The impact of the leverage effect on the implied volatility smile: evidence for the German option market
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The impact of the leverage effect on the implied volatility smile: evidence for the German option market A. W. Rathgeber1 · J. Stadler1 · S. Stöckl2
© The Author(s) 2020
Abstract It is a widely known theoretical derivation, that the firm’s leverage is negatively related to volatility of stock returns, although the empirical evidence is still outstanding. To empirically evaluate the leverage we first complement previous simulation studies by deriving theoretical predictions of leverage changes on the volatility smile. Even more important, we empirically test these predictions with an event study using intra-day Eurex option data and a unique data set of 138 ad-hoc news. For our theoretically derived predictions we observe that changes in leverage of DAX companies from 1999 to 2014 cause significant changes to the implied volatility smile. Keywords Implied volatilty smile · Leverage effect · Event study · Tick data Mathematics Subject Classification C13 · G32 · G14
1 Introduction The fact that changes in leverage lead to changes in volatility of stock returns is even before the publication of Modigliani Millers seminal paper a well-known phenomenon. The main idea behind the theory of this phenomenon is that a firm holds assets and issues equity. The equity holders claim the residual, of which riskiness positively depends on the leverage. Due to option’s implied volatility being linked to realized stock volatility, the implied volatility should also depend on the leverage as a ratio
The authors would like to thank Henning J. Fock for his previous work, for the very helpful advice and discussions on this topic. Furthermore, we thank Deutsche Gesellschaft für Ad-hoc-Publizität mbH for providing us with the ad-hoc news from 1999 to 2014.
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A. W. Rathgeber [email protected]
1
Institute for Materials Resource Management, University of Augsburg, Universitätsstrasse 12, 86159 Augsburg, Germany
2
IDEA Beratungs- und Forschungsgesellschaft UG (haftungsbeschränkt), Herbststrasse 2d, 86456 Gablingen, Germany
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of market value of debt and equity. Hence, increases in stock prices yield in lower leverages accompanied by lower volatilities and vice versa. Black (1976) was the first to show empirically a negative correlation between stock price returns and the volatility of stock returns, whereas Christie (1982) was the first who termed this observation leverage effect. However, Black (1976) also gave an alternative explanation on correlation between stock returns and volatility which he called the volatility feedback hypothesis. According to him as well as Pindyck (1984), French et al. (1987), Campbell and Hentschel (1992), or Bekaert and Wu (2000) the volatility feedback hypothesis explains the increase in volatility after some unexpected bad news regarding markets or a particular company. The resulting feedback leads to fluctuating stock prices and induces by statistical definition a higher standard deviation of the stock prices. Due to volatility persistence, investors re
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