Fast resolution of a single factor HeathJarrowMorton model with stochastic volatility

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Abstract

This paper considers the single factor HeathJarrowMorton model for the interest rate curve with stochastic volatility. Its natural formulation, described in terms of stochastic differential equations, is solved through Monte Carlo simulations, that usually involve rather large computation time, inefficient from a practical (financial) perspective. This model turns to be Markovian in three dimensions and therefore it can be mapped into a 3D partial differential equations problem. We propose an optimized numerical method to solve the 3D PDE model in both low computation time and reasonable accuracy, a fundamental criterion for practical purposes. The spatial and temporal discretizations are performed using finite-difference and CrankNicholson schemes respectively, and the computational efficiency is largely increased performing a scale analysis and using Alternating Direction Implicit schemes. Several numerical considerations such as convergence criteria or computation time are analyzed and discussed. © 2011 Elsevier B.V. All rights reserved.

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Valero, E., Torrealba, M., Lacasa, L., & Fraysse, F. (2011). Fast resolution of a single factor HeathJarrowMorton model with stochastic volatility. Journal of Computational and Applied Mathematics, 236(6), 1637–1655. https://doi.org/10.1016/j.cam.2011.09.027

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