A Control Variate Method for Monte Carlo Simulations of Heath-Jarrow-Morton Models with Jumps

Abstract

This paper examines the pricing of interest rate derivatives when the interest rate dynamics experience infrequent jump shocks modelled as a Poisson process and within the Markovian HJM framework developed in Chiarella & Nikitopoulos (2003). Closed form solutions for the price of a bond option under deterministic volatility specifications are derived and a control variate numerical method is developed under a more general state dependent volatility structure, a case in which closed form solutions are generally not possible. In doing so, we provide a novel perspective on the control variate methods by going outside a given complex model to a simpler more tractable setting to provide the control variates.

Keywords: HJM model, jump process, bond option prices, control variate, Monte Carlo simulations

JEL Classification: E43, G33, G13