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A PDE based Implementation of the Hull&White Model for Cashflow Derivatives

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  • Sascha Meyer
  • Willi Schwarz

Abstract

A new implementation for the one-dimensional Hull&White model is developed. It is motivated by a geometrical approach to construct an invariant manifold for the future dynamics of forward zero coupon bond prices under a forward martingale measure. This reduces the option-pricing problem for cashflow derivatives to the solution of a series of heat equations. The heat equation is solved by a standard Crank-Nicolson scheme. The new method avoids the calibration used in traditional solution approaches. The computation of prices for European and Bermudan swaptions shows the convergence behavior of our new implementation. We also demonstrate the efficiency of our new approach resulting in a speed improvement by one order of magnitude compared to traditional trinomial tree implementations. Copyright Physica-Verlag 2003

Suggested Citation

  • Sascha Meyer & Willi Schwarz, 2003. "A PDE based Implementation of the Hull&White Model for Cashflow Derivatives," Computational Statistics, Springer, vol. 18(3), pages 417-434, September.
    • Handle: RePEc:spr:compst:v:18:y:2003:i:3:p:417-434
    DOI: 10.1007/BF03354607
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    References listed on IDEAS

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    1. Tomas Björk & Bent Jesper Christensen, 1999. "Interest Rate Dynamics and Consistent Forward Rate Curves," Mathematical Finance, Wiley Blackwell, vol. 9(4), pages 323-348, October.
    2. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
    3. Hull, John & White, Alan, 1990. "Pricing Interest-Rate-Derivative Securities," The Review of Financial Studies, Society for Financial Studies, vol. 3(4), pages 573-592.
    4. Alan Brace & Dariusz G¸atarek & Marek Musiela, 1997. "The Market Model of Interest Rate Dynamics," Mathematical Finance, Wiley Blackwell, vol. 7(2), pages 127-155, April.
    5. Vasicek, Oldrich Alfonso, 1977. "Abstract: An Equilibrium Characterization of the Term Structure," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 12(4), pages 627-627, November.
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