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Fast resolution of a single factor Heath-Jarrow-Morton model with stochastic volatility

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  • Eusebio Valero
  • Manuel Torrealba
  • Lucas Lacasa
  • Franc{c}ois Fraysse

Abstract

This paper considers the single factor Heath-Jarrow-Morton 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 discretization are performed using finite-difference and Crank-Nicholson 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.

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  • Eusebio Valero & Manuel Torrealba & Lucas Lacasa & Franc{c}ois Fraysse, 2011. "Fast resolution of a single factor Heath-Jarrow-Morton model with stochastic volatility," Papers 1108.1688, arXiv.org.
    • Handle: RePEc:arx:papers:1108.1688
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    References listed on IDEAS

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    5. David Heath & Robert Jarrow & Andrew Morton, 2008. "Bond Pricing And The Term Structure Of Interest Rates: A New Methodology For Contingent Claims Valuation," World Scientific Book Chapters, in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 13, pages 277-305, World Scientific Publishing Co. Pte. Ltd..
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