Pricing S&P 500 index options with Heston´s model

This paper studies the price of S&P 500 index options by using Heston´s (1993) stochastic volatility option pricing model. The Heston model is calibrated by a two-step estimation procedure to incorporate both the information from time-series asset return and the information from cross-sectional option data. We find that both the Black-Scholes model and the Heston model overprice the out-of-the-money option and under price the in-the-money options, but the degree of the bias is different. The Heston model significantly outperforms the Black-Scholes model in almost all moneyness-maturity group. On average, the Heston model can reduce pricing errors by about 25%. However, pricing bias still exists in the Heston model, In particular, the Heston model always overprices short-term options, indicating that some other factors, such as the random jump, may also be needed to explain the option price.