A lattice based model for evaluating bonds and interest sensitive claims under stochastic volatility

We propose a flexible lattice model for pricing bonds and interest sensitive claims under stochastic volatility, which is able to accommodate different dynamics specifications, and permits correlation between the interest rate and volatility diffusion. The model is based on the forward shooting grid method where the volatility process, as the primary state variable, is discretized by means of a recombining binomial tree. Then, the interest rate, as the auxiliary state variable, is discretized by attaching a subset of representative realizations to each node of the volatility lattice to cover the range of possible interest rates at each time slice. Finally, we develop a bivariate lattice presenting four branches for each node, where the joint probabilities for the possible jumps embed the correlation. Since the model works on representative interest rate values, a linear interpolation technique is used when solving backward through the lattice to compute the bond present value or the interest sensitive claim price.