Discount-Bond Derivatives on a Recombining Binomial Tree
AbstractInterest-rate derivative models governed by parabolic partial differential equations (PDEs) are studied with discrete-time recombining binomial trees. For the Buehler-Kaesler discount-bond model, the expiration value of the bond is a limit point of tree sites. Representative calculations give a close approximation to the continuum results. Next, situations are considered in which spatial inhomogeneity of the drift velocity can cause binomial jump probabilities to become negative. When the continuous-time boundary conditions are applied near the tree points at which this occurs, good agreement is obtained with Hull and White's explicit-finite-difference treatment of the Cox- Ingersoll-Ross model. Finally, to mimic the effect of a drift-velocity divergence which prevents interest rates from becoming negative, Neumann boundary conditions are applied in the Vasicek model. Discrete-time computations are performed for a mean-reverting situation and for a case with constant negative short-rate drift; the ensuing bond values have nonnegative interest rates and forward rates. The results are compared with the Vasicek solution and with the leading term in a spectral expansion.
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Bibliographic InfoPaper provided by EconWPA in its series Finance with number 9702003.
Length: 12 pages
Date of creation: 18 Feb 1997
Date of revision: 31 Jul 1997
Note: Type of Document - LaTeX 2.09 (SBTex); prepared on IBM PC ; to print on PostScript; pages: 12 ; figures: One LaTeX figure
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discount bonds; debt options; option pricing; binomial trees;
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