A binomial option pricing model under stochastic volatility and jump

Numerous papers have investigated the pricing of options on traded assets when either the underlying asset follows a jump diffusion process or the volatility of the underlying asset is assumed to be stochastic. This paper extends the literature by combining the transformation technique of Hilliard and Schwartz (1996) and the discrete-time jump diffusion model of Amin (1993) to develop a simple tree. The advantage of this approach is that it can easily value American options under a stochastic volatility and jump environment. We investigate how stochastic volatility and jump parameters affect the option values. From the simulation results, we find that the jump parameters significantly affect the American and European option values, especially for the near at-the-money options. We also demonstrate that our model can capture the volatility smile observed in the market.