Path-Dependent Interest Rate Option Pricing with Jumps and Stochastic Intensities

Abstract

We derive numerical series representations for option prices on interest rate index for affine jump-diffusion models in a stochastic jump intensity framework with an adaptation of the Fourier-cosine series expansions method, focusing on the European vanilla derivatives. We give the price for nine different Ornstein-Uhlenbeck models enhanced with different jump size distributions. The option prices are accurately and efficiently approximated by solving the corresponding set ordinary differential equations and parsimoniously truncating the Fourier series.