How important is the correlation between returns and volatility in a stochastic volatility model? Empirical evidence from pricing and hedging in the S&P 500 index options market

Abstract

Abstract This paper examines the importance of allowing for correlation between returns and volatility in a continuous time stochastic volatility option pricing model. Specifically it tests the closed-form stochastic volatility model of Heston (Review of Financial Studies 6, 1993, 327–343) that allows for non-zero correlation, in terms of pricing and hedging options on the S&P 500 index. It is found that non-zero correlation in the stochastic volatility model leads to significant improvements in mispricing of out-of-the-money options and overall pricing performance compared to if correlation is constrained to be zero. In terms of hedging, non-zero correlation results in significantly lower hedging errors for out-of-the-money options.