American option pricing under stochastic volatility: Empirical evaluations

Over the past few years, model complexity in quantitative finance has increased substantially in response to earlier models that did not capture critical events for risk management. However, it is still not clear that the increased complexity is matched by additional accuracy in the ultimate result.;We studied the empirical performance of a stochastic volatility model that has gained wide acceptance among both practitioners and academics. Specifically its focus is on pricing and hedging of American options using Heston's model, which is compared against the benchmark constant volatility model of Black and Scholes. The stochastic volatility model is calibrated with data on S&P 100 Index European style options using two-step procedure based on indirect inference and non-linear least squares. This approach provides the advantage of incorporating information from both equity and options market.;The calibrated model is then used to price American style options through a modification of the least-squares Monte-Carlo (LSM) algorithm of Longstaff and Schwartz to account for stochastic volatility. The performance of this model is then assessed by comparing it against the constant volatility model of Black and Scholes on the basis of pricing and hedging errors.;Empirical results from the study support the need for stochastic models. However, the resulting pricing and hedging process procedures are time consuming. Thus an approximation method is also developed in the dissertation that considerably reduces the computation time without compromising the accuracy of result and retaining the randomness of volatility in the modeling of asset process.;The approximate method to price American options makes use of the fact that accurate pricing of these options does not require exact determination of the early exercise boundary. Thus, the procedure mixes the two models of constant and stochastic volatility. The idea is to obtain early exercise boundary through constant volatility model using the approximation methods of AitSahlia and Lai or Ju and then utilize this boundary to price the options under stochastic volatility models. The data on S&P 100 Index American options is used to analyze the pricing performance of the mixing of the two models. The performance is studied with respect to percentage pricing error and absolute pricing errors for each money-ness maturity group.