Volatility and Expected Option Returns

Guanglian Hu, Kris Jacobs
2015 Social Science Research Network  
We provide a theoretical and empirical analysis of the relationship between expected option returns and the volatility of the underlying securities. We show analytically that in a Black-Scholes framework, the expected return from holding a call option is a decreasing function of the volatility of the underlying. The expected return from holding a put option is an increasing function of the volatility of the underlying. These predictions are strongly supported by the data. In the cross-section
more » ... stock option returns, returns on call (put) option portfolios decrease (increase) with underlying stock volatility. This strong negative (positive) relation between call (put) option returns and volatility is not due to cross-sectional variation in expected stock returns. It holds in various option samples with di¤erent maturities and moneyness, and it is robust to alternative measures of underlying volatility and di¤erent weighting methods. Time-series evidence also supports the predictions from option pricing theory. Future returns on S&P 500 index call (put) options are negatively (positively) related to S&P 500 index volatility. JEL Classi...cation: G12
doi:10.2139/ssrn.2695569 fatcat:iqrunwrtm5fwvbiucdiyb4bbyy