Stock Index Options Pricing Models

The purpose of this research is to apply stochastic modeling methods to determine the prices of stock index options. In this paper, three models are implemented and compared for accuracy based on the S&P 500 index (SPX) options data for 1996. These models include the Black-Scholes Model (BS), a stochastic volatility model (SV) which accounts for volatility in the underlying stock price, and a stochastic volatility model with jump in the underlying stock price (SVJ). This jump in the stock index prices is accounted for in the SVJ model using a compound Poisson distribution. The SV model is nested in the SVJ model, with jump-related parameters being set to zero. These three mathematical models are implemented in MATLAB. The models are calibrated using data from one day at a time for the SPX options on the Chicago Board Options Exchange based on the criteria of the least sum of squared errors. The models are tested for consistency by calibrating and measuring the squared error for each day in an entire year\u27s worth of option price data