Performances of Simple Option Models When Volatility Changes

In this study, the pricing performances of alternative simple option models are examined by creating a simulated market environment in which asset prices evolve according to a stochastic volatility process. To do this, option prices fully consistent with Heston[9]'s model are generated. Assuming this prices as market prices, the trading positions utilizing the Black-Scholes[4] model, a semi-parametric Corrado-Su[7] model and an ad-hoc modified Black-Scholes model are evaluated with respect to the true option prices obtained from Heston's stochastic volatility model. The simulation results suggest that both the Corrado-Su model and the modified Black-Scholes model perform well in this simulated world substantially reducing the biases of the Black-Scholes model arising from stochastic volatility. Surprisingly, however, the improvements of the modified Black-Scholes model over the Black-Scholes model are much higher than those of the Corrado-Su model.