The Quantitative Assessment of the Model Risk of Option Pricing Models When Volatility is Stochastic

Abstract

Using Monte Carlo simulation experiments, we examine the model risk of writing call option contracts when the underlying process driving security prices is characterized by stochastic volatility and trading occurs discretely. Simulations in this study reveal that discrete rebalacing risk is the main risk factor of total model risk while model misspecification risk and parameter estimation risk are relatively unimportant when single instrument hedge is utilized. These simulation results suggest that hedging based on the misspecified Black-Scholes model yields the hedging performance as good as that of the fully sprecified stochastic volatility model even when the true process driving security price movement is characterized by stochastic volatility. Hedging based on the Black-Scholes model is the simplest to implement. This may explain why the Black-Scholes formula is one of the best choices of option professionals even though it is widely accepted that the constant volatility assumption of the Black-Scholes model is violated in real world financial market. The results of this paper also suggest that for risk managers of financial institutions, the Black-Scholes option formular can be used as a viable risk management tool even under the financial markets characterized by stochastic volatilities.