Pricing American Interest Rate Options Under the Jump-Extended Vasicek Model

Abstract

This paper shows how to price American interest rate options under the exponential jumps-extended Vasicek model, or the Vasicek-EJ model. We modify the Gaussian jump-diffusion tree of Amin [1993] and apply to the exponential jumps-based short rate process under the Vasicek-EJ model. The tree is truncated at both ends to allow fast computation of option prices. We also consider the time-inhomogeneous version of this model, denoted as the Vasicek-EJ model that allows exact calibration to the initially observable bond prices. We provide an analytical solution to the deterministic shift term used for calibrating the short rate process to the initially observable bond prices, and show how to generate the jump-diffusion tree for the Vasicek-EJ model. Our simulations show fast convergence of European option prices obtained using the jump-diffusion tree, to those obtained using the Fourier inversion method for options on zero-coupon bonds (or caplets), and the cumulant expansion method for options on coupon bonds (or swaptions).