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

Carl Chiarella, Christina Nikitopoulos-Sklibosios () and Erik Schlogl

Applied Mathematical Finance, 2007, vol. 14, issue 5, 365-399

Abstract: This paper examines the pricing of interest rate derivatives when the interest rate dynamics experience infrequent jump shocks modelled as a Poisson process. The pricing framework adapted was developed by Chiarella and Nikitopoulos to provide an extension of the Heath, Jarrow and Morton model to jump-diffusions and achieves Markovian structures under certain volatility specifications. Fourier Transform 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, a novel perspective is provided on 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 (search for similar items in EconPapers)
Date: 2007
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DOI: 10.1080/13504860701255359

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