a guarantee.
