Approximating Stochastic Volatility by Recombinant Trees
A general method to construct recombinant tree approximations for stochastic volatility models is developed and applied to the Heston model for stock price dynamics. In this application, the resulting approximation is a four tuple Markov process. The first two components are related to the stock and volatility processes and take values in a two dimensional Binomial tree. The other two components of the Markov process are the increments of random walks with simple values in \{âˆ’1, +1\}. The resulting efficient option pricing equations are numerically implemented for general American and European options including the standard put and calls, barrier, lookback and Asian type pay-offs. The weak and extended weak convergences are also proved.