Pricing and Hedging with Volatility Skew
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In this study, the pricing and hedging performances of the Black-Scholes model and the volatility skew method is examined in the presence of stochastic volatility. To show this stock prices consistent with the Heston’s (1993) stochastic volatility model are generated. Our choice of the Heston (1993) model of stochastic volatility stems from the fact that it provides a closed-form formula necessary in Monte Carlo simulation experiments. The preliminary empirical study utilizing Rubinstein’s data (1994) reveals that the stochastic volatility model and volatility skew method substantially reduces in-sample pricing errors of the Black-Scholes model. Our simulation results also confirms that the volatility skew method can effectively reduce the pricing errors of the Black-Scholes model caused by stochastic volatility. However, in terms of hedging performance, we do not find any significant difference between the Black-Scholes model and the volatility skew method.
Abstract
In this study, the pricing and hedging performances of the Black-Scholes model and the volatility skew method is examined in the presence of stochastic volatility. To show this stock prices consistent with the Heston’s (1993) stochastic volatility model are generated. Our choice of the Heston (1993) model of stochastic volatility stems from the fact that it provides a closed-form formula necessary in Monte Carlo simulation experiments. The preliminary empirical study utilizing Rubinstein’s data (1994) reveals that the stochastic volatility model and volatility skew method substantially reduces in-sample pricing errors of the Black-Scholes model. Our simulation results also confirms that the volatility skew method can effectively reduce the pricing errors of the Black-Scholes model caused by stochastic volatility. However, in terms of hedging performance, we do not find any significant difference between the Black-Scholes model and the volatility skew method.
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