Multifactor Generalization of "Discount-Bond Derivatives on a Recombining Binomial Tree"
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.
|Date of creation:||02 Jun 1997|
|Date of revision:|
|Note:||Type of Document - LaTeX; prepared on IBM PC ; pages: 5 ; figures: None|
|Contact details of provider:|| Web page: http://econwpa.repec.org|
When requesting a correction, please mention this item's handle: RePEc:wpa:wuwpfi:9706001. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (EconWPA)
If references are entirely missing, you can add them using this form.