Jacobi stochastic volatility factor for the LIBOR market model

We propose a new method to efficiently price swap rate derivatives under the LIBOR market model with stochastic volatility and displaced diffusion. This applies series expansion techniques built around Gaussian (Gram–Charlier) or mixture densities polynomial processes. The standard pricing for considered relies on dynamics freezing recover Heston-type which analytical formulas are available. approach is time-consuming, efficient approximations based Gram–Charlier expansions have been proposed recently. In this article, we first discuss fact that class of model, including Heston one, classical sufficient condition ensuring convergence not satisfied. Then an approximating Jacobi process can prove stability Gram–Charlier-type expansions. For approximation, able strong towards original model; moreover, give estimate rate. also result when factor bounded from below. finally illustrate our results numerical examples.