implied volatility smirk and future stock returns: evidence from the german market dr. rakesh gupta...

Department of Accounting, Finance and Economics

Implied Volatility Smirk and Future Stock Returns:

Evidence from the German Market

Dr. Rakesh GuptaSenior Lecturer Finance/Financial PlanningDepartment of Accounting, Finance and EconomicsGriffith Business SchoolGriffith UniversityTel: +61 7 3735 7593Email: [email protected]

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tel:+61%207%203735%207593

mailto:[email protected]


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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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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Background & Motivation

• 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.

• Black-Scholes Model:

• However, B-S model is just relied on only 5 different variables.

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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%



Volatility increases as the option becomes increasingly in-the-money or out-of-the-money

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• What is volatility smile?

Department of Accounting, Finance and Economics 6


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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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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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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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).




Informed investors trade in option markets mainly for two reasons:

1) Take advantage of the option leverage ( Black, 1975; Back, 1993)

2) 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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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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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).


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)


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 (2000-2009) 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


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.


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.



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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Literature Review Option IVS Why IVS matters the future stock returns?

1) 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

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Literature Review2) 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.

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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.


Literature Review 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

• Support

• Cannot explain

Department of Accounting, Finance and Economics22


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.

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Data and Methodology Sample period: 2000-2009 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- VOLt

ATMC

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Data & Methodology OTM Puts are defined as:

Strike price to stock price (0.8-0.95) ATM Calls are defined as:

Strike price to stock price (0.95-1.05)

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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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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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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Data and Methodology 1) Relationship between IVS and Excess DAX Index Returns (2)

(3)

2) The Global Financial Crisis Effect (5)

(6)

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Empirical Results Summary Statistics

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Empirical Results

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Empirical Results

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Robustness Check Using Options with Different Time to Maturity Robustness Check has been conducted by using options with time to maturity between 10-60 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 RangeATM Calls are redefined as 0.97-1.03

OTM Puts are redefined as 0.85-0.97

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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Robustness Check

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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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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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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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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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References Amin, K.I., and Ng, V.K. (1993), “ Option valuation with systematic stochastic volatility”,

The Journal of Finance, Vol. 48 No. 3, pp. 881-910. Atilgan, Y., Bali, T., and Demirtas, K. O. (2010), “Implied volatility spreads, skewness

and expected market returns,” Working Paper [1511970], 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. 435-472.

Bakshi, G., Cao, C., and Chen, Z. (1997), “Empirical performance of alternative option pricing models,” The Journal of Finance, Vol. 52 No. 5, pp. 2003-2049.

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. 155-173.

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. 181-238.

Black, F. (1975), “Fact and fantasy in the use of options,” Financial Analysts Journal, Vol. 31 No. 4, pp. 36-72.

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. 711-753.

Chakravarty, S., Gulen, H., and Mayhew, S. (2004), “Informed trading in stock and option markets,” The Journal of Finance, Vol. 59 No. 3, pp. 1235-1258.

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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. 1049-1075.

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. 1957-1967.

Doran, J., and Krieger, K. (2010), “Implications for asset returns in the implied volatility skew,” Financial Analysts Journal, Vol. 66 No. 1, pp. 65-76.

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. 431-465.

Garleanu, N., Pedersen, L.H., and Poteshman, A.M. (2009), “Demand-based option pricing,” Review of Financial Studies, Vol. 22 No. 10, pp. 4259-4299.

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. 791-809.

Manaster, S., and Rendleman, R.J. (1982), “Option prices as predictors of equilibrium stock prices,” The Journal of Finance, Vol. 37 No. 4, pp. 1043-1057.

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. 493-521.

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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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. 3-50. 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. 871-908. 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.191-220.

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. 1049-1055.

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. 641-662.

Yan, S. (2011), “Jump risk, stock returns, and slope of implied volatility smile,” Journal of Financial Economics, Vol. 99 No. 1, pp. 216-233.

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implied volatility smirk and future stock returns: evidence from the german market dr. rakesh gupta...

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