Hedging & Pricing of Options using least squares through simulation: Application to the Black-Scholes and the Heston Models

The enormous growth of derivatives markets necessitates the pricing and hedging of derivative contracts accurately and efficiently. This work extends the pricing approach introduced by Longstaff and Schwartz to a stochastic volatility model, namely the Heston Model. The method employed is also used to compute the Option Greeks extending the approach of the paper Hedging using simulation: a least squares approach by Tebaldi. A number of options are considered ranging from plain vanilla to exotics such as Power put and Binary (Asset-or-Nothing) put options in the Black-Scholes model. Finally the methodology is applied to the Heston Model wherein a plain vanilla European call is priced and hedged and the plain vanilla American put option is priced. The price as well as Option Greeks are compared against well-known procedures used in the industry today. Researchers as well as academicians concerned with hedging of derivative contracts would find this work useful.