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How Does Implied Volatility Behave Around
Interest Rate Announcements of the FED and ECB?
An examination of the VIX and the VDAX between 2000 and 2014 June 2014 Supervisor: P.P.M. Smid Student: I. Jansen Student number: S2404451 Word count: 12869 Abstract
This thesis examines the link between interest rate announcements of the FED and the ECB and the implied volatility indices Chicago Board Options Exchange Market Volatility Index (VIX) and the Volatility Deutscher Aktienindex (VDAX). In the full research period there is an indication of a decrease in the level of the VIX and the VDAX on the announcement day, the magnitude of this effect is unstable over time. The spillover effect measures if the VIX and the VDAX are reacting to interest rate announcements of the other continent, this effect is significant. The robustness test corresponds with the main findings of the research; interest rate announcements lower the level of implied volatility.
JEL classification: G10, G14
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Volatility is one of the most important concepts throughout the whole financial industry (Brooks, 2008). In finance, volatility is measured as the standard deviation of the return of financial assets. Both practitioners and the academic world have investigated the modeling and forecasting of volatility intensively over de past decade. The volatility of financial assets serves many purposes in daily practice. It is used in value-at-risk (VAR) models to indicate the largest potential loss on a trading position (Sironi and Resti, 2007). It is important to enter an accurate and adequately calculated measure of volatility in VAR models to give valuable and accurate estimates of potential trading losses. Another practice where volatility is used is option pricing (Black and Scholes, 1973). An option is a tradable derivative that gives the owner the right to buy or sell the underlying asset at a predetermined price in the future. In order to price options several inputs are needed which, are either stated in the option contract or observable in the financial market. One of the inputs to calculate the theoretical price of an option is the estimated volatility of the underlying asset for the remaining lifetime of the option contract. For traders and other practitioners in financial markets it is of great importance to have a good estimate of volatility and to know how it generally develops and behaves over time.
Volatility measures can, amongst other types, be distinguished into two types: historical volatility and implied volatility. Historical volatility gives an indication of how erratic the returns of a specific asset or portfolio of assets have been in the past. It is calculated as the standard deviation of the historical return. On the other hand, implied volatility gives an indication how volatile the return of financial assets is expected to be in the future and is derived from current option prices. Han and Park (2013) make a comparison of the historical and implied volatility of the Standard and Poor’s 500 index (S&P). They conclude that of these two volatility measures, implied volatility is the better forecaster for future volatility. Fleming (1998) concludes, models that use implied volatility instead of historical volatility as a parameter give better forecasts of the future realized volatility. This indicates the importance for practitioners to know how implied volatility is behaving under certain market conditions.
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with the VIX as underlying value; these products have gained substantial popularity in the past year. For traders who trade in these products it is important to know how the VIX fluctuates over time and around events. This research examines how the VIX and the Volatility Deutscher Aktienindex (VDAX) behave around interest rate announcements of the Federal Reserve System (FED) and the European Central Bank (ECB).
Cutler et al. (1989) describe the negative correlation between stock prices and interest rates. If markets have a semi-strong efficient form, stock markets should adjust to announcements of relevant public information immediately (Fama, 1970). When the investigated markets are indeed efficient they should absorb the impact of an interest rate announcement right after the release. When markets work out the implications of the interest rate announcements, the market has the opportunity to set new market prices based on this new information. This effect on stock prices will simultaneously have an effect on the index in which these stocks are included. The VIX and the VDAX are implied volatility indices derived from the prices of index options with the S&P and the Deutscher Aktienindex (DAX) as underlying asset. A change in the level of the S&P and the DAX will most likely have an effect on the price of the corresponding index options. When option prices change the level of the VIX and the VDAX will most likely change as well.
At each interest rate announcement there is a possibility that the central banks will adjust the interest rate. This can affect the uncertainty about future stock and index returns. Ederington and Lee (1993) mention there is a small industry focusing on predicting announcements. Even if the announcements are accurately predicted by this industry no one knows before the announcement if the predictions are correct. So an announcement brings uncertainty into the market by construction. Because of the negative correlation between stock prices and interest rates (Cutler et al., 1989), the markets are watching the interest rate announcements of the ECB and the FED. This gives rise to the main research question of this study: How do the VIX and the VDAX behave around interest rate announcements of the FED and the ECB?
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reaction of implied volatility after a macro-economic announcement is not stable over time. This gives rise to the first sub-question: Is the reaction of the VIX and the VDAX after an interest rate announcement of the FED and ECB stable over time?
Füss et al. (2011) prove that the level of the VIX and the VDAX is affected by macro-economic announcements from other continents. To see if an interest rate announcement causes the same effect the following sub-question is formulated: Is the level of the VIX and the VDAX affected by interest rate announcements of the central bank on the other continent? The research questions are answered with the investigation of the VIX and the VDAX from January 2000 till January 2014. These time series are collected from Bloomberg. The abnormal change in the level of volatility is calculated on the days around the announcement of the interest rate of the FED and ECB. These abnormal changes are analyzed to how the VIX and the VDAX behave on the days that surround an interest rate announcement. Knowing how implied volatility has behaved around interest rate announcements can add valuable insights for traders who trade in derivatives of the VIX and the VDAX or who are using the VIX and the VDAX in e.g. VAR models. This research continues as follows: Section 2 gives a summary relevant theory together with a review of past empirical results. Section 3 describes the hypothesis, methodology and the data. Section 4 contains the results of the research and section 5 gives the conclusions.
1. Theoretical background
Options pricing models can be used to calculate the theoretical price of an option. Among others, Black and Scholes (1973) present a model to perform this task, hereinafter referred to as Black-Scholes model. In the Black-Scholes model one of the important inputs is volatility. Other variables that are used in the model are the current price, the strike price, the remaining lifetime of the option and the interest rate. The volatility input in the Black-Scholes model should represent the expected volatility of the underlying asset during the remaining time of the option contract and is assumed to be constant. Donders and Vorst (1996) mention that in most cases volatility is not independently and identically distributed i.e. constant over time.
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communicable estimate of the potential maximum loss on a trading position at a certain confidence level. For example, the VAR on a single asset can be calculated as the product of the market value, the historical daily volatility of the asset and the required confidence level (Sironi and Resti, 2007). When the daily volatility is higher than the estimated historical volatility, the loss will be larger than the VAR. In this case VAR measures will have no value at all.
The Black-Scholes formula can be solved backwards to calculate future volatility that is implied by the market i.e. implied volatility (Hull, 2012). Implied volatility serves as a proxy for future volatility of the underlying asset. If the Black-Scholes model is completely realistic, the implied volatility is equal for all options on the same underlying asset with different strike prices and maturities. In practice this is not the case. The implied volatility varies with different strike prices and maturities, known as volatility smiles and volatility term structure (Deng et al., 2008).
A theoretical explanation for the relationship between interest rate announcements and implied volatility can be found in the Mixture of Distributions Hypothesis (MDH) (Ho et al. 2013). The theory behind the MDH is that daily trading volume and implied volatility are driven by the flow of information to the financial markets. Good news causes prices to increase and bad news causes prices to decrease. In both cases of news arrival there is above average trading activity. During this period of above average trading activity the trading volume and implied volatility is higher compared to days without news (Luu and Martens, 2003). After the market absorbs the news, the market converts to a new equilibrium and the trading volume and implied volatility decreases.
Donders and Vorst (1996) establish a theory for the possible distribution of volatility during the remaining lifetime of options. Donders and Vorst (1996) state that volatility might be independent and identical distributed on days without news announcements. On the day of a scheduled news announcement volatility is expected to be higher. The average volatility during the remaining lifetime of the option on the day of a scheduled news announcement is modeled as:
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where is the number of days until the expiration of the option, the volatility on normal days and the volatility on days of a scheduled news announcements. Equation (1) implies the level of volatility is higher on the days of a news announcement. Donders and Vorst (1996) suggest the volatility reverts back to an independently and identically distributed variable after the news announcement.
To conclude, the discussed theory of Black and Scholes (1973) and Sironi and Resti (2007) assume volatility to be constant over time. Ho et al. 2013 and Donders and Vorst (1996) establish theories where volatility is not constant and is expected to be higher during announcements.
1.2 Empirical results
In recent years there is a lot of research done on how implied volatility behaves around firm specific news and macro-economic announcements (Donders and Vorst 1996; Ederington and Lee 1993; Füss et al. (2011) describe how macro-economic announcements affect the level of the VIX and the VDAX. Gross domestic product, producer price index and consumer price index are included in the research. One of the properties all the observations in the timeframe have in common is that the date of all announcements is known in advance. Only the content of the announcement is unknown. The link that is established in this paper is how the market reacts to announcements of which the announcement date is known in advance. How markets react to news of extreme announcements from an unexpected event is completely different from known announcements (Straetmans et al. 2008).
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all announcements the VIX is responding more sensitive compared to the VDAX. Füss et al. (2011) conclude that the level of the VIX is responding to European announcements and the VDAX to American announcements. The effect of a decreasing volatility after an macro-economic announcement proves to be significant from continent to continent. It is called the spillover effect.
Donders and Vorst (1996) study the effect of scheduled firm specific news on stock option implied volatility. Scheduled news is defined as news for which the announcement date is known prior to this date, but of which the content of the announcement is not known in advance. To describe how volatility is behaving around these news releases the researchers construct four periods. The period before, the day of, and the three days after the news release, in addition a control period is constructed with the days that do not fall in one of the three periods mentioned before.
Donders and Vorst (1996) find significant proof for the hypothesis that implied volatility before a scheduled firm specific news release. After the news release implied volatility show a sharp decrease, and decreases with approximately three percentage-points. In addition, Donders and Vorst (1996) present another interesting conclusion. The return of the stocks on the release day have a significant negative correlation with the change in the level of implied volatility of the options. The motivation behind this test is found in the following reasoning. The news will lower or higher the price of the stock immediately after the release and will take away part of the future uncertainty. This future uncertainty is reflected in the implied volatility and will therefore be lower if the stock shows a large change in price. The authors regress the stock return on the release day against the change in implied volatility of the release day.
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announcement day. In the following 10 minutes the level of implied volatility drops fast. Ederington and Lee (1993) observe that volatility remains significantly higher for the two hours that follow the announcement. After two hours the volatility gradually reverts to the long-term average.
The discussed empirical research of Donders and Vorst (1996), and Füss et al. (2011) indicate that implied volatility decreases after known announcement. In addition Ederington and Lee (1994) conclude that volatility decreases after macro-economic announcements. The three researches prove that volatility is not constant over time and decreases after announcements. This endorses the expectation for the relation that is researched in this paper. It is expected that implied volatility index, VIX and the VDAX, will decrease after an interest rate announcement of the FED and ECB.
Another important relation in this research that has to be described is the relation between interest rate announcements and stock market return. Markets are paying attention to interest rate announcement for a variety of reasons. Cutler et al. (1989) find significant evidence for a negative relationship between stock prices and interest rates. The authors show that a one per cent increase of in the long-term interest rates reduces stock prices between 1.9 and 2.6 percentage-points. When central banks are increasing the interest rate, commercial and investment banks need to pay more to borrow money. In this case commercial banks will increase the charged interest rates to their clients as well. Households are affected through higher interest rate charges on credit cards bills and mortgages payments. This will result in a lower disposable income for households. Businesses are indirectly affected because consumers can spend less on products that are not directly linked to interest rates. When the interest rate is decreased, households will have a higher disposable income. Besides commercial banks investment banks will adjust their charged interest rate as well with a change in the interest rate set by central banks. This will affect businesses in a more direct way. If interest rates are increased, businesses will pay higher interest rates and might not borrow as much as preferred. This can result in a lower operational growth accompanied with possible lower future revenue and profits.
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reduce economic growth. In van der Meer et al. (2014) the authors indicate that stocks do bad when there is an indication that central banks are trying to cool down the economy with a tighter monetary policy. Stocks are likely to do well when central banks are encouraging economic growth. Financial market participants are interested in interest rates announcements to indicate if central banks are changing their monetary policy.
2. Hypotheses, Methodology and Data Collection
This paper researches how implied volatility is behaving on the day, and the days that surround, of an interest rate announcement by the FED and ECB. Three hypotheses are constructed to test the research questions. The three hypotheses derived from the research questions are mentioned in the introduction and the discussed theory. The main question of this research is: How do the VIX and the VDAX behave around interest rate announcements of the FED and the ECB? This research question is set up to test the reaction of implied volatility on the day of an interest rate announcement and results in the following testable hypothesis:
H1: there is a negative relationship between the level of implied volatility and interest rate announcements.
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, (2)
where is the abnormal change in the level of the VIX at day in the announcement period. The announcement period is defined as the three days before an interest rate announcement, the day of an interest rate announcement and the three days after an interest rate announcement of the FED. Each announcement period consists of seven calculations for and is calculated as:
, (3)
where is the continuously compounded change in the level of the VIX on day and is calculated as:
, where is the level of the VIX
on day .
and combined subtract the change in the level of the VIX on day in the announcement period with the 60-day local average change in the level of the VIX. The right hand side of equation (2) is specified as:
s (4) s (5) s (6) s (7) s (8) s (9) s (10)
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Combined the equations (4) till (10) cover the full announcement period an interest rate announcement of the FED.
in equation (2) is the continuously compounded daily return of the S&P on day and is calculated as:
, where is the level of the S&P
on day . Further, is the absolute value of the percentage point change of the interest rate change if the interest rate is changed by the FED and zero otherwise. is the dummy variable for an interest rate increase and takes the value of 1 when the interest rate is increased and zero otherwise. is the dummy variable for an interest rate decrease and takes the value of 1 when the interest rate is decreased and zero otherwise. To avoid the dummy variable trap there is no constant added to equation (2). The regression is tested one-sided with the classical linear regression model (CLRM).
Equation (2) is transformed to the equation (11) to test the effect of an interest rate announcement of the ECB on the level of the VDAX.
, (11)
where is the abnormal change in the level of the VDAX at day in the announcement period and is calculated as:
, (12)
where is the continuously compounded change in the level of the VDAX on day and is calculated as:
where is the level
of the VDAX on day . Combined the functions
and give the average daily change in the level of the VDAX in the 30 days before and the 30 days after the announcement period. The right hand side of equation (11) is specified as:
12 s (14) s (15) s (16) s (17) s (18) s (19)
where is the third day before an interest rate announcement of the ECB and the second day before an interest rate announcement and so on. Together, the equations (13) till (19) cover the full announcement period of an interest rate announcement of the ECB.
in equation (11) is the continuously compounded daily return of the DAX on day and is defined as:
, where is the level of the
DAX on day . Further , and follow the same logic as described for equation (2).
The first sub-question of this research is formulated as: Is the reaction of implied volatility stable over time? Füss et al. (2011) showed that the reaction of implied volatility to macroeconomic announcements is not the same in all sub-periods of their research. To test if the reaction of implied volatility to interest rate announcements of the FED and ECB is stable over time the following hypothesis is formulated.
H2: the negative reaction of implied volatility to an interest rate announcement is not stable over time.
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, (20)
where is the squared change in the level of the VIX on day , the change in the level of the VIX is calculated as:
where is the level of
the VIX on day . Accordingly, Ck is the cumulative sum of squares of the change in the level of implied volatility. In the following equation the cumulative sum of squares is centered and normalized.
, (21)
where is the centered and normalized function of equation (20) is the total sum of squares, k is the number of the observation and T the number of total observations in the sample. If the changes in the level of implied volatility have a homogeneous variance will oscillate around 0. The following equation is used to calculate the test statistic of the ICSS.
, (22)
where T is the total number of observations in the sample. The test statistic will also oscillate around 0 when the change in the level of implied volatility has a constant variance in the entire sample.
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The second sub-question is formulated as: Is the level of the VIX and the VDAX affected by interest rate announcements of the central bank on the other continent? Füss et al. (2011) name this the spillover effect. The spillover effect is defined as the reaction of the level of the VIX after an interest rate announcement of the ECB and the level the VDAX after an announcement of the FED. The spillover effect measures if the interest rate announcement of the FED or ECB spills over to the other continent. To see if an interest rate announcement of the FED and ECB has an effect on the implied volatility index on the other continent the following hypotheses are constructed. The hypothesis is split up in two to avoid confusion.
H3: the negative effect of an interest rate announcement of the FED on the level of the VIX does spill over to the level of the VDAX.
H4: the negative effect of an interest rate announcement of the ECB on the level of the VDAX does spill over to the level of the VIX.
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The data that is collected for the research consists of the latest calculated levels of VIX and the VDAX on each trading day. For the VIX this is the level at 16:15 eastern American time (EST) and for the VDAX at 17:45 central European time (CET). Both the VIX and the VDAX are published 15 minutes after the last quoted prices of the underlying stock index i.e. S&P and the DAX. The VIX measures the expected annualized standard deviation of the S&P index for in the next 30 days (Chicago Board Options Exchange, 2009). For example a VIX of 20 corresponds to an expected annualized standard deviation of 20% in the next 30 days i.e. an expected standard deviation of 5.774% ( ) on return of the S&P in the next 30 days. The VDAX measures the expected annualized volatility of the DAX for the next 45 days (Deutsche Börse, 2007). All daily data points from November 1999 till March 2014 are collected from Bloomberg.
The VIX is constructed with a generalized version of the Black-Scholes formula that uses the forward price of the S&P at 16:00 EST (Chicago Board Options Exchange, 2009). The other variables of this model are also measured at 16:00. For the VIX the individual implied volatility of two call and two put options on the S&P are calculated. These options are those where the difference between the strike price and the current index level is the smallest. Further, the option must be the two monthly option series that are closest to expiration with a minimum time to expiration of one week. For example, on the second Friday in January the VIX is calculated with a call and a put option on the S&P that expire in January and a call and a put option that expire in February. On the next Monday, the VIX is calculated with the options that expire in February and March. The 30-day weighted average of the implied volatility of these options is taken to calculate the VIX. For the full calculation method see the explanation of Chicago Board Options Exchange (2009).
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weighted average of these two implied volatilities is calculated to construct the 45 day window of the VDAX. For the full procedure for the calculation of the VDAX see the guide of Deutsche Börse (2007).
The other part of the data consists of the continuously compounded daily return of the S&P and the DAX. As pointed out earlier, the daily change in the level the VIX and the VDAX are calculated with the variables that are observed at 16:00 EST and 17:30 CET. The VIX is calculated with the forward price of the S&P at 16:00 EST, the VDAX is calculated with the forward price of the DAX at 17:30 CET. Given the high correlation between the daily return of futures on indices and the return of the corresponding indices there is no problem with synchronicity with the use of the daily returns of the S&P at 16:00 EST and the daily return of the DAX at 17:30 CET. The daily returns of the S&P and the DAX are calculated
and
, where and is the level of the S&P
and the DAX on day .
Table 1: Summary statistics
This table shows the summary statistics of the continuously compounded change in the level of the VIX and the VDAX from November 1999 till March 2014 and the continuously compounded return of
the S&P and the DAX. Mean, SD, Max and Min give the mean, standard deviation, maximum and minimum of the variables. The probability gives the probability for the time series to be normally
distributed.
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The last set of data consists of the days of the interest rate announcements of the FED and the ECB. The FED announces the interest rate eight times a year. Usually in the end of January, middle May, the end of April, middle June, early August, middle September, early November and middle December. These dates where collected from the press website of the FED1. In the announcement of the FED there one interest rate announced namely the federal funds rate.
The ECB publish the interest rate two times a month in 2000 and the first 10 months of 2001, however since November 2001 the ECB announces the interest rate once a month. The interest rate announcements are collected from the press website of the ECB2. The interest rates that are announced by de ECB are the main refinancing rate, marginal lending facility and de deposit facility. The total number of observations consists of 116 interest rate announcements of the FED and 191 of the ECB. Together with these dates, the change of the interest rate is collected. From January 2000 till December 2013 the FED changed the interest rate 42 times. During this sample the ECB changed the interest rate 35 times.
For the second and third hypothesis in this research the data is divided into five sub-periods. These sub-periods are constructed using the ICSS algorithm (Inclan and Tiao, 1994). Equations (20), (21) and (22) are used to module the data and to detect the structural breaks in volatility. Because both series have over 3600 observations analyzing the data with the ICSS once would not reveal all structural changes. Inclan and Tiao (1994) call this the masking effect. To overcome the masking effect Inclan and Tiao (1994) propose to divide the data in smaller sub-periods after the ICSS is applied for the first time. The ICSS is applied to the smaller sub-periods separately to isolate remaining sudden changes in the variance of the daily change in the VIX and the VDAX. Because the spillover effect is tested under hypothesis 3 structural changes are only incorporated at points where VIX and the VDAX simultaneously have a sudden change in volatility (Füss et al. 2011).
Table 2 shows the dates at which the sub-periods begin. Figure 1 presents the level of the VIX and the VDAX for the full sample and shows the five sub-periods. The first sub-period lasts from January 2000 till September 2001. This period includes the dot-com bubble. The second sub-period includes 9/11 and the aftermath other events in this sub-period are the start of the Latin American Crisis and the SARS
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epidemic. These two events are accompanied with relatively high levels of implied volatility. After these events the implied volatility drops to relative stable levels until August 2008. These relatively low levels of implied volatility are included in sub-period three. In August 2008 the credit crisis starts, this is accompanied with relatively high levels of implied volatility. The high peak in figure 1 in September 2008 is formed at the default of Lehman Brothers. These events are included in the fourth sub-period and later in this sub-period the debt crisis in the Eurozone occurs. The last sub-period has a relatively stable level of implied volatility compared to prior years.
Table 2: Time series
This table shows the time series of the research. The full sample is 14 years. Start and end dates of the full sample and the sub-periods are in the first two columns. The columns labeled FED and ECB presents the amount interest rate announcements of the central banks. The number in the brackets indicates in how many of the interest rate announcements the interest rate is changed.
Start date End date FED ECB
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Figure 1: Structural breaks in VIX and the VDAX
This figure shows the level of the VIX and the VDAX for the full sample. Each vertical solid line indicates the start of a new sub-period.
3. Results
Table 3 shows the results of the regression analysis of the abnormal change in the level of the VIX around interest rate announcements of the FED. In the full sample the abnormal change in the level of the VIX the day before an interest rate announcement and the announcement day is significant (99%). The coefficients indicate that on the day before an announcement the abnormal change in the level of the VIX is 1.177 percentage-points and -1.285 on the announcement day. This indicates that the market expects the 30-day volatility of the S&P to be higher when the announcement is not public and lower after the interest rate announcement.
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same abnormal change in the level of the VIX on the day of an announcement as in the full sample. In this case a negative abnormal change in the level of the VIX is 1.437 percentage-points, the coefficient is significant (99%). On the first day after the announcement, the reaction of the VIX is also significantly negative in the first sub-period.
The results of the S&P coefficients correspond with the literature: Füss et al. (2011) describe a negative relationship between return and implied volatility. The coefficients of the S&P are significantly (99%) negative in all sub-periods. Indicating that a one-percentage point increase in the level of the S&P causes a negative abnormal change in the level of the VIX during the announcement period of the FED. The estimated coefficients range from 2.701 to 6.006 percentage-points. There are no interest rate increases of the FED in the second and fourth sub-period and no interest rate changes in the fifth sub-period. All coefficients that are concerned with the content of the interest rate announcement are insignificant.
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Table 3: Results of the effects of FED interest rate announcements on the VIX
This table shows the results of the regression analysis as specified in equation (2) for al sub-periods, each test is performed on a one-sided distribution. The sub-periods are constructed as presented in table 2. T indicates the day relative to the day of an interest rate announcement of the. S&P is the variable for the S&P 500-index, change is the variable for the absolute value of the interest rate change. In addition, increase is the dummy for an interest rate increase and decrease the dummy variable for an interest rate decrease. The p-values of the coefficients are shown below the coefficients ** is statistically significant at 99% level and * statistically significant at 95% level. Furthermore, the adjusted R2 is shown for each regression. BPG shown the p-value of the Breusch-Pagan-Godfrey test, JB shows the p-value of the Jarque-Bera test and BG the p-value of
the Breusch-Godfrey test.
(2)
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Table 4 shows the results of the regression analysis of the abnormal change in the level of the VDAX after an interest rate announcement of the ECB. The full sample indicates a significant (99%) abnormal change of -0.779 percentage-points in the level of the VDAX on the day of an interest rate announcement by the ECB. On the first day after the announcement the abnormal change in the level of VDAX is -0.822 percentage-points and is significant (99%). This indicates that the market expects the future 45-day volatility of the DAX to be lower on the two day that follow an interest rate announcement of the ECB. On the third day after an interest rate announcement in the full sample the effect is partly offset because the abnormal change in the level of the VDAX is positive and significant (99%).
In the first sub-period the announcement day and the two days that follow show that the abnormal change of the level of the VDAX is: -2.253, -1.441 and 1.469 percentage-points. All the coefficients are significant (99%). This indicates that the implied 45-day volatility of the DAX decreases on the day of, and the first day after, an interest rate announcement of the ECB. On the second day after the announcement the abnormal change in the level of the VDAX rises with an estimated 1.469 percentage-points.
The DAX coefficients indicate a significant (99%) negative correlation between the DAX and the VDAX during the announcement period of the ECB. A one per cent increase of the DAX causes an abnormal decrease ranging from 1.130 to 4.108 percentage-points of the VDAX. The coefficient for an interest rate increase is significant (95%) in the full sample: an interest rate increase of the ECB increases the abnormal change of the VDAX with 0.894 percentage-points. The adjusted R2 of the regressions indicate the model is a good fit. In addition, there is significant heteroscedasticity in the third and fifth sub-sample. There is significant (95%) indication the residuals of the regressions do not follow a normal distribution. In the first, fourth and fifth sub-period there is no significant autocorrelation, the other samples have significant (99%) autocorrelation in the residuals.
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Table 4: Results of the effects of ECB interest rate announcements on the VDAX
This table shows the results of the regression analysis as specified in equation (11) for al sub-periods, each test is performed on a one-sided distribution. The sub-periods are constructed as presented in table 2. T indicates the day relative to the day of an interest rate announcement of the ECB. DAX is the variable for the return of the DAX-index, change is the variable for the absolute value of the interest rate change. In addition, increase is the dummy for an interest rate increase and decrease the dummy variable for
an interest rate decrease. The p-values of the coefficients are shown below the coefficients ** is statistically significant at 99% level and * statistically significant at 95% level. Furthermore, the adjusted R2 is shown for each regression. BPG shown the p-value of the Breusch-Pagan-Godfrey test, JB shows the p-value of the Jarque-Bera test
and BG the p-value of the Breusch-Godfrey test.
(11)
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Table 5 shows the results for the regression for the effect of an interest rate announcement of the ECB on the abnormal change in the level of the VIX. In the full sample and the first and third sub-sample the abnormal change in the level of the VIX is significantly (99%) negative on the first day after an interest rate announcement of the ECB. It indicates that the implied volatility for the next 30 days is considered to be lower on the day after the announcement. On the second day after announcement the abnormal change in the level of the VIX is positive and larger than the decrease on the day before. This is observed in the full sample and the first and third sub-sample. It indicates that the loss in the 30-day implied volatility on day T+1 is over compensated by the increase of day T+2.
On the interest rate announcement day of the ECB, only the first sub-period shows a significant (99%) negative abnormal change in the level of the VIX with 1.538 percentage-points. On day T-3 both the full sample and the second, third and fifth sub-period indicate a significant (99%) positive abnormal change in the level of the VIX. Indicating that on the third day before an ECB interest rate announcement, the market implies the volatility of the return of the S&P will be higher in the coming 30 days.
The negative correlation between the VIX and the S&P in table 5 is also significant (99%) in all samples of the regressions. Again, it indicates that the return of the S&P during the announcement period is negatively correlated with the abnormal change in the level of the VIX. The dummy variable that captures the effect of an interest rate increase is significant (95%) in the full sample and the first sub-period. There is an indication that after an interest rate announcement of the ECB an interest rate increase adds 1.189 and 3.116 percentage-points to the abnormal change in the level of the VIX.
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Table 5: Results of the spillover effect of ECB interest rate announcements on VIX
This table shows the results of the regression analysis as specified in equation (23) for al sub-periods, each test is performed on a one-sided distribution. The sub-periods are constructed as presented in table 2. T indicates the day relative to the day of an interest rate announcement of the ECB. S&P is the variable for the return of the S&P
500-index, change is the variable for the absolute value of the interest rate change. In addition, increase is the dummy for an interest rate increase and decrease the dummy variable for an interest rate decrease. The p-values of the coefficients are shown below the coefficients ** is statistically significant at 99% level and * statistically significant at 95% level. Furthermore, the adjusted R2 is shown for each regression. BPG shown the p-value of the Breusch-Pagan-Godfrey test, JB shows the p-value of the Jarque-Bera
test and BG the p-value of the Breusch-Godfrey test.
(23)
26
Table 6 shows the regression for the reaction of the VDAX after an interest rate announcement of the FED. Day T in this table is the day after an interest rate announcement of the FED. Because the level of the VDAX is already published at the moment of the FED interest rate announcement at 08:00 PM central European time the days are shifted up one day. In the table the abnormal change in the level of the VDAX is significantly (99%) negative in the full sample and the first three sub-samples. This indicates that on average the level of the VDAX is decreasing on the day after an interest rate announcement of the FED. In the full sample and the first two sub-samples the abnormal change in the level of the VDAX is also significantly (95% and 99%) negative on the second day after an interest rate announcement of the FED. Combined, this means the level of the VDAX is decreasing on the first and second day after an interest rate announce of the FED these sub-periods, indicating the the implied 45-day volatility of the DAX is decreasing in these samples.
In the third sub-period the coefficients for the absolute value of the interest rate change and the interest rate change is significant (95%). The absolute value of the interest rate change coefficient suggests a 1% interest rate change coincides with a decrease in the abnormal change in the level of implied volatility of 4.783 percentage-points. Further, an interest rate increase is accompanied with a significant (95%) 1.284 percentage-point increase in the level of the VDAX. The relation between the DAX and the VDAX during the announcement period of the ECB is significant in all sub-periods (99%) in the announcement period of the FED.
The adjusted R2 indicates the model is a good fit besides the fourth sub-sample. There is significant (99%) heteroscedasticity in the full sample and the fourth sub-period, the p-value of the Breusch-Pagan-Godfrey test in the other sub samples does not reject homoscedasticity. The residuals of the regressions do not follow a normal distribution in the full sample and the last four sub periods. There is no significant autocorrelation in the residuals of six regressions.
27
Table 6: Results of the spillover effect of FED interest rate announcements on VDAX
This table shows the results of the regression analysis as specified in equation (24) for al sub-periods, each test is performed on a one-sided distribution. The sub-periods are constructed as presented in table 2. T indicates the day relative to the day after an interest rate announcement of the ECB. DAX is the variable for the return of the
DAX-index, change is the variable for the absolute value of the interest rate change. In addition, increase is the dummy for an interest rate increase and decrease the dummy variable for an interest rate decrease. The p-values of the coefficients are shown below the coefficients ** is statistically significant at 99% level and * statistically significant at 95% level. Furthermore, the adjusted R2 is shown for each regression. BPG shown the p-value of the Breusch-Pagan-Godfrey test, JB shows the p-value of the Jarque-Bera
test and BG the p-value of the Breusch-Godfrey test.
(24)
28
While the dummy variable for the days and the underlying index return have significant coefficients in some samples the variables that are concerned with the content is not. The variables are significant in four of the 24 regressions. Reduced models, originated from equations (2), (11), (23) and (24), are made to see if the regressions improve when the interest rate variables are excluded. The reduced regression equations are presented below:
, (25) , (26) , (27) . (28)
In line with the findings of the full model the tables indicate a negative change in the level of implied volatility after an interest rate announcement of the FED and the ECB. The reported relation between the level of the VIX and the VDAX and the corresponding underlying index in the full model is found in the reduced model as well. A comparison of the significant coefficients from table 3, 4, 5 and 6 and table 7, 8, 9 and 10 indicate no consistent difference. The overall fit of the regressions does marginally improve as the largest positive change in adjusted R2 is 0.019. It can be concluded the overall fit of the model does not improve with the exclusion of the interest rate variables.
Combined the full and reduced models indicate the reaction in the level of the VIX and the VDAX after an interest rate announcement is negative. Both models indicate a negative abnormal change in the level of implied volatility after interest rate announcements in the full sample. In addition, a negative correlation with the
29
Table 7: Results of the effects of FED interest rate announcements on VIX for all sub-periods without interest variables
This table shows the results of the regression analysis as specified in equation (25) for al samples, each test is performed on a one-sided distribution. The sub-periods are constructed as presented in table 2. T indicates the day relative to the day of an interest rate announcement of the FED. S&P is the variable for the S&P 500-index. The p-values of the coefficients are shown below the coefficients ** is statistically significant at 99% level and * statistically significant at 95% level. Furthermore, the adjusted R2
30
Table 8: Results of the effects of ECB interest rate announcements on the VDAX for all sub-periods without interest variables
This table shows the results of the regression analysis as specified in equation (26) for al samples, each test is performed on a one-sided distribution. The sub-periods are constructed as presented in table 2. T indicates the day relative to the day of an interest rate announcement of the ECB. DAX is the variable for the return of the DAX-index.
The p-values of the coefficients are shown below the coefficients ** is statistically significant at 99% level and * statistically significant at 95% level. Furthermore, the adjusted R2 is shown for each regression. BPG shown the p-value of the Breusch-Pagan-Godfrey test, JB shows the p-value of the Jarque-Bera test and BG the p-value of the
31
Table 9: Results of the spillover effect of ECB interest rate announcements on VIX for all sub-periods without interest variables
This table shows the results of the regression analysis as specified in equation (27) for al sub-periods, each test is performed on a one-sided distribution. The sub-periods are constructed as presented in table 2. T indicates the day relative to the day of an interest rate announcement of the ECB. S&P is the variable for the return of the S&P 500-index. The p-values of the coefficients are shown below the coefficients ** is statistically significant at 99% level and * statistically significant at 95% level. Furthermore, the
32
Table 10: Results of the spillover effect of FED interest rate announcements on VDAX for all sub-periods without interest variables
This table shows the results of the regression analysis as specified in equation (28) for al sub-periods, each test is performed on a one-sided distribution. The sub-periods are constructed as presented in table 2. T indicates the day relative to the day of an interest rate announcement of the ECB. DAX is the variable for the return of the DAX-index.
The p-values of the coefficients are shown below the coefficients ** is statistically significant at 99% level and * statistically significant at 95% level. Furthermore, the adjusted R2 is shown for each regression. BPG shown the p-value of the Breusch-Pagan-Godfrey test, JB shows the p-value of the Jarque-Bera test and BG the p-value of the
33 5.1 Robustness test
To indicate whether the main results of the regression analysis hold when another test is applied, the cumulative average residuals (CAR) methodology, as described in Brown and Warner (1980), is applied. The methodology uses the average residuals for a number of days around an event. In this research the number of days will be seven and the event will be the interest rate announcements of the FED and ECB. The residuals of the event days are divined as the abnormal change in the level of implied volatility (ACIV). The formulas to calculate the ACIV are (3) and (12).
, (3) . (12)
The CAR methodology is followed to calculate the cumulative average abnormal change in the level of implied volatility (CAACIV) and is calculated as:
, (29)
, (30)
where is the average abnormal change in the level of implied volatility on day in the announcement period of the VIX and the VDAX and is calculated as:
, (31)
, (32)
34
Table 11 shows the result of the CAACIV calculated in equation (29) and (30). Figure 2 presents a graphical representation of the CAACIV. The results of the VIX after an announcement of the FED indicate that before an interest rate announcement the CAACIV builds up. For the VDAX indicate a smaller elevation of the CAACIV in the three days before an interest rate announcement of the ECB. On the day of the interest rate announcement both indices show a decrease. This indicates that on average the abnormal change in the level of implied volatility is negative on the day of an interest rate announcement. In the three days after the interest rate announcement the CAACIV of the VIX and the VDAX are moving in an opposite direction and no pattern is observed. The results for the spillover effect indicate a similar reactions for the VIX and the VDAX around interest rate announcements on the other continent. Before the announcement of the FED the VDAX is elevated and decreases on the day after the announcement. The reaction of the VIX on the day of an interest rate announcement of the ECB is small. Interestingly, on day three after the interest rate announcements the CAACIV of both the VIX and the VDAX end at almost zero. The abnormal changes in implied volatility seem disappear after three days of an interest rate announcement. The results of this robustness test coincide with the results that are found in the main hypothesis. On the day of an interest rate announcement the level of the VIX and the VDAX lowers after an interest rate announcement of the FED and ECB.
Table 11: Results of the cumulative average abnormal change
Results of the cumulative average abnormal change in the level of implied volatility as specified in equation (31) and (32) in the announcement period of the interest rate announcements of the FED and
ECB. T indicates the day relative to an announcement day of the FED and ECB.
35
Figure 2: Graphical representation of the results of the CAACIV in table 11
This figure shows the results from table 11.
4. Conclusions
Option pricing and VAR theory assumes volatility to be constant, from the discussed literature it is clear this assumption does not hold in financial markets. On the days that surround news and macro-economic announcements past research (Donders and Vorst, 1996 and Füss et al., 2011) proves the level of implied volatility increases before an announcement and decreases sharply after. The objective of this research is to investigate how the VIX and the VDAX behave on the days around and interest rate announcement of the FED and ECB.
36
corresponding underlying indices is significantly negative. The variables that measure the effect of interest rate changes of the FED and ECB have no significant effect on the abnormal change in the level of the VIX and the VDAX.
In Füss et al. (2011) there is significant proof for a different reaction of the VIX and the VDAX after an announcement over time. The second investigation tests if the reaction of the VIX and the VDAX after an interest rate announcement is stable in constructed sub-periods from the full sample. In the sub-periods, where the reaction the VIX and the VDAX is significant, the magnitude of the reaction is differs compared to the full sample. This indicates there is support for the hypothesis that the reaction of the VIX and the VDAX after an interest rate announcement is not stable over time.
The third analysis tests if the decreasing effect of an interest rate announcement on the level of the VIX and the VDAX spills over between America and Europe. In full sample the effect is significant; there is an indication that the VDAX reacts stronger to an interest rate announcement of the FED compared to the reaction of the VIX after an announcement of the ECB. The data provides proof for the hypothesis that the implied volatility decreasing effect of an interest rate announcement spills over between America and Europe in the full sample.
When the control variables for interest rate changes are excluded from the regression the model does not improve. Indicating that the conclusions for the model are stable.
The robustness test indicates the conclusion drawn under the first and third hypotheses remains valid when applying the CAR methodology. Both the level of the VIX and the VDAX are decreasing on the day of an interest rate announcement of the FED and ECB. In addition the level of the VDAX is decreasing after an announcement of the FED. The reaction of the VIX after an announcement of the ECB is negligible. The main finding of this research is that over the last 14 years the level of the VIX and the VDAX are decreasing after an interest rate announcement of the FED and ECB.
37 4.1 Limitations and further research
A first limitation of this research is found in the used volatility indices. As discussed in the literature review, implied volatility is a proxy for the future returns of an underlying asset. An estimation error in these variables can cause a misleading indication of implied volatility. Deng et al. (2008) report about volatility smiles and skews, these effects can be present in the VIX and the VDAX as well. Both the
Chicago Board of Exchange and Deutsche Börse set criteria for the used option series. At some point in time the used option series for the calculations are replaced with option series with longer maturities. On this day the change in the level of the VIX and the VDAX can be biased due to the volatility term structure. Concluding, the VIX and the VDAX might not reflect the exact future volatility expected by the market. Because of this the indicated decrease in implied future return after an interest rate announcement might be inconsistent with reality.
Secondly, interest rate changes of the FED and ECB have no significant effect on the change in the level of the VIX and the VDAX in the majority of the samples. On the other hand, on the day of an interest rate announcement the VIX and the VDAX decrease significantly in some samples. It is remarkable that there is an indication of a negative change in the VIX and the VDAX after an interest rate announcement but it does not react differently when the interest rate is actually changed.
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