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Multifactor Generalization of "Discount-Bond Derivatives on a Recombining Binomial Tree"


  • J. Chalupa


The security dynamics described by the Black-Scholes equation with price-dependent variance can be approximated as a damped discrete-time hopping process on a recombining binomial tree. In a previous working paper, such a nonuniform tree was explicitly constructed in terms of the continuous-time variance. The present note outlines how the previous procedure could be extended to multifactor Black-Scholes with price- and time-dependent coefficients. The basic idea is to derive new coordinates which give a Black-Scholes equation with all the "sigmas" equal to unity. In the discrete-time tree coresponding to this equation, nodes are uniformly spaced and the hopping probabilities are not constant. When the new coordinates are mapped back onto prices, the ensuing tree is nonuniform. A derivative can be valued with the new coordinates or the original prices.

Suggested Citation

  • J. Chalupa, 1997. "Multifactor Generalization of "Discount-Bond Derivatives on a Recombining Binomial Tree"," Finance 9706001, EconWPA.
  • Handle: RePEc:wpa:wuwpfi:9706001
    Note: Type of Document - LaTeX; prepared on IBM PC ; pages: 5 ; figures: None

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    More about this item


    option pricing; multinomial trees; multifactor models;

    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing


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