1. Implied Volatility Smirk and Future Stock Returns: Evidence from the German Market
Dr. Rakesh Gupta Senior Lecturer Finance/Financial Planning Department of Accounting, Finance and Economics Griffith Business School Griffith University Tel: 
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2. Outline 1.0 Background and Motivations 2.0 Gaps and Contributions
3.0 Theoretical Framework
4.0 Literature Review
5.0 Data and Methodology
6.0 Empirical Results
7.0 Conclusions
8.0 References
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3. Background &Motivation
What is implied volatility ?
Implied volatility (IV) refers to the value of the volatility of an underlying asset.
It is a reflection of expectation for future volatility based on actual option prices.
IV usually derived from Black-Scholes option pricing model
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4. Background & Motivation
Black-Scholes Model:
However, B-S model is just relied on only 5 different variables.
C/P= Price of the options
S= Price of underlying stock
K= Option strike price
T-t= Time to maturity
r= Risk free rate
δ= the volatility of returns of the underlying asset.
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5. Background & Motivation
Therefore, the B-S model can be represented by a simply equation called F. Fair value of an option A? Stock price:$67.5, Strike price: $70, expires at 38 days, Treasury bill: 0.01 δ ?
F(S, K, T, R,δ)= Option value
$1.10
δ = 24%
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6. Background & Motivation
What is volatility smile?
Volatility increases as the option becomes increasingly in-the-money or out-of-the-money
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7. Background & Motivation
In reality, the implied volatility changes with strike price and with time to maturity, when plotting the implied volatility against moneyness, implied volatilities present a heavily skewed smirk pattern. This implies that OTM put options are more expensive than the corresponding OTM call options.
IVS can be defined in several ways. The most commonly used definition is the implied volatility difference between OTM put options and ATM call options.
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8. Background & Motivation
OTM put options: capture negative information (Ball and Torous, 1985; Naik and Lee, 1990; Amin and Ng, 1993; Bakshi et al. 1997; Bates, 2000; Pan, 2002; Yan, 2011).
ATM call options: one of the most liquid options traded and generally reflects investors’ consensus about market uncertainty (Xing et al., 2009, Lubnau and Todorova, 2012)
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9. Background & Motivation
How does information become incorporated into stock prices?
Distinct characteristics of different markets, investors choose to trade in specific markets when new information comes.
Information is likely to be incorporated into prices in these markets first.
Increasing important role of derivative market
Rapid expansion of derivatives
Lower-cost, less restrict venue for trading
Efficient tool for hedging the downside risk
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10. Background & Motivation
Information linkage between the option and stock markets
The unidirectional link from the stock market to the option market <=perfect market assumption
Information asymmetry results in these two market adjusting information at different speeds
If informed traders can gain excess returns in the equity market, then option performances will no longer be exogenous of stock prices ( Easley et al., 1998).
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11. Background & Motivation
Informed investors trade in option markets mainly for two reasons:
Take advantage of the option leverage ( Black, 1975; Back, 1993)
Lower transaction cost and less short sell constraints in the option market compared to equity make, option trading become more attractive for informed traders (Back, 1993)
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12. Background & Motivation
The information asymmetry and the preference of option trading may result in
Option markets adjust new information more quickly than the equity market
lead-lag relation
Therefore, the option trading may convey information about the subsequent price changes in options as well as underlying assets.
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13. Background & Motivation
Most previous studies are focusing on option trading activities to investigate the relationship between the option and stock markets ( Easley et al., 1998; Pan and Poteshman, 2006)
However, the predictability and information content of implied volatility smirk for future stock returns are issues subject to only recent interest (Xing et al., 2009; Atilgan et al., 2010).
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14. Gaps & Contribution
Previous three studies investigate the relation between IVS and future stock returns based on U.S. market evidence
Only focus on the American type of option
The implied volatility information is observed from OptionMetrics
Utilize daily closing prices
The analyses are both before the global financial crisis (GFC)
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15. Gaps & Contribution This paper examines in the German market
European type options, use B-S model to calculate the implied volatility.
Covering a more recent period ( ) including GFC
Transactions of 30 minutes before market close in order to mitigate bid-ask spread effect.
Use intraday data, which allows more precise estimates
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16. Gaps & Contribution
Estimating the information spill-over from option index to the underlying market is of importance to both academics and practitioners. It will contribute to the literature that investigates the information linkage between the option and stock markets by providing evidence from the market outside the U.S market.
Shed light on the predictive power of the IVS for future stock returns in accordance with stock index level analysis.
Contributes to the debate on the information linkage between the option and stock markets
It will also contribute to the existing literature in the area of market efficiency in the German market.
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17. Theoretical Framework
Weak-form efficient market hypothesis (EMH)
The past information cannot predict future stock returns since it has been already incorporated into stock prices
This paper tries to approve that the information contents in option prices are valuable to forecast future stock returns.
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18. Literature Review Information linkage between stock and option markets
Evidence is mixed on debate for the lead-lag relationship between option and stock markets (Manaster and Rendleman, 1982; Vijh, 1988; Stephan and Whaley, 1990; Chan et al., 1993; Easley et al., 1998; Chan et al., 2002; Chakravarty et al., 2004; Pan and Poteshman, 2006).
The information asymmetry and preference of trading venue suggest that option trading may be first to reflect information. Hence, there is an information spill-over from option markets to stock markets.
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19. Literature Review Option IVS Why IVS matters the future stock returns?
The driving force of the IVS
IVS contains jump risk premium (Pan, 2002 and Xing et al. 2009)
Option prices are incorporated with jump risk premium and investor’ s aversion towards the negative jump is the driving force of volatility smirk
The jump premium is more likely to be an insurance paid by investors, who become more worried about an market crash during the extreme volatile period. Therefore, the jump risk premium is highly correlated with the market volatility.
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20. Literature Review 2) Demand-based option pricing model and IVS
High demand of OTM puts will lead the option contract makers to increase the option price (premium) to compensate the addition risk
High demand will result in a higher option price and the price effects will transmit into volatility patterns, which show a steeper IVS.
Bollen and Whaley (2004) advocate that a market marker is not willing to seel an unlimited number of one particular option contract. The volatility risk and hedging costs exposure will increase when the market maker’s position becomes larger and imbalanced. Consequently, the market maker will charge a higher price. Garleanu et al. (2009) also demonstrate that the demand-pressure will have an effect on option prices. The implied volatility is also highly dependent on the buying and selling action of investors.
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21. Literature Review Study 1: Xing et al. (2009)
Fama-MacBeth (FM) 1973 regression and long-short portfolio strategy are employed.
The findings show a significant negative relationship between the option IVS and future equity returns.
Firms with the steeper skews underperform with the firms with flatter skews.
The predictability will persist at least 6 months.
Both volatility skew (VSKEW) and historical skew (HSKEW) present weak predictability for future returns.
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22. Literature Review Cannot explain Support Study 2 Atilgan et al. (2009)
The negative relationship exists between IVS and expected S&P 500 index returns
Consider a set of macroeconomic vairbles
Two types of explanations:
1) Skewness Explanation:
a) physical Skewness
b) risk-neutral Skewness
2) Information Explanation:
a) earnings announcement periods
b) consumer sentiment variables
Cannot explain
Support
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23. Literature Review Study 3 Doran and Krieger (2010)
- Five distinct measurement to explain the summarise a subset of the information contained in IVS and its relationship with future returns.
- Trading simulation strategies are employed and find that the option-based measures of IVS have strong predictive power in forecasting the future direction of the underlying asset price.
Besides defining the IVS as the implied volatility difference between the OTM puts and the ATM calls ( known as ZZX in this study), Doran and Krieger (2010) also contains four other measurements of the IVS. They are above and minus below (AMB), the implied volatility difference between OTM calls and ATM calls (COMA), the implied volalitilty difference between OTM puts and ATM puts (POMA), and the implied volatility difference between ATM calls and ATM puts (CM).
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24. SKEWt=VOLtOTMP- VOLtATMC
Data and Methodology
Sample period:
Source: Karlsruher Kapitalmarktdatenbank
All transaction prices of the European index options on the DAX 30 from a window of 30 minutes before market closes.
IVS measurement
SKEWt=VOLtOTMP- VOLtATMC
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25. Data & Methodology OTM Puts are defined as:
Strike price to stock price ( )
ATM Calls are defined as:
Strike price to stock price ( )
To ensure options have enough liquidity, this paper only includes options with the time to maturity between 10 to 90 days.
Two approaches of calculating IVS:
1) High-Volume-Volatility-Smirk (HVVS)
2) Volume-Weighted-Volatility-Smirk (VWVS)
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26. Data & Methodology DAX 30 Index Returns
The daily closing price is established by obtaining the last observed price and is used logarithmic returns to calculate the DAX series.
Excess returns of the DAX 30 index = Daily DAX 30 index returns – daily one month Euribor rate.
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27. Data & Methodology Option Volume and Option Open Interest
Option open interest and volume data are obtained from the Datastream. The original data of option volume and change in open interest (call option open interest minus put option open interest) are classified into quintiles for each date. The number that represents each quintile (1 to 5) is treated as the specific control variables (1=low, 5=high).
Implied Volatility Indices
The square of the VDAX is employed to control the relationship between conditional volatility and conditional expected returns.
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28. Data and Methodology
1) Relationship between IVS and Excess DAX Index Returns
𝑅 𝑡+1 =𝛼+ 𝛽 1 ∗ 𝑉𝑊𝑉𝑆 𝑡 + 𝛽 2 ∗ 𝐸 𝑡 𝑉𝐴𝑅 𝑡+1 + 𝛽 3 ∗ 𝐿𝑅𝐸𝑇 𝑡 + 𝛽 4 ∗ 𝑂𝐼 𝑡 + 𝛽 5 ∗ 𝑉𝑂𝐿 𝑡 + 𝜀 𝑡+1 , (2)
𝑅 𝑡+1 =𝛼+ 𝛽 1 ∗ 𝐻𝑉𝑉𝑆 𝑡 + 𝛽 2 ∗ 𝐸 𝑡 𝑉𝐴𝑅 𝑡+1 + 𝛽 3 ∗ 𝐿𝑅𝐸𝑇 𝑡 + 𝛽 4 ∗ 𝑂𝐼 𝑡 + 𝛽 5 ∗ 𝑉𝑂𝐿 𝑡 + 𝜀 𝑡+1, (3)
2) The Global Financial Crisis Effect
𝑅 𝑡+1 =𝛼+ 𝛽 1 ∗ 𝑉𝑊𝑉𝑆 𝑡 + 𝛾 1 ∗𝐺𝐹𝐶+ 𝛾 2 ∗𝐺𝐹𝐶∗ 𝑉𝑊𝑉𝑆 𝑡 + 𝛽 2 ∗ 𝐸 𝑡 𝑉𝐴𝑅 𝑡+1 + 𝛽 3 ∗ 𝐿𝑅𝐸𝑇 𝑡 + 𝛽 4 ∗ 𝑂𝐼 𝑡 + 𝛽 5 ∗ 𝑉𝑂𝐿 𝑡 + 𝜀 𝑡 (5)
𝑅 𝑡+1 =𝛼+ 𝛽 1 ∗ 𝐻𝑉𝑉𝑆 𝑡 + 𝛾 1 ∗𝐺𝐹𝐶+ 𝛾 2 ∗𝐺𝐹𝐶∗ 𝐻𝑉𝑉𝑆 𝑡 + 𝛽 2 ∗ 𝐸 𝑡 𝑉𝐴𝑅 𝑡+1 + 𝛽 3 ∗ 𝐿𝑅𝐸𝑇 𝑡 + 𝛽 4 ∗ 𝑂𝐼 𝑡 + 𝛽 5 ∗ 𝑉𝑂𝐿 𝑡 + 𝜀 𝑡 (6)
Where Rt+1 is the excess return of the DAX 30 index at the time t+1, VWVSt and HVVSt are the IVS measurements at time t. Et[VARt+1] represents the expected conditional variance of the market portfolio (DAX 30 index) returns at time t. It is the square VDAX implied volatility index, named SQVDX. The LRETt denots the lagged excess return on the DAX 30 index. The OIt and VOLt capture the open interest and option volume effects on future index returns at time t. The variables that capture OI and VOL are presented in quintiles. The GFC is a dummy variable, which is the equal to one when the year is greater tha 2008, and zero otherwise. The GFC*VWVSt and GFC*HVVSt represent slope dummy variables, which are equal to the VWVSt and HVVSt respectively, when the GFC effect is equal to one and zero otherwise.
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29. Empirical Results Summary Statistics 29
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30. Empirical Results
Overall, none of the control variables consistently show a significant relationship with future market returns, in addition, both measures of volatility smirk show insignificant negative relationship with future index returns.
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31. Empirical Results
Panel A presents the regression results for the non-GFC period. In general both the VWVS and HVVS measures of IVS do not show any significant predictive power for future DAX 30 index returns.
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32. Panel B presents the regression results during the GFC period
Panel B presents the regression results during the GFC period. The coefficient estimates for both measures of IVS increased compared to the corresponding non-GFC period. VWVS measure of IVS shows a weak significant negative relationship with market index return except for the 40-day horizon. The market downturn heightened fair of market participants, this result in a weak statistical significance against market efficiency. However if cut off the results significance level to 5%, there is no significant results for VWVS, except for 20-day and 60-day horizons and the market efficiency holds.
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33. Table 5.4 presents the GFC effects on both DAX 30 index returns and the two measures of IVS (VWVS and HVVS). The results show that the GFC does not present any significant impact on DAX 30 index returns. The GFC does not have an effect on the two measures of IVS (VWVS and HVVS). Most of the coefficient estimates of GFC dummy on market returns are negative and insignificant. These insignificant results indicate that the GFC does not have a significant effect on index returns compared to the corresponding non-GFC sample period. Further, the slope dummies of the GFC also present negative and insignificant coefficient estimates, indicating the relationship between IVS measures and stock returns for the GFC period does not differ significantly from that for the non-GFC period.
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34. Robustness Check Using Options with Different Time to Maturity
Robustness Check has been conducted by using options with time to maturity between days. The results are similar to previous analysis in using option with 10 to 90 days of time to maturity, indicating that although the more liquid options are taken for the analysis, results are similar for all maturity range, and results can be generalised for all maturity.
Using Different Moneyness Range
ATM Calls are redefined as
OTM Puts are redefined as
Similar to the results of Table 5.2, both the VWVS and HVVS measures of volatility smirk present insignificant coefficient estimates for all time horizons, implying that with different definitions of moneyness range, the IVS remain statistically insignificant related to DAX 30 index returns over the sample period.
Using Equal Weighted Volatility Smirk
The equal-weighted measure of volatility smirk is employed for robust test. Table 5.5 presents the results.
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35. Robustness Check
𝑅 𝑡+1 =𝛼+ 𝛽 1 ∗ 𝐸𝑊𝑉𝑆 𝑡 + 𝛽 2 ∗ 𝐸 𝑡 𝑉𝐴𝑅 𝑡+1 + 𝛽 3 ∗ 𝐿𝑅𝐸𝑇 𝑡 + 𝛽 4 ∗ 𝑂𝐼 𝑡 + 𝛽 5 ∗ 𝑉𝑂𝐿 𝑡 + 𝜀 𝑡+1 , (4)
Where Rt+1 is the excess return of the DAX 30 index at the time t+1, EWVSt is the equal-weighted measure of the IVS at time t.
The EWVS measures of IVS does not represent a significant negative relationship with DAX 30 index returns over the sample period. These results are consistent with the results of previously used two measure of IVS, which also report insignificant coefficients.
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36. Conclusion
This paper investigated whether the shape of the IVS contains relevant information for future returns of the underlying stock market.
The analysis shows that IVS does not have a significant relationship with DAX 30 index returns after considering:
control variables
GFC dummies.
The results remain insignificant during the GFC period.
Results of the study are robust after consideration of different option maturities and using different moneyness ranges.
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37. Conclusion
This study contributes to existing literature by providing a comprehensive study of lead-lag relationship between option IVS and future index returns in the German market.
To the best of the author’s knowledge, this is the first empirical study that examines the relationship between European-style option IVS and future index returns.
The results confirm the conclusion made by previous studies, which state that the German market is a relatively efficient market, in a sense that information is adjusted into stock prices efficiently once it is available.
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38. Conclusion
The information content in option IVS cannot forecast expected market returns.
Our results contradict previous studies based on the U.S. market data, which show that the IVS has strong predictive power for future stock returns. The discrepancy may be due to the frequency of the data, the distinct techniques of calculating implied volatility, or the various investor preferences in different markets.
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39. Conclusion Limitations of this study arises from the data sample:
analysis could be enhanced if the data for macro factors was available with a higher frequency.
The GFC period for this study is considered over a period of two years based on the existing studies. But it may have extended over a period longer than the two year period considered in the study.
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40. References
Amin, K.I., and Ng, V.K. (1993), “ Option valuation with systematic stochastic volatility”, The Journal of Finance, Vol. 48 No. 3, pp
Atilgan, Y., Bali, T., and Demirtas, K. O. (2010), “Implied volatility spreads, skewness and expected market returns,” Working Paper [ ], Georgetown McDonough School of Business, Georgetown University, Washington, 14 July.
Back, K. (1993), “Asymmetric information and options,” Review of Financial Studies, Vol. 6 No. 3, pp
Bakshi, G., Cao, C., and Chen, Z. (1997), “Empirical performance of alternative option pricing models,” The Journal of Finance, Vol. 52 No. 5, pp
Ball, C.A., and Torous, W.N. (1985), “On jumps in common stock prices and their impact on call option pricing,” The Journal of Finance, Vol. 40 No. 1, pp
Bates, D.S. (2000), “Post-'87 crash fears in the S&P 500 futures option market,” Journal of Econometrics, Vol. 94 No. 1-2, pp
Black, F. (1975), “Fact and fantasy in the use of options,” Financial Analysts Journal, Vol. 31 No. 4, pp
Bollen, N.P., and Whaley, R.E. (2004), “Does net buying pressure affect the shape of implied volatility functions?” The Journal of Finance, Vol. 59 No. 2, pp
Chakravarty, S., Gulen, H., and Mayhew, S. (2004), “Informed trading in stock and option markets,” The Journal of Finance, Vol. 59 No. 3, pp
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41. References Cont’d
Chan, K., Chung, Y.P., and Fong, W.M. (2002), “The informational role of stock and option volume,” Review of Financial Studies, Vol. 15 No. 4, pp
Chan, K., Chung, Y.P., and Johnson, H. (1993), “Why option prices lag stock prices: A trading‐based explanation,” The Journal of Finance, Vol. 48 No. 5, pp
Doran, J., and Krieger, K. (2010), “Implications for asset returns in the implied volatility skew,” Financial Analysts Journal, Vol. 66 No. 1, pp
Easley, D., O'Hara, M., and Srinivas, P.S. (1998), “Option volume and stock prices: evidence on where informed traders trade,” The Journal of Finance, Vol.53 No.2, pp
Garleanu, N., Pedersen, L.H., and Poteshman, A.M. (2009), “Demand-based option pricing,” Review of Financial Studies, Vol. 22 No. 10, pp
Lubnau, T.M., and Todorova, N. (2012), “Technical trading with open interest: evidence from the German market,” Applied Financial Economics, Vol. 22 No. 10, pp
Manaster, S., and Rendleman, R.J. (1982), “Option prices as predictors of equilibrium stock prices,” The Journal of Finance, Vol. 37 No. 4, pp
Naik, V., and Lee, M. (1990), “General equilibrium pricing of options on the market portfolio with discontinuous returns,” Review of Financial Studies, Vol. 3 No. 4, pp
Page, S., and Taborsky, M. A. (2011), “The myth of diversification: risk factors vs. asset classes,” Journal of Portfolio Management, Vol. 37 No. 4, pp. 1-2.
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42. References Cont’d
Pan, J. (2002), “The jump-risk premia implicit in options: Evidence from an integrated time-series study,” Journal of Financial Economics, Vol. 63 No.1, pp
Pan, J., and Poteshman, A.M. (2006), “The information in option volume for future stock prices,” The Review of Financial Studies, Vol. 19 No.3, pp
Stephan, J.A., and Whaley, R.E. (1990), “Intraday price change and trading volume relations in the stock and stock option markets,” The Journal of Finance, Vol. 45 No. 1, pp
Vijh, A.M. (1988), “Potential biases from using only trade prices of related securities on different exchanges: A comment,” The Journal of Finance, Vol. 43 No. 4, pp
Xing, Y., Zhang, X., and Zhao, R. (2009), “What does the individual option volatility smirk tell us about future equity returns?” Journal of Financial and Quantitative Analysis, Vol. 45 No. 3, pp
Yan, S. (2011), “Jump risk, stock returns, and slope of implied volatility smile,” Journal of Financial Economics, Vol. 99 No. 1, pp
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