Pricing Options on Traded Assets Under Stochastic Interest Rates and Volatility : A Binomial Approach

A number of papers have investigated the pricing of options on traded assets when the interest rate or the volatility of the underlying is assumed to be stochastic. This article extends the work by using the binomial technology to price options where it is assumed that, in addition to the underlying, both interest rates and volatility may be stochastic. We use the transformations of Nelson and Ramaswamy (1990) and Hilliard and Schwartz (1996) to obtain a set of three diffusions with unit volatility. Thus, the tree recombines in a simple binomial pattern for each of the state variables so that each node branches to a set of eight nodes. Joint probabilities, possibly depending on pairwise correlations, are given for each of the possible jumps. Numerical methods for computing the *Greeks* are also developed