An Arbitrage-free Two-factor Model of the Term Structure of Interest Rates: A Multivariate Binomial Approach
AbstractWe build a no-arbitrage model of the term structure, using two stochastic factors on each date, the short-term interest rate and the forward premium. The model is essentially an extension to two factors of the lognormal interest rate model of Black-Karazinski. It allows for mean reversion in the short rate and in the forward premium. The method is computationally efficient for several reasons. First, interest rates are defined on a bankers' discount basis, as linear functions of zero-coupon bond prices, enabling us to use the no-arbitrage condition to compute bond prices without resorting to cumbersome iterative methods. Second, the multivariate-binomial methodology of Ho-Stapleton-Subrahmanyam is extended so that a multi-period tree of rates with the no-arbitrage property can be constructed using analytical methods. The method uses a recombining two-dimensional binomial lattice of interest rates that minimizes the number of states and term structures. Third, the problem of computing a large number of term structures is simplified by using a limited number of bucket rates in each term structure scenario. In addition to these computational advantages, a key feature of the model is that it is consistent with the observed term structure of volatilities implied by the prices of interest rate caps and floors. We illustrate the use of the model by pricing American-style and Bermudan-style options on interest rates. Option prices for realistic examples using forty time periods are shown to be computable in seconds.
Download InfoTo our knowledge, this item is not available for download. To find whether it is available, there are three options:
1. Check below under "Related research" whether another version of this item is available online.
2. Check on the provider's web page whether it is in fact available.
3. Perform a search for a similarly titled item that would be available.
Bibliographic InfoPaper provided by New York University, Leonard N. Stern School of Business- in its series New York University, Leonard N. Stern School Finance Department Working Paper Seires with number 98-070.
Date of creation: 05 May 1998
Date of revision:
Contact details of provider:
Postal: U.S.A.; New York University, Leonard N. Stern School of Business, Department of Economics . 44 West 4th Street. New York, New York 10012-1126
Phone: (212) 998-0100
Web page: http://w4.stern.nyu.edu/finance/
More information through EDIRC
You can help add them by filling out this form.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Thomas Krichel).
If references are entirely missing, you can add them using this form.