An empirical assessment of the Credit Valuation Adjustment for interest rate swaps

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Amsterdam Business School

MSC Business Economics, Finance track

Lisanne van der Hijden – 10674934 October 2014

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This article empirically assesses the Credit Valuation Adjustment (CVA) for OTC derivatives as an additional Capital Charge under Basel III regulation and as the incorporation of counterparty credit risk into the market value of an interest rate swap under IFRS accounting rules. CVA is the market value of counterparty credit risk for interest rate swaps. This article finds that the additional capital requirement under Basel III is significant. The additional capital gives banks a better ability to absorb losses related to credit risk. To analyze the size of Bilateral Valuation Adjustment (BVA), it is compared to the risk neutral market value of the swap. Financial institutions have the highest credit risk exposure for swaps that have longer maturities and that are more in-the-money. The BVA for these swaps significantly decreases the market value, giving a more conservative view of the expected cash flows.

Key concepts: Counterparty Credit Risk, OTC derivatives, Interest rate swaps, Capital Requirement Basel II, Basel III, IFRS, Credit Valuation Adjustment, Debit Valuation Adjustment, Bilateral Valuation Adjustment.

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1 Introduction

Financial institutions and other participants in financial markets actively trade in the derivatives market. Hull (2012) defines a derivative as a financial instrument whose value depends on the value of other underlying variables. There are three types of derivatives depending on floating interest rates: forward rate agreements, interest rate options and interest rate swaps. An interest rate swap is an agreement to exchange cash flows in the future based on an underlying floating interest rate. The single currency interest rate swap market had a daily turnover of 1,415 billion US dollars in April 2013 (BIS, 2014). A swap agreement is traded through an exchange or Over The Counter (OTC). For exchange traded swaps, all details are standardized to contract terms set by the exchange. The exchange provides a transparent and liquid market place with daily margin requirements and the exchange makes sure that both counterparties receive all contractual payments. An advantage of OTC traded swaps is that the involved parties privately negotiate the terms of the contract and they tailor the contract specifics to their needs. On the other hand, there is no third party to guarantee the payments, which exposes both parties to counterparty credit risk (Hull and White, 1995).

Counterparty credit risk is the risk that one of the parties in a contract defaults before the expiration of the contract and is not able to meet its contractual payments. The Credit Valuation Adjustment (CVA) quantifies this risk of default and incorporates it in the market value of an interest rate swap. CVA is the difference between the risk neutral market value and the risk bearing market value that takes into account the possibility of counterparty default.

Regulatory frameworks require banks to hold capital to cover for mark-to-market losses for counterparty risk. The Basel III document states: “a bank must add a capital charge to cover the risk of mark-to-market losses on the expected counterparty risk (such losses being known as credit valuation adjustments, CVA) to OTC derivatives” (Basel Committee on Banking Supervision (BCBS), 2011). These reforms in the counterparty credit risk framework became effective in January 2013. Basel II (BCBS, 2005) already required holding capital for the credit risk of default of the counterparty, but it does not take mark-to-market losses into account.

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Accounting standards require companies to materialize credit risk in their financial statements. The International Financial Reporting Standards (IFRS) are applicable to all companies in the European Union. IFRS requires companies to incorporate the default risk of both parties into the market value of an interest rate swap (IFRS 13, 2011). A financial institution must account for credit risk exposure to their counterparties. But in addition to the possibility that the counterparty defaults, the financial institution is also able to default during the life of the contract. Debit Valuation Adjustment (DVA) is the incorporation of the risk of the financial institutions’ own default in the market value of interest rate swaps.Both CVA and DVA are one-sided, or unilateral. The Bilateral Valuation Adjustment (BVA) corrects the market value of the swap contract for default probability of both parties.

Current literature focuses on the calculation methodologies and mathematical background of CVA. This article empirically assesses the market value of CVA for regulatory and accounting purposes. For regulatory purposes, Basel III CVA is evaluated relative to the earlier applicable Basel II Capital Charge. As this is a capital requirement for financial institutions, it only takes into account the probability of default of the counterparty. If Basel III is a significant additional capital requirement, banks have to withdraw a significant amount of capital from the market. For accounting purposes, the market value has to incorporate an adjustment for counterparty credit risk of both parties in the contract. Therefore, this article compares BVA to the market value of the interest rate swap. Financial institutions bare the most risk on the contracts that are most in-the-money. If BVA for these contracts is a large negative adjustment, it significantly decreases the asset value of interest rate swap. This article evaluates the effect of different input parameters on the market value and determines the relevance of the CVA of a single contract. This article calculates CVA for fixed-for-floating interest rate swaps between European financial institutions and non-financial counterparties with different credit qualities. The research questions are:

1. Is Basel III Credit Valuation Adjustment a significant capital requirement in addition to the Basel II Capital Charge?

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2. Is the Bilateral Valuation Adjustment a significant adjustment to the market value of an interest rate swap?

Section 2 looks into the literature on interest rate swaps and credit risk. Section 3 outlines the methodology used to calculate the risk neutral market value of the interest rate swaps, the Basel II Capital Charge, the Basel III Credit Valuation Adjustment and the Bilateral Valuation Adjustment. Section 4 shows the results of all calculations. Section 5 analyzes all results, looking for answers to the research questions and section 6 states conclusions on the research questions.

2 Literature review

2.1 Regulation

The Bank of International Settlement (BIS) guides the international cooperation between 60 central banks. BIS strives for financial stability and guides monetary policy. One of the focus points of their regulatory frameworks is dealing with counterparty credit risk. Basel I, published by BIS in 1988, weighs counterparty credit risk exposure according to relative riskiness. This relative risk weight is a method to assess the capital adequacy of banks. To assess the capital adequacy of a financial institution, the notional amounts of outstanding contracts are multiplied with a credit conversion factor (CCF). The resulting amounts are weighted according to the nature of the counterparty (BCBS, 1988).

For interest and exchange rate related items, such as interest rate swaps, this exposure to counterparty credit risk is calculated slightly differently. Banks are not exposed to credit risk for the full notional value of the contract, but only to the cost of replacing the cash flows (of contracts with a positive value). The replacement cost is calculated using the Current Exposure Method (CEM). This method adds a factor (“add-on”) to the risk neutral market value. The add-on represents the potential future exposure during the remaining life of the contract. For this add-on, a credit conversion factor is used to calculate the percentage of the notional value that determines the potential future exposure. The Basel Capital Accord Amendment in 1995 expands the add-on matrix for contracts with a residual maturity of five years and over (BCBS, 1995).

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Where Basel I and the Amendment only calculate the exposure in case of default; Basel II requires a Minimum Capital Charge related to counterparty credit risk exposure. Table 1 presents the credit conversion factor matrices to calculate the add-on.

Table 1: percentage of notional to calculate add-on for potential future exposure. Panel a shows the original matrix from Basel I (1988) and panel b shows the extended matrix from the 1995 amendment.

Basel III goes a step further in quantifying counterparty credit risk and defines the capital charge for mark-to-market losses, the Credit Valuation Adjustment (CVA), in addition to the capital charge for default risk (BCBS, 2011). The CEM capital charge (Basel II) covers the risk of a counterparty default. The CVA capital charge (Basel III) accounts for the losses incurred due to deterioration of the credit worthiness of a counterparty. During the financial crisis, credit deterioration was a greater source of losses than actual defaults (BIS, 2009). The Total Capital Charge is the sum of the Basel II capital charge and the Basel III CVA capital charge. In addition to these capital charges, BIS is also strengthening standards on collateral management and initial margining. Banks must determine their capital requirements based on distressed inputs. They also address the systematic risk arising from interconnectedness of banks and other financial institutions through the derivatives market.

2.2 Market overview

The market for OTC derivatives shows growth. This originally opaque market increases in transparency through regulation and documentation. The ISDA agreement provides a standard setup for contract documentation and the BIS publishes a market overview semiannually. Since 1995 the BIS publishes a triennial survey that documents trends and patterns in the OTC derivatives and global foreign exchange markets to increase the ability for policymakers and

Basel I - 1988

Residual Maturity

Interest rate contracts

Less than one year 0.0% One year and over 0.5%

Basel I Am endm ent - 1995

One year or less 0.0% Over one year to five years 0.5% Over 5 years 1.5%

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market participants to monitor the derivatives market. The next paragraphs present an overview of the current OTC derivatives market and more specifically the market over Euro derivatives and interest rate swaps.

In April 2013, Euro interest rate derivatives have the highest daily turnover average of the OTC interest rate derivatives market. Between 2010 and 2013 daily turnover increased by 37% to 1,146 billion. The daily turnover average of swaps (all currencies) increased by 11% over the last 3 years to 1,415 billion in April 2013 (BIS, 2013). Figure 1 shows this increase in daily turnover for swaps and Euro interest rate derivatives.

Figure 1: Turnover of OTC interest rate derivatives by instrument and by currency. Daily average turnover in April, in Billions of US dollars. Panel a (by instrument): increase in daily swap turnover by 11 % from 2010 to 2013. Panel b (by currency): increase in daily turnover in Euro interest rate derivatives by 37% from 2010 to 2013.

Source: BIS Triennial Survey

Notional amounts for the OTC derivatives market increases between end-2012 and end-2013, but gross market values decrease over this period. Figure 2 shows the increase in notional and decrease in gross market value. The notional amount outstanding is $633 trillion at end-2012 and $710 trillion at end-2013. The gross market values declines from $25 trillion end-2012 to $19 trillion end-2013. Interest rate derivatives are the main driver of this decline. Market values decreased as interest rates narrowed from the trade date of the contract (BIS, 2014).

0 500 1000 1500 2000 2500 2001 2004 2007 2010 2013 Turnover by instrument

FRAs Swaps Options and other

0 500 1000 1500 2000 2500 2001 2004 2007 2010 2013 Turnover by currency

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Figure 2: Notional amount and gross market value of the OTC derivatives market. Notional amount outstanding and gross market value end-June and end-December, in trillions of US dollars. Panel a (notional): increase in notional from $633 trillion at end-2012 to $710 trillion at 2013. Panel b (gross market value): decrease in gross market value from $25 trillion at end-2012 to $19 trillion at end-2013.

Source: BIS OTC Derivatives Statistics

Interest rate derivatives represent the largest part of the gross market value in the OTC derivatives market; they account for 75 percent of gross market value at end-2013, totaling $14 trillion. Euro interest rate derivatives represent the largest share of outstanding interest rate derivatives with total gross market value of $6.8 trillion at end-2013. US dollar interest rate derivatives have a gross market value of $4.3 trillion at end-2013 (BIS, 2014). Figure 3 panel a shows a shift in gross market value from US dollar towards Euro contracts.

The notional for the medium and long-term contracts increases between 2012 and end-2013. The outstanding notional of contracts with a residual maturity of one to five years increases from $180 trillion to $234 trillion. The outstanding notional of contracts with a residual maturity of more than five years increases from $119 trillion to $152 trillion (BIS, 2014). Figure 3 panel b shows this increase in longer maturity contracts.

* contracts of non-reporting institutions

0 100 200 300 400 500 600 700 800 2008 2009 2010 2011 2012 2013

OTC derivatives market by notional

Foreign Exchange Interest rate Equity Commodity CDS Unallocated*

* contracts of non-reporting institutions

0 5 10 15 20 25 30 35 2008 2009 2010 2011 2012 2013

OTC derivatives market by gross market value

Foreign Exchange Interest rate Equity Commodity CDS Unallocated*

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Figure 3: Gross market value and notional amount of interest rate derivatives market. Gross market value by currency and notional amount outstanding by maturity June and end-December, in trillions of US dollars. Panel a (gross market value): Euro contracts have a gross market value of $6.8 trillion at end-2013. Panel b (notional): The notional for the medium and long-term contracts increased, 66 % of contracts have a maturity of over one year at end-2013.

Source: BIS OTC Derivatives Statistics

2.3 Interest rate swaps

The volatility of interest rates increased since the late 70s, this resulted in a higher interest rate risk exposure for financial institutions and other market participants (Bicksler and Chen, 1986). Interest rate swaps arise as an instrument to hedge this interest rate risk. Bicksler and Chen (1986) demonstrate that a swap is a combination of holding a fixed (floating) bond and selling a floating (fixed) bond. This most common type of swap is a “plain vanilla” fixed-for-floating interest rate swap. In a swap contract, companies agree to exchange periodical payments. Non-financial companies pay cash flows equal to a predetermined fixed rate of the notional. In exchange they receive cash flows equal to a floating rate on the same notional for the same period. The non-financial company often pays the fixed side of the contract, as it wants to offset a floating rate obligation (Hull, 2012). With the swap, the financial institution provides an opportunity to transform a floating rate obligation into a fixed rate obligation, hedging the company’s interest rate risk. The notional amount of the swap is often not exchanged; it is only

0 20 40 60 80 100 2008 2009 2010 2011 2012 2013

Notional amounts, by maturity

Over 5 years

Over 1 year and up to 5 years One year or less

0 5 10 15 20 25 2008 2009 2010 2011 2012 2013

Gross market values, by

currency

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used for the calculation of the interest rate payments. As the notional has the same value for the fixed and the floating leg, the exchange would have no value to either of the counterparties. Figure 4: Structure of a fixed-for-floating interest rate swap. A financial institution gives a non-financial company the opportunity to offset a floating rate obligation.

The floating rate is set two days prior to each interest period based on the Euro Interbank Offered Rate (EURIBOR). The 3m EURIBOR is the rate at which European banks are willing to offer their 3-month deposits. As this floating rate is reset during the life of the contract, both counterparties face interest rate risk due to the uncertainty of the market movements. Between 2008 and 2013 EURIBOR develops from a higher flat curve to a lower increasing curve. When floating rates decrease, fixed rate payers receive low floating rates for the high contractual fixed rates. Therefore swaps move far out-of-the-money for the fixed rate payer, often the non-financial counterparty. On the other side, swaps move far in-the-money for the financial institution, that loses a lot of value in case of counterparty default. Figure 5 shows the development of the EURIBOR curve between 2008 and 2013.

floating

Company _InstitutionFinancial floating

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Figure 5: Development of EURIBOR curve. In 2008 the EURIBOR interest rate curve was a nearly flat curve around 4.5 percent. Over the years it gradually moved towards an ascending curve in 2013 with shorter maturities having values below 1 percent and the longer maturities just over 2 percent.

Source: Bloomberg

In perfect markets the fixed rate is set, such that the market value of the interest rate swap at trade date is zero (i.e. the swap is at-the-money). Then, no arbitrage opportunities are available to either of the counterparties. However, in real life markets the fixed rate of the swap is set that the risk neutral market value at trade date is positive for the financial institution. The company pays a premium to the financial institution for providing the possibility to hedge against interest rate risk.

International Swaps and Derivatives Association (ISDA) Master Agreement governs all swap specifications such as fixed rate, floating rate, spread notional and day count convention. This agreement specifies that all transactions between the same counterparties are netted and considered as a single transaction in the event that there is an early termination. Collateral has become an important feature in OTC derivative markets. Therefore an ISDA Master Agreement is typically accompanied by a Credit Support Annex (CSA), which specifies that the out-of-the-money counterparty has to post collateral.

0% 1% 2% 3% 4% 5% 6% - 5 10 15 20 25 30 35 40 45 50 EU R IBO R Years 2008 2009 2010 2011 2012 2013

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The risk neutral market value of an interest rate swap is determined using the Discounted Cash Flow (DCF) method (KPMG, 2012). Originally, the discount rates were determined using the EURIBOR index. However, during the recent financial crisis 3m EURIBOR showed a significant spread over the risk free rate due to market uncertainty. Therefore, discount rates are discounted under the Euro Over Night Index Average (EONIA) (Hull and White, 2013). EONIA is the average interest rate at which selected European banks are willing to offer deposits with a maturity of one day. Due to the short term of these rates, the EONIA is considered to be a risk free curve and therefore best suited for obtaining the risk neutral market value of interest rate swaps.

2.4 Credit risk

Credit risk is the risk arising from the possibility that one of the parties in a derivative transaction defaults. In case of default, the company is not able to fulfill its payment obligations as specified in the contract (Gregory, 2010). Credit risk is associated with credit-linked events, such as changes in credit quality, including downgrades or upgrades in credit rating, variation in credit spreads and cases of default. Rating agencies, such as Moody’s, S&P and Fitch provide ratings describing the creditworthiness of a company. The highest rating, where there is little chance of default, is Aaa for Moody’s or AAA for S&P and Fitch. Table 2 presents cumulative default probabilities for different credit ratings and different maturities. Companies with a rating above Baa, or BBB respectively, are considered to be investment grade. To further specify the credit quality of a counterparty, Moody’s makes the division for A rating category into A1, A2 and A3. S&P and Fitch make this division for A rating category into A+, A and A- to create finer rating measures.

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Table 2: Average cumulative default rates. The probability that a party with a certain rating defaulted before the different maturity dates. In 20 years, 0.2 percent of companies with an Aaa rating by Moody’s defaulted and 83.8 percent of companies with Caa-C rating by Moody’s defaulted.

Source: Moody’s (2014)

Bielecki and Rutkowski (2002) define three categories of credit risk. They explain the categories by means of three types of products: corporate bonds, vulnerable claims and credit derivatives. Corporate bonds are subject to unilateral risk and recovery is determined based on the notional. Vulnerable claims are subject to either unilateral or bilateral risk and recovery is based on the market value of the product. Credit derivatives transfer the risk of default of a reference entity from a buyer of the contract to the seller of the contract. An interest rate swap is a vulnerable claim with bilateral risk. As the recovery for an interest rate swap is determined based on the market value rather than the notional of the contract, the underlying parameters have impact on the future cash flows. These underlying parameters are changing with the market and therefore both parties are subject to credit risk. When the floating rate is above (below) the fixed rate of the contract, the market value is positive for the fixed (floating) payer and negative to the floating (fixed) rate payer (Canabarro and Duffie, 2003).

The market perception of credit risk is determined by credit derivatives. Credit default swap (CDS) contracts are the most liquidly traded credit derivative contracts. CDS contracts have three parties of interest, the buyer, the seller and a reference entity. The buyer pays a periodical fee to the seller in exchange for insurance against the default of a reference entity during the life of the contract. CDS spreads are quoted as spreads over the swap curve rather than the treasuries curve as the former better reflects the funding costs faced by market participants (Chan-Lau, 2006).

Average Cum ulative Global Default Rates, 1983-2013

Rating 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Aaa 0.0% 0.0% 0.0% 0.0% 0.1% 0.1% 0.2% 0.2% 0.2% 0.2% 0.2% 0.2% 0.2% 0.2% 0.2% 0.2% 0.2% 0.2% 0.2% 0.2% Aa 0.0% 0.1% 0.2% 0.3% 0.5% 0.6% 0.7% 0.8% 0.9% 1.0% 1.1% 1.4% 1.6% 1.7% 1.9% 2.0% 2.2% 2.5% 3.0% 3.4% A 0.1% 0.2% 0.5% 0.8% 1.1% 1.5% 1.8% 2.3% 2.7% 3.0% 3.4% 3.7% 4.0% 4.4% 4.9% 5.5% 6.1% 6.8% 7.4% 7.9% Baa 0.2% 0.5% 1.0% 1.4% 1.9% 2.5% 2.9% 3.4% 3.9% 4.5% 5.1% 5.7% 6.5% 7.3% 8.0% 8.9% 9.7% 10.6% 11.3% 11.9% Ba 1.1% 3.3% 5.8% 8.6% 10.9% 13.0% 14.9% 16.7% 18.4% 20.1% 21.8% 23.5% 25.1% 26.9% 28.7% 30.1% 31.5% 32.7% 34.3% 35.3% B 3.9% 9.3% 14.8% 19.7% 24.1% 28.3% 32.1% 35.4% 38.3% 40.8% 42.9% 44.9% 46.8% 48.7% 50.4% 51.7% 52.9% 54.5% 55.6% 57.1% Caa-C 13.2% 24.2% 33.0% 40.1% 46.3% 51.0% 54.7% 58.3% 62.3% 65.9% 69.1% 71.5% 75.2% 76.9% 78.9% 82.8% 83.8% 83.8% 83.8% 83.8%

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Hull et al. (2004) investigate the relation between CDS spreads and credit ratings. The market determines CDS spreads continuously, where credit ratings show a discreet pattern. Hull et al. (2004) find that credit spreads decrease on a downgrade review announcement rather than an actual downgrade. They also test whether a decrease in CDS spreads is a prelude for a downgrade or negative outlook. For upgrades this strong relationship was not found, which might be due to a smaller sample.

2.4.1 Netting and collateral arrangements

Credit risk can be controlled by limiting trading to high rated counterparties and by diversifying the portfolio in terms of counterparties. Credit risk can be reduced through netting agreements and collateral arrangements. Netting agreements provide the opportunity to net exposures of different contracts with the same counterparty. A netting agreement offsets negative market values against positive market values to decrease exposure. In case of default, netting protects parties from paying out all payable positions but only receiving a recovery amount for receivable positions. Brigo et al. (2013) test the effectiveness of netting agreements. They find that netting has a bigger positive impact when contracts are more negatively correlated. As negatively correlated contracts offset each other’s market value, exposure is reduced. Lower exposure means that less value is lost in case of default, reducing counterparty credit risk. Another way to secure against counterparty credit risk is a collateral arrangement. Exposure is limited because the out-of-the-money counterparty is required to post collateral. Then, the in-the-money counterparty is only subject to gap risk, the risk arising from market movements between collateral calls (Singh, 2010).

2.5 Credit Valuation Adjustment

Credit risk related to counterparties in interest rate swaps is considered in the literature since the early 90s. The first publication on the default risk of swaps is from Cooper and Mello (1991). Their theoretical approach assumes perfect and competitive markets, analyzing single period interest rate and currency swaps between one risky and one riskless counterparty. They derive equilibrium swap rates, including default risk, consistent with equilibrium rates for risky debt. They find values for the default risk of swaps that is significantly lower than debt market spreads.

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Sorensen and Bollier (1994) suggest to correct the fixed rate of the swap for credit risk, as a higher coupon rate compensates for the risk of a lower-rated bond. Their approach takes into consideration the credit condition of both parties, their existing combined swap book, the shape and volatility of the yield curve and exchange rates. They acknowledge the bilateral nature of credit risk, but conclude that due to information asymmetries between participants credit risk may be difficult to price. Jarrow and Turnbull (1995) consider two types of credit risk concerned when pricing derivative securities. On one hand, the risk of default from the underlying asset (i.e. with options on debt). On the other hand, the risk of default of the writer of the derivative security. With the use of arbitrage-free valuation techniques they derive a risk-neutral valuation procedure applied to corporate debt which can also be used for OTC traded swaps.

The calculation of CVA calculation consists of three inputs: The Loss Given Default, Default Probabilities and the Expected Exposure. The following paragraphs provide literature on all three inputs.

2.5.1 Loss Given Default

The holders of OTC derivatives contracts have the same seniority as senior bond holders; therefore they are among those creditors receiving the highest recoveries (Gregory, 2010). When the counterparty defaults, a recovery amount is paid determined by the recovery rate. The non-recovered part is called loss-given-default or LGD. The recovery rate and LGD are stated as a constant percentage of the exposure. A study of the Federal Reserve board by Covitz and Han (2005) shows that the average recovery rate of corporate debt of non-financial corporations is 40 percent. The LGD used for the CVA calculations is therefore 60 percent.

2.5.2 Probability of Default

The Probability of Default is determined by CDS spreads. CDS contracts provide insurance against the default of a certain entity. CDS spreads represent the market’s price of buying protection against default of the reference entity. Market participants want to pay more insurance for an entity that is more likely to default. Thus, higher CDS spreads correspond with a higher Probability of Default. As CDS spreads are market driven and risk is incorporated in the CDS spreads, the

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default probabilities are a risk neutral representation of the default probabilities of a company (Chan-Lau, 2006).

EY (2014) provide some advantages and disadvantages of the use of a CDS spreads to determine the Probability of Default. Advantages are that spreads are market observable, information is current and that it is easy to source from third party data providers. Disadvantages are that data is not available for many entities, that the data might not be representative for all assets in the entity and that liquidity problems occur due to low trading volumes. However, the disadvantages are mainly relevant when calculating CVA for a specific counterparty. This article calculates CDS spread averages for credit rating group based on financial institutions and non-financial companies with spreads on the most liquidly traded CDS contracts. Therefore, CDS spreads are a representative estimation of credit risk of the financial institutions and the non-financial counterparty credit categories.

2.5.3 Expected Exposure

CVA and BVA calculations require the determination of Expected Exposure. However, the calculation methodology is not specified in the Basel III document (EY, 2014). The advanced approach requires Monte Carlo simulations of the underlying swap parameters, providing a value of the derivative under each market scenario. An alternative method sees the Expected Exposure at the event of default as a swaption to enter in the remainder of the swap. Sorensen and Bollier (1994) are the first to define the replacement cost for a swap as a set of options. One swap party is short an option to receive fixed and long an option to pay floating payments. Simultaneously the other party owns the opposite pair of options. The option prices depend on the default probabilities and the interest rate volatility. As their suggestion for pricing counterparty credit risk in a swap contract is to adjust the fixed rate, they conclude that the value of these options have an effect on the fixed-coupon swap rates. Brigo and Masetti (2005) define the theory as used by Bloomberg to calculate CVA. They state: “the component of the IRS priced due to counterparty risk is the sum of swaption prices with different maturities, each weighted with the probability of defaulting around that maturity”. They present the credit risk in an OTC derivative between one default free and one defaultable transaction as a sequence of vulnerable options.

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A swaption is a string of call options for the long position and a string of put options for the short position. This swaption valuation methodology is used by Bloomberg (Bielecki et al., 2011) As both the Probability of Default and the Expected Exposure depend on market parameters they are correlated. This relationship is referred to as wrong way or right way risk (Pykhtin and Zhu, 2007). Wrong way risk is the case when Probability of Default and Expected Exposure move in the same direction. An example is when the financial institution buys credit protection from the non-financial counterparty as this gives a correlation between the credit spreads of both parties. When credit spreads increase, the value of the protection increases, making the exposure for the non-financial counterparty higher (Hull and White, 2012). For the calculation methodology with swaptions this relationship is acknowledged but the size cannot be evaluated.

2.6 Bilateral Valuation Adjustment

Duffie and Huang (1996) are the first to theoretically model credit risk for swaps subject to bilateral default. They suggest discounting the cash flows with a switching discount rate equal to the discount rate of the out-of-the-money counterparty, taking into account credit risk asymmetry. Brigo, Buescu and Morini (2012) theoretically address the modeling of the Bilateral Valuation Adjustment (BVA). They compare two valuation methodologies, the simplified methodology and the fully bilateral methodology. The simplified methodology uses unilateral CVA and Unilateral DVA for the calculations. This method saves computational effort as it does not correct for the probability that the other party in the contract is able to defaults.The fully bilateral methodology corrects CVA and DVA to include the probability of default of the other party. Brigo, Buescu and Morini (2012) theoretically find a considerable difference between the simplified and the fully bilateral calculation outcomes. Therefore, the simplified method does not give a good approximation of BVA.

3 Methodology

This article calculates the risk neutral value of fixed-for-floating interest rate swaps with different fixed rates and residual maturities. The risk neutral market values provide the basis for the calculation of the Basel II Capital Charge, the Basel III Credit Valuation adjustment and the

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Bilateral Valuation Adjustment. Following paragraphs explain data collection and valuation methodologies.

3.1 Interest rate swaps

First, I specify all input parameters to calculate the risk neutral market value of all interest rate swaps. The notional amount of the swap is set at €10 million. The payment frequency is quarterly and the floating rate index is the 3m EURIBOR. The floating rate is reset at 31 July, 31 October, 31 December and 30 April of every year. The 3m EURIBOR is quoted on an actual/360 basis. However the rate of the fixed leg is quoted either on a 30/360 or an actual/360 basis. The day count has an effect on the fixed payments as the fixed rate is quoted annually. For the calculations in this acticle I chose a day count of actual/360 for the fixed leg, to have the same day count for both legs.

Different dates are specified: the trade date, effective date, maturity date and valuation date. The trade dates are every 30 April between 2008 and 2013. On these dates, the fixed rates are determined assuming a market value of zero at trade date. I chose these dates to contain dates from before the crisis hit Europe and to have intervals of one year until the valuation date. As 30 April is not the end of any fiscal- or book- year, the parameters are not subject to any seasonal effects. The effective and valuation date are the same for all swaps and are both set at 30 April 2014. The maturity date is 30 April of either 2015, 2019, 2024 or 2034 depending on the term of the contract. Table 3 presents all maturity dates and the fixed rates for every trade date and residual maturity.

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Table 3: All fixed rates determined per trade date and residual maturity of the interest rate swap contract. For swaps with a trade date in 2008, the fixed rates for all residual maturities are above 4 percent. For swaps with a trade date in 2013, the fixed rates have decreased and are now increasing with residual maturity from 0.2 percent for a residual maturity of one year to 1.9 percent for a residual maturity of 20 years.

Now, all input parameters are specified and the quarterly payments (πi) are calculated and

multiplied with the discount factor (Di). The sum of the discounted payments is the risk neutral

market value of the fixed leg and the floating leg. The market value the floating rate payer (the financial institution (FI)) is the present value of the fixed rate leg minus the present value of the floating rate leg, for the floating rate payer (the non-financial counterparty (NFC)) vice versa. Formula 1 presents the discounted market value calculation for the financial institution.

𝑀𝑀𝑀𝑀𝐹𝐹𝐹𝐹 _{= � 𝜋𝜋} 𝑖𝑖𝑓𝑓𝑖𝑖𝑓𝑓𝑓𝑓𝑓𝑓× 𝐷𝐷𝑖𝑖 𝑇𝑇 𝑖𝑖=1 − � 𝜋𝜋𝑖𝑖𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑖𝑖𝑓𝑓𝑓𝑓× 𝐷𝐷𝑖𝑖 𝑇𝑇 𝑖𝑖=1 (1)

3.2 Basel II Capital Charge

Paragraph 186, 187 and 317 of the Basel II document explain the original capital requirement for credit risk using the Current Exposure Method. Formula 2 presents the CEM formula:

Basel II 𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶 𝐶𝐶ℎ𝐶𝐶𝑎𝑎𝑎𝑎𝑎𝑎 = (𝑅𝑅𝐶𝐶 + 𝐶𝐶𝑎𝑎𝑎𝑎 𝑜𝑜𝑜𝑜) − 𝐶𝐶𝐴𝐴 × 𝑎𝑎 × MCR (2)

Where;

RC = replacement cost;

Add-on = the amount for potential future exposure; CA = the volatility adjusted collateral amount;

Fixed rates 2008 2009 2010 2011 2012 2013 1 yr 30-apr-15 4.611 1.354 0.907 1.779 0.594 0.198 5 yrs 30-apr-19 4.245 2.545 2.083 2.823 1.182 0.607 10 yrs 30-apr-24 4.438 3.295 2.965 3.354 1.989 1.331 20 yrs 30-apr-34 4.706 3.742 3.475 3.750 2.439 1.941 Maturity date Residual Maturity

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r = the risk weight of the counterparty; MCR = minimum capital ratio (8%).

The replacement cost as per 30 April 2014 is determined by the risk neutral market value of a swap. The add-on determines the potential future credit exposure, which is expressed as a percentage of the notional of the swap. Table 4 provides the percentages as originally presented under Basel I and extended under the 1995 amendment for swaps with a residual maturity over five years. The volatility adjusted collateral amount is zero as it is assumed that no eligible collateral is applied to the transactions. The risk weight is determined per counterparty. Table 5 shows the weights for corporates specified per credit category. The minimum capital ratio for risk bearing assets as defined by the Basel documents is 8 percent.

Table 4: Add-on percentage of the notional. Percentage of the notional to determine the potential future exposure. Basel I provides percentages for swaps with a residual maturity of less than one year (0.0%) and of a residual maturity of one year and over (0.5%). The amendment of 1995 requires a higher percentage for swaps with a residual maturity of more than five years (1.5%)

Table 5: Counterparty risk weight. The replacement cost and the add-on are multiplied with the risk weight of a counterparty. This table presents the risk weights for claims on corporates for the Current Exposure Method calculations under Basel II.

Basel I - 1988

Less than one year 0.0% One year and over 0.5%

Basel I Am endm ent - 1995

One year or less 0.0% Over one year to five years 0.5% Over 5 years 1.5%

Basel II - Counterparty risk w eight

Credit assessm ent AAA to AA- A+ to A- BBB+ to BB- Below BB- Unrated

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3.3 Basel III Valuation Adjustment

Paragraph 98 of the Basel III document explains the additional capital requirement that banks are subject to in addition to the Basel II Capital Charge: the Credit Valuation Adjustment for credit risk. Formula 3 presents the CVA formula:

𝐶𝐶𝑀𝑀𝐶𝐶 = 𝐿𝐿𝐿𝐿𝐷𝐷𝑀𝑀𝑀𝑀𝑇𝑇× � 𝑀𝑀𝐶𝐶𝑥𝑥 𝑇𝑇 𝑖𝑖=1 �0; 𝑎𝑎𝑥𝑥𝐶𝐶 �−_{𝐿𝐿𝐿𝐿𝐷𝐷}𝑠𝑠𝑖𝑖−1𝐶𝐶𝑖𝑖−1 𝑀𝑀𝑀𝑀𝑇𝑇� − 𝑎𝑎𝑥𝑥𝐶𝐶 �− 𝑠𝑠𝑖𝑖𝐶𝐶𝑖𝑖 𝐿𝐿𝐿𝐿𝐷𝐷𝑀𝑀𝑀𝑀𝑇𝑇� × � 𝐸𝐸𝐸𝐸𝑖𝑖−1𝐷𝐷𝑖𝑖−1+ 𝐸𝐸𝐸𝐸𝑖𝑖𝐷𝐷𝑖𝑖 2 �� (3)

Formula 3 contains three parts: the Loss Given Default (LGD), the Probability of Default (PD) and the Expected Exposure (EE). The LGD stays at a constant rate of 60 percent. The summation sums the multiplication of the EE and the PD for every interest rate period. The probability that a counterparty defaults between two interest payments is written as:

𝑃𝑃𝑎𝑎𝑜𝑜𝑃𝑃𝐶𝐶𝑃𝑃𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝑖𝑖 𝑜𝑜𝑜𝑜 𝐷𝐷𝑎𝑎𝑜𝑜𝐶𝐶𝐷𝐷𝐶𝐶𝐶𝐶 = 𝑎𝑎𝑥𝑥𝐶𝐶 �−_{𝐿𝐿𝐿𝐿𝐷𝐷}𝑠𝑠𝑖𝑖−1𝐶𝐶𝑖𝑖−1

𝑀𝑀𝑀𝑀𝑇𝑇� − 𝑎𝑎𝑥𝑥𝐶𝐶 �−

𝑠𝑠𝑖𝑖𝐶𝐶𝑖𝑖

𝐿𝐿𝐿𝐿𝐷𝐷𝑀𝑀𝑀𝑀𝑇𝑇� (3.1)

Where;

ti = the time of the i-th interest rate period;

si = the credit spread of the counterparty at time ti;

LGDMKT = the loss given default of the counterparty;

And, the Expected Exposure during an interest period discounted to the valuation date is written as:

𝐸𝐸𝑥𝑥𝐶𝐶𝑎𝑎𝐸𝐸𝐶𝐶𝑎𝑎𝑎𝑎 𝐸𝐸𝑥𝑥𝐶𝐶𝑜𝑜𝑠𝑠𝐷𝐷𝑎𝑎𝑎𝑎 = �𝐸𝐸𝐸𝐸𝑖𝑖−1𝐷𝐷𝑖𝑖−1₂+ 𝐸𝐸𝐸𝐸𝑖𝑖𝐷𝐷𝑖𝑖� (3.2) Where;

EEi = the Expected Exposure of financial institution at time ti;

Di = the default-risk-free discount factor at time ti;

Once the Expected Exposure and Probability of Default parts of the CVA formula from the Basel III document are defined the CVA formula is simplified to Formula 4:

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Where;

EEFI_{= the Expected Exposure the financial institution is subject to at time t}_i_;

PDNFC_{= the Probability of Default of the non-financial counterparty.}

The data for the Basel III CVA calculations is collected from Bloomberg. The World CDS Monitor contains data on CDS spreads. The Swap Manager calculates a string of swaption values that determine the Expected Exposure values. The following paragraphs explain how data is collected and how the different input parameters for the CVA calculation are calculated.

Expected Exposure

Following Brigo and Massetti (2005) and Bielecki et al. (2010), this article uses the methodology with swaptions to calculate the Expected Exposure at every interest rate payment. For the financial institution, the swaptions are strings of options to pay the floating leg combined with a string of options to receive the fixed leg. A swaption provides the market value to enter into the remainder of the swap, and thus the value lost when the counterparty defaults. The Bloomberg Swap Manager provides a tool to calculate the value of these swaptions for every interest rate period.

Probability of Default

The CDS contracts must be actively traded to give an updated representation of the credit risk associated with a certain company. The valuation date of the CDS spreads is the same as the valuation date of the swaps; 30 April 2014. The World CDS monitor provides all traded CDS spreads for companies in different industries and across different geographical areas. For the non-financial companies, the CDS spreads of all European companies in the sectors Basic Materials, Communications, Consumer, Energy, Industrial, Technology and Utilities are extracted from Bloomberg. These are all sectors except for the Financial sector, as these spreads are used for the financial institutions. This results in a total dataset of 289 companies.

If no CDS spread is available for a company, a proxy spread that is appropriate based on rating, industry and region of the counterparty (Basel III, 2011). For this article, credit classes are created based on credit ratings of Fitch, Moody’s and Standard & Poor using European averages across

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industries. From the 289 companies in the dataset, I exclude 123 companies. First, I exclude a company if none or only one of the rating agencies provides a rating on the company (100 companies excluded). Second, I exclude a company with an incomplete CDS spread curve (5 companies excluded). I divided the remaining 184 companies into credit rating categories based on the highest credit rating obtained from a rating agency, corrected for outlook. If the credit outlook of a company is negative for two or more rating agencies, the company moved down one credit rating category. None of the companies had a positive outlook of two or more rating agencies. The number of companies in the AA and B categories is insignificant (18 companies excluded). The final dataset contains 166 companies in 9 different rating categories, with the credit spread sample ranging from A+ to BB- ratings. Table 6 presents the division in rating categories for non-financial companies.

Table 6: Selection of credit rating categories for CDS spread curves of non-financial companies. The 184 companies with a rating and a complete CDS spread curve are divided into rating categories. The number of companies in the AA and B categories is insignificant, these categories are therefore excluded. The final dataset contains 166 companies in 9 different rating categories.

Once all data points are extracted from Bloomberg, the CDS spread curves for the different rating categories are determined by taking the average per rating category. The averages provide the

Rating Categories

Rating Am ount Rating Am ount

B 10 B- 2 B 2 B+ 6 BB 30 BB- 8 BB 13 BB+ 9 BBB 87 BBB- 21 BBB 32 BBB+ 34 A 49 A- 29 A 12 A+ 8 AA 8 AA- 3 AA 4 AA+ 1 184 184 -5 10 15 20 25 30 35 40 B- B B+ _BB- BB _BB+ BBB- BBB _BBB+ A- A A+ _AA- AA _AA+ Credit Categories

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spread used to determine the periodical default probabilities for each credit category. All companies have equal weighting following the Markit iTraxx indices (Markit, 2013). Table 7 presents the CDS spread curves per credit rating category.

Table 7: CDS Spread curves for different credit rating categories. CDS spreads gradually increase from higher (A+) to lower (BB-) credit ratings and from shorter (6m) to longer residual maturities (10y).

3.3 Debit Valuation Adjustment

The market value adjustment for accounting purposes requires financial institutions to adjust the market value of their interest rate swaps for the credit quality of both parties in the agreement. Therefore, DVA has to be calculated in addition to CVA. The calculation of DVA for an interest rate swap is performed in a similar way as the calculation of the CVA. Only, the Expected Exposure of the non-financial counterparty and Probability of Default of the financial institution replace the Expected Exposure and the Probability of Default. Formula 5 presents the DVA formula:

𝐷𝐷𝑀𝑀𝐶𝐶 = 𝐿𝐿𝐿𝐿𝐷𝐷𝑀𝑀𝑀𝑀𝑇𝑇 × ∑𝑇𝑇𝑖𝑖=1𝑀𝑀𝐶𝐶𝑥𝑥(0; 𝐸𝐸𝐸𝐸𝑁𝑁𝐹𝐹𝑁𝑁𝑖𝑖 × 𝑃𝑃𝐷𝐷𝐹𝐹𝐹𝐹𝑖𝑖), (5)

Where;

EENFC_{= the Expected Exposure the non-financial counterparty is subject to at time t}_i_;

PDFI_{= the Probability of Default of the financial institution.}

CDS Spread Curves (as per 30/04/2014)

Credit Category 6M 1Y 2Y 3Y 4Y 5Y 7Y 10Y

BB- 71.96 93.30 150.93 198.19 251.36 315.00 356.39 386.00 BB 34.33 44.77 85.28 128.04 173.53 221.62 272.84 302.93 BB+ 31.63 44.57 74.16 102.90 143.53 183.16 246.01 280.28 BBB- 26.45 37.33 57.55 79.81 106.00 130.42 165.69 185.92 BBB 16.64 20.70 34.38 50.83 72.83 90.66 122.29 140.09 BBB+ 11.58 15.73 26.62 40.00 57.47 72.12 94.66 108.76 A- 8.27 11.18 20.61 31.60 47.28 56.81 80.04 94.06 A 8.15 10.69 16.02 26.51 40.44 50.55 71.20 85.07 A+ 6.59 7.89 14.89 23.33 34.01 43.11 59.42 72.10

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Expected Exposure

The methodology for the calculation of the Expected Exposure for DVA is the same as for CVA. Only, for the non-financial counterparty, the swaptions are strings of options to pay the fixed leg combined with a string of options to receive the floating leg.

Probability of Default

For the Probability of Default for the financial institutions, I use the senior and subordinate financial indices of iTraxx. iTraxx provides indices with the most liquidly traded CDS contracts. Markit reviews and updates all indices semi-annually to contain the companies with the most liquidly traded CDS contracts. The senior and subordinate financial indices contain the 25 financial institutions. The senior index uses the CDS spread for their senior claims and the subordinate index uses the CDS spread for their subordinated claims. Table 8 shows the senior and subordinate CDS spread curves.

Table 8: CDS Spread curves for senior and subordinate financials. CDS spreads gradually increase from higher (A+) to lower (BB-) credit ratings and from shorter (6m) to longer residual maturities (10y).

3.4 Bilateral Valuation Adjustment

The Bilateral Valuation Adjustment (BVA) corrects the market value of an interest rate swap for the credit quality of both parties in the swap agreement. In addition to the capital requirements under the Basel documents, IFRS requires financial institutions to correct the market value of interest rate swaps for credit risk. The simplified methodology uses Unilateral CVA and Unilateral DVA for these calculations. However, these unilateral value adjustments assume that the other party in the contract does not default during the life of the contract. This methodology is referred to as the Simplified Bilateral Value Adjustment (SBVA). An advantage of this formula is that only

CDS Spread Curve Financials (as per 30/04/2014)

6M 1Y 2Y 3Y 4Y 5Y 7Y 10Y

Senior 17.01 21.86 36.74 50.16 68.39 77.87 103.39 118.49 Subordinate 29.72 46.59 60.90 79.37 106.62 121.53 150.42 167.27

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the unilateral CVA and DVA have to be calculated to be able to get the Bilateral Value adjustment. Formula 6 shows the SBVA formula.

𝑆𝑆𝑆𝑆𝑀𝑀𝐶𝐶 = − �𝐿𝐿𝐿𝐿𝐷𝐷𝑀𝑀𝑀𝑀𝑇𝑇 × � 𝑀𝑀𝐶𝐶𝑥𝑥 𝑇𝑇 𝑖𝑖=1 (0; 𝐸𝐸𝐸𝐸𝐹𝐹𝐹𝐹 𝑖𝑖× 𝑃𝑃𝐷𝐷𝑁𝑁𝐹𝐹𝑁𝑁𝑖𝑖)� + �𝐿𝐿𝐿𝐿𝐷𝐷𝑀𝑀𝑀𝑀𝑇𝑇 × � 𝑀𝑀𝐶𝐶𝑥𝑥 𝑇𝑇 𝑖𝑖=1 (0; 𝐸𝐸𝐸𝐸𝑁𝑁𝐹𝐹𝑁𝑁 𝑖𝑖× 𝑃𝑃𝐷𝐷𝐹𝐹𝐹𝐹𝑖𝑖)� (6) The more sophisticated Fully Bilateral Value Adjustment (FBVA) does not only take into account that both counterparties in an interest rate swap contract are subject to default risk, FBVA also acknowledges that if one of both parties defaults the contract is closed out. Using this methodology the Probability of Default is corrected for the probability that the counterparty has not defaulted until that point in time. Each period Probability of Default is multiplied with the Survival Probability (SP) of the counterparty. Formula 7 defines the Survival Probability:

𝑆𝑆𝐷𝐷𝑎𝑎𝑆𝑆𝐶𝐶𝑆𝑆𝐶𝐶𝐶𝐶 𝑃𝑃𝑎𝑎𝑜𝑜𝑃𝑃𝐶𝐶𝑃𝑃𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝑖𝑖 = 1 − 𝐶𝐶𝐷𝐷𝐶𝐶𝐷𝐷𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝑆𝑆𝑎𝑎 𝐷𝐷𝑎𝑎𝑜𝑜𝐶𝐶𝐷𝐷𝐶𝐶𝐶𝐶 𝑃𝑃𝑎𝑎𝑜𝑜𝑃𝑃𝐶𝐶𝑃𝑃𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝑖𝑖 (7) The Probability of Default corrected for the counterparty survival is the Conditional Probability of Default (CPD). Formula 8 shows the CPD for the financial institution adjusted for the SP of the non-financial counterparty.

𝐶𝐶𝑃𝑃𝐷𝐷𝐹𝐹𝐹𝐹

𝑖𝑖 = 𝑃𝑃𝐷𝐷𝐹𝐹𝐹𝐹𝑖𝑖× 𝑆𝑆𝑃𝑃𝑁𝑁𝐹𝐹𝑁𝑁0→𝑖𝑖 (8)

Formula 9 shows the CPD for the non-financial counterparty adjusted for the SP of the financial institution.

𝐶𝐶𝑃𝑃𝐷𝐷𝑁𝑁𝐹𝐹𝑁𝑁

𝑖𝑖 = 𝑃𝑃𝐷𝐷𝑁𝑁𝐹𝐹𝑁𝑁𝑖𝑖 × 𝑆𝑆𝑃𝑃𝐹𝐹𝐹𝐹0→𝑖𝑖 (9)

Formula 10 shows the FBVA formula that uses conditional probabilities of default of Formula 8 and Formula 9. 𝐹𝐹𝑆𝑆𝑀𝑀𝐶𝐶 = − �𝐿𝐿𝐿𝐿𝐷𝐷𝑀𝑀𝑀𝑀𝑇𝑇 × � 𝑀𝑀𝐶𝐶𝑥𝑥 𝑇𝑇 𝑖𝑖=1 (0; 𝐸𝐸𝐸𝐸𝐹𝐹𝐹𝐹 𝑖𝑖× 𝐶𝐶𝑃𝑃𝐷𝐷𝑁𝑁𝐹𝐹𝑁𝑁𝑖𝑖)� + �𝐿𝐿𝐿𝐿𝐷𝐷𝑀𝑀𝑀𝑀𝑇𝑇 × � 𝑀𝑀𝐶𝐶𝑥𝑥 𝑇𝑇 𝑖𝑖=1 (0; 𝐸𝐸𝐸𝐸𝑁𝑁𝐹𝐹𝑁𝑁 𝑖𝑖× 𝐶𝐶𝑃𝑃𝐷𝐷𝐹𝐹𝐹𝐹𝑖𝑖)� (10)

4 Results

Section 4 uses the methodology to determine the risk neutral market value, the Basel II Capital Charge, the Basel III CVA and the Bilateral Valuation Adjustment. Section 5 presents the analysis

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4.1 Interest rate swaps

The discounted cash flows of the fixed and the floating leg are used to determine the risk neutral market value. As the analysis is performed from the perspective of the financial institution, the market value is the present value of the fixed leg minus the present value of the floating leg. Table 9 shows the market values of all swaps. The swaps with a fixed rate determined with trade date in 2008, 2009, 2010, 2011 and 2012 are in-the-money for the financial institution. These swaps are an asset to the financial institution. The swaps with a fixed rate determined with trade date in 2013 are out-of-the-money for the financial institution. These swaps are a liability to the financial institution. For the swaps that are in-the-money (out-of-the-money) for the financial institution, the expectation of the 3m EURIBOR is lower (higher) than the determined fixed rate. Table 9: Risk neutral market value of the interest rate swaps. From the perspective of the financial institution, the swaps that are out-of-the-money are the swaps with trade dates in 2013. From all in-the-money swaps, the swaps with trade dates in 2008 are the furthest in-the-money.

4.2 Basel II Capital Charge

The Basel II Capital Charge is a capital requirement for bank to prepare for losses due to counterparty default. Formula 2 explains the calculation of the Basel II Capital Charge. Table 10 shows the Basel II Capital Charge for all swaps calculated per 30 April 2014. The replacement costs are only taken into account, when the market value is positive. For the swaps with a trade date in 2013 the market values are negative, for these swaps the Basel II Capital Charge is only based on the potential future exposure. For contracts with a residual maturity of less than 1 year, the potential future exposure is expected to be zero. The Capital Charge for these short term contracts is based only on the mark-to-market value. As for the Basel II Capital Charge a risk

Risk neutral m arket value (as per 30 April 2014)

2008 2009 2010 2011 2012 2013 1 yr 438,928 108,977 63,688 152,021 32,002 -8,123 5 yrs 1,750,721 896,513 664,194 1,036,070 211,324 -77,371 10 yrs 2,800,384 1,691,230 1,371,380 1,748,645 424,365 -214,021 20 yrs 4,368,905 2,702,606 2,239,405 2,716,211 448,750 -412,795 Residual Maturity

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weight is defined per group of credit ratings, the credit risk value is the same for counterparties in different credit rating groups. Table 10 shows the highest Basel II Capital Charge values for contracts with a residual maturity of 20 years for counterparties with a lower credit rating corresponding with a higher risk factor. When comparing Basel II Capital Charges for contracts with different trade dates, the contracts traded in 2008 have the highest mark-to-market values which results in the highest Capital Charge.

Table 10: Basel II Capital Charge. The Basel II Capital Charge is calculated with Formula 2: (𝑅𝑅𝐶𝐶 + 𝐶𝐶𝑎𝑎𝑎𝑎 𝑜𝑜𝑜𝑜) − 𝐶𝐶𝐴𝐴 × 𝑎𝑎 × 𝑀𝑀𝐶𝐶𝑅𝑅. The table shows the highest Basel II Capital Charge values

for contracts with longer residual maturity (20 years) and higher mark-to-market values (i.e. contracts with trade date in 2008).

4.3 Basel III Valuation Adjustment

The Basel III Credit Valuation Adjustment (CVA) is a capital requirement for financial institutions to prepare for mark-to-market losses due to counterparty risk. The financial institution incurs

Basel II Capital Charge (as per 30 April 2014) Residual m aturity Year of trade date A+ to A- BBB+ to BB-1 year 2008 17,557 35,114 2009 4,359 8,718 2010 2,548 5,095 2011 6,081 12,162 2012 1,280 2,560 2013 - -5 years 2008 72,029 144,058 2009 37,861 75,721 2010 28,568 57,136 2011 43,443 86,886 2012 10,453 20,906 2013 2,000 4,000 10 years 2008 118,015 236,031 2009 73,649 147,298 2010 60,855 121,710 2011 75,946 151,892 2012 22,975 45,949 2013 6,000 12,000 20 years 2008 180,756 361,512 2009 114,104 228,208 2010 95,576 191,152 2011 114,648 229,297 2012 23,950 47,900 2013 6,000 12,000

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quality. CVA is an addition to the Basel II Capital Charge for counterparty default. Formula 4 explains the calculation of the Basel III CVA. Table 11 shows the Basel III CVA for all swaps calculated per 30 April 2014. Table 11 shows that CVA strictly increases with decreasing credit quality and that CVA increases with longer residual maturity. Swaps with a higher market value (i.e. swaps that are more in-the-money) have a higher CVA values.

To analyze the effect of different input parameters, I compare the CVA values of two swaps with similar fixed rates, but different residual maturities. Swap 2009-5 years and 2012-20 years have interest rates of 2.545 and 2.439 respectively. The CVA of the swap with the longer residual maturity is 11.13 (A+) to 5.01 (BB-) times higher than CVA for the swap with the shorter residual maturity. Which means that residual maturity has a greater impact on the CVA value of a swap than the fixed interest rate. I make similar comparison between two swaps with similar risk neutral market values, but different residual maturities. Swap 2008-5 years and 2011-10 years have market value of 1,750,721 and 1,748,645 respectively. The CVA of the swap with the longer residual maturity is 3.13 (A) to 2.23 (BB-) times higher than the CVA for the swap with the shorter residual maturity.

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Table 11: Basel III Credit Valuation Adjustment. The Basel III CVA is calculated with Formula 4: CVA = 𝐿𝐿𝐿𝐿𝐷𝐷𝑀𝑀𝑀𝑀𝑇𝑇 × ∑𝑇𝑇𝑖𝑖=1𝑀𝑀𝐶𝐶𝑥𝑥(0; 𝐸𝐸𝐸𝐸𝐹𝐹𝐹𝐹𝑖𝑖× 𝑃𝑃𝐷𝐷𝑁𝑁𝐹𝐹𝑁𝑁𝑖𝑖). The table shows the highest Basel III CVA

values for swaps with a longer residual maturity, higher mark-to-market values and for swaps with counterparties with a lower credit quality.

4.4 Debit valuation adjustment

The Debit Valuation Adjustment is the market value adjustment for financial institution’s own credit risk. Accounting rules require companies to adjust the market value of an interest rate swap to incorporate counterparty credit risk. Next to the adjustment for counterparty default (CVA) the possibility of the financial institution’s own default (DVA) has to be included in the market value. Formula 5 explains the calculation of DVA. Table 12 shows the DVA for all swaps

Basel III Credit Valuation Adjustm ent (as per 30 April 2014) Residual m aturity Year of trade date A+ A A- BBB+ BBB BBB- BB+ BB BB-1 year 2008 198 257 264 371 510 863 1,031 1,076 2,243 2009 50 64 66 93 128 217 259 270 564 2010 30 38 40 56 76 129 155 161 336 2011 69 90 92 129 178 301 360 375 782 2012 16 21 21 30 41 70 84 87 181 2013 2 2 2 3 4 7 8 8 17 5 years 2008 11,372 13,244 15,449 19,339 24,497 36,740 48,781 58,318 87,071 2009 5,584 6,504 7,585 9,501 12,039 18,076 23,984 28,655 42,872 2010 4,059 4,728 5,513 6,909 8,756 13,152 17,448 20,838 31,207 2011 6,521 7,596 8,858 11,093 14,055 21,094 27,994 33,450 50,011 2012 1,442 1,679 1,955 2,449 3,099 4,636 6,169 7,379 10,969 2013 315 365 426 530 666 982 1,323 1,595 2,296 10 years 2008 59,387 69,977 78,435 93,082 118,121 160,232 225,899 251,281 326,689 2009 33,996 40,054 44,906 53,302 67,647 91,853 129,391 143,939 187,482 2010 27,480 32,377 36,287 43,045 54,634 74,122 104,449 116,077 151,019 2011 35,212 41,488 46,515 55,214 70,074 95,153 134,038 149,123 194,248 2012 11,790 13,895 15,509 18,241 23,155 30,975 43,968 48,325 61,469 2013 5,144 6,067 6,720 7,773 9,865 12,828 18,482 19,868 24,058 20 years 2008 245,421 283,824 309,604 351,238 437,447 554,505 763,765 806,762 957,610 2009 155,579 179,745 195,826 221,683 275,785 348,427 478,876 504,433 595,931 2010 133,150 153,762 167,398 189,270 235,338 296,723 407,504 428,512 504,611 2011 156,259 180,532 196,687 222,665 277,009 349,991 481,035 506,729 598,688 2012 62,175 71,574 77,482 86,714 107,404 132,990 182,012 188,569 215,016 2013 38,708 44,455 47,917 53,202 65,699 80,193 109,435 111,955 124,195

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calculated per 30 April 2014. Table 12 shows that DVA is higher for subordinated counterparties than for senior counterparties and that it increases with longer residual maturities. All swaps that are in-the-money for the financial institution are out-of-the-money for the non-financial counterparty. The swaps that are out-of-the-money for the non-financial counterparty and have a residual maturity of 1 year have relatively small possibility of getting in-the-money. Either, the Expected Exposure for these swaps is negative and therefore set to zero, which gives a DVA value of zero. Or, the Expected Exposure is slightly positive, which gives a very small DVA value.

Table 12: Debit Valuation Adjustment. The DVA is calculated with Formula 5: 𝐷𝐷𝑀𝑀𝐶𝐶 = 𝐿𝐿𝐿𝐿𝐷𝐷𝑀𝑀𝑀𝑀𝑇𝑇 ×

∑𝑇𝑇 𝑀𝑀𝐶𝐶𝑥𝑥

𝑖𝑖=1 (0; 𝐸𝐸𝐸𝐸𝑁𝑁𝐹𝐹𝑁𝑁𝑖𝑖× 𝑃𝑃𝐷𝐷𝐹𝐹𝐹𝐹𝑖𝑖) . Swaps of subordinate financial institutions have a higher DVA

than swaps of senior financial institutions. The table shows the highest DVA values for swaps with a longer residual maturity, lower or negative mark-to-market values.

Debit Valuation Adjustm ent (as per 30 April 2014) Residual

m aturity

Year of

trade date Senior Subordinate

1 year 2008 - -2009 0 0 2010 1 2 2011 - -2012 2 5 2013 12 23 5 years 2008 251 380 2009 1,002 1,507 2010 1,301 1,958 2011 860 1,294 2012 2,570 3,889 2013 4,602 7,067 10 years 2008 8,185 11,075 2009 14,280 19,276 2010 17,330 23,413 2011 13,809 18,639 2012 32,397 44,198 2013 49,883 69,015 20 years 2008 46,158 58,062 2009 74,256 93,858 2010 85,898 108,824 2011 73,945 93,459 2012 155,421 199,629 2013 207,018 268,508

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4.5 Bilateral Valuation Adjustment

Brigo, Buescu and Morini (2012) theoretically find a considerable difference between the Simplified Bilateral Valuation Adjustment (SBVA) and the Fully Bilateral Valuation Adjustment (FBVA). This article calculates the SBVA and FBVA for different interest rate swaps to empirically analyze the difference in value. The first paragraph calculates both FBVA and SBVA, the second paragraph compares outcomes and determines whether SBVA can be used as a proxy for the Bilateral Valuation Adjustment.

4.5.1 Simplified and Fully Bilateral Valuation Adjustment

Accounting rules require companies to adjust the market value of an interest rate swap to incorporate counterparty credit risk. Now Unilateral CVA and Unilateral DVA are calculated, the Simplified Bilateral Valuation Adjustment (SBVA) is determined using Formula 6. Table A1 and Table A2 present the market values for SBVA calculated per 30 April 2014 for senior and subordinate financial institutions respectively. For the Fully Bilateral Valuation Adjustment (FBVA), the Probabilities of Default are adjusted to account for the probability that the other party in the contract is also able to default. Formula 8 determines the Conditional Probabilities of Default (CPD) for the financial institution. Formula 9 determines the CPD for the non-financial counterparty. With the CPD from Formula 8 and the CPD from Formula 9, the FBVA is determined using Formula 10. Table 13 and Table 14 present the market values for the FBVA calculated per 30 April 2014 for senior and subordinate financial institutions respectively. When CVA is higher than DVA, FBVA is negative. When DVA is higher than CVA, FBVA is positive.

When the interest rate swap is more in-the-money for the financial institution at the valuation date, the lost value due to counterparty default is higher for the financial institution than for the non-financial counterparty. Therefore CVA is higher than DVA and SBVA and FBVA are negative. When the market expectation of the development of EURIBOR shows an increasing trend, the possibility exists that the interest rate swap goes out-of-the-money during the life of the contract. This possibility increases DVA, giving positive SBVA and FBVA. Swaps traded in 2012 and with a residual maturity of 5 years, 10 years or 20 years are in-the-money at valuation date but have higher DVA than CVA. These swaps are in-the-money for the financial institution at valuation

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date. But, for counterparties with higher credit rating (i.e. lower CVA), SBVA and FBVA are positive.

When comparing the bilateral adjustment for senior and subordinate financial institutions, Table 13 and Table 14 show less negative or more positive SBVA values for subordinate financial institutions. Senior and Subordinate financial institutions are exposed to the same credit risk from their counterparties, thus CVA is the same. But DVA is higher for subordinate financials as the risk of their own default is higher.

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Table 13: FBVA for senior financial institutions. The FBVA is calculated with Formula 10:

𝐹𝐹𝑆𝑆𝑀𝑀𝐶𝐶 = − �𝐿𝐿𝐿𝐿𝐷𝐷𝑀𝑀𝑀𝑀𝑇𝑇 × ∑𝑇𝑇𝑖𝑖=1𝑀𝑀𝐶𝐶𝑥𝑥(0; 𝐸𝐸𝐸𝐸𝐹𝐹𝐹𝐹𝑖𝑖× 𝐶𝐶𝑃𝑃𝐷𝐷𝑁𝑁𝐹𝐹𝑁𝑁𝑖𝑖)� + �𝐿𝐿𝐿𝐿𝐷𝐷𝑀𝑀𝑀𝑀𝑇𝑇 × ∑𝑇𝑇𝑖𝑖=1𝑀𝑀𝐶𝐶𝑥𝑥(0; 𝐸𝐸𝐸𝐸𝑁𝑁𝐹𝐹𝑁𝑁𝑖𝑖×

𝐶𝐶𝑃𝑃𝐷𝐷𝐹𝐹𝐹𝐹

𝑖𝑖)�. FBVA is negative when CVA is higher than DVA. FBVA is positive when DVA is higher

than CVA. The table shows larger absolute FBVA values for swaps with a longer residual maturity with counterparties with lower credit quality. The table shows higher negative FBVA values for swaps that are more in-the-money. The table shows higher positive FBVA for swaps that are out-of-the-money.

Fully Bilateral CVA for Senior financial institutions (as per 30 April 2014)

Residual m aturity Year of trade date A+ A A- BBB+ BBB BBB- BB+ BB BB-1 year 2008 -198 -256 -264 -370 -509 -861 -1,029 -1,074 -2,239 2009 -50 -64 -66 -93 -128 -216 -259 -270 -563 2010 -29 -38 -39 -55 -76 -128 -154 -160 -335 2011 -69 -89 -92 -129 -178 -301 -359 -375 -781 2012 -14 -18 -19 -28 -39 -68 -81 -85 -179 2013 10 10 10 9 8 5 4 3 -6 5 years 2008 -10,860 -12,684 -14,846 -18,655 -23,702 -35,727 -47,479 -56,795 -85,107 2009 -4,470 -5,369 -6,433 -8,313 -10,804 -16,749 -22,531 -27,107 -41,140 2010 -2,687 -3,342 -4,116 -5,489 -7,306 -11,645 -15,859 -19,188 -29,443 2011 -5,525 -6,575 -7,815 -10,007 -12,912 -19,838 -26,585 -31,925 -48,261 2012 1,122 885 607 111 -542 -2,090 -3,624 -4,838 -8,457 2013 4,233 4,174 4,102 3,980 3,819 3,445 3,053 2,736 1,908 10 years 2008 -47,886 -57,870 -65,957 -80,027 -103,737 -144,238 -206,252 -231,169 -304,813 2009 -18,319 -24,119 -28,826 -37,011 -50,792 -74,389 -110,319 -124,782 -167,792 2010 -9,301 -14,039 -17,870 -24,526 -35,769 -54,946 -84,242 -95,913 -130,711 2011 -19,908 -25,907 -30,778 -39,247 -53,502 -77,921 -115,093 -130,072 -174,596 2012 19,862 17,629 15,893 12,927 7,722 -702 -14,319 -19,165 -33,440 2013 42,930 41,691 40,774 39,248 36,440 32,218 24,863 22,635 16,325 20 years 2008 -172,670 -207,374 -231,144 -269,879 -348,177 -457,268 -649,136 -692,671 -840,297 2009 -68,495 -90,963 -106,214 -130,956 -181,416 -250,889 -373,499 -400,182 -491,970 2010 -38,221 -57,691 -70,832 -92,101 -135,714 -195,299 -300,899 -323,260 -400,752 2011 -69,373 -91,932 -107,248 -132,096 -182,763 -252,536 -375,664 -402,477 -494,695 2012 87,762 77,357 70,611 59,916 37,098 7,805 -46,281 -55,430 -88,246 2013 155,878 148,087 143,117 135,312 118,465 97,460 58,200 52,274 30,798

An empirical assessment of the Credit Valuation Adjustment for interest rate swaps

Amsterdam Business School

MSC Business Economics, Finance track

Contents

1 Introduction

2 Literature review

2.1 Regulation

2.2 Market overview

2.3 Interest rate swaps

Notional amounts, by maturity

Gross market values, by

currency

2.4 Credit risk

2.5 Credit Valuation Adjustment

2.6 Bilateral Valuation Adjustment

3 Methodology

3.1 Interest rate swaps

3.2 Basel II Capital Charge

3.3 Basel III Valuation Adjustment

3.3 Debit Valuation Adjustment

3.4 Bilateral Valuation Adjustment

4 Results

4.1 Interest rate swaps

4.2 Basel II Capital Charge

4.3 Basel III Valuation Adjustment

4.4 Debit valuation adjustment

4.5 Bilateral Valuation Adjustment