An Arbitrage-Free Two-Factor Model of the Term Structure of Interest Rates: A Multivariate Binomial Approach

Posted: 15 Oct 1998

See all articles by Sandra Peterson

Sandra Peterson

affiliation not provided to SSRN

Richard C. Stapleton

University of Strathclyde - Department of Accounting and Finance

Marti G. Subrahmanyam

New York University (NYU) - Leonard N. Stern School of Business

Multiple version iconThere are 2 versions of this paper

Date Written: April 1998

Abstract

We build a no-arbitrage model of the term structure, using two stochastic factors on each date, the short-term interest rate and the premium of the forward rate over the short-term interest rate. The model can be regarded as 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 iterative methods. Second, the multivariate- binomial methodology of Ho-Stapleton-Subrahmanyam is extended so that a multiperiod 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 over time. 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.

JEL Classification: G10, G12, G13

Suggested Citation

Peterson, Sandra and Stapleton, Richard C. and Subrahmanyam, Marti G., An Arbitrage-Free Two-Factor Model of the Term Structure of Interest Rates: A Multivariate Binomial Approach (April 1998). Available at SSRN: https://ssrn.com/abstract=136692

Sandra Peterson

affiliation not provided to SSRN

Richard C. Stapleton

University of Strathclyde - Department of Accounting and Finance ( email )

Curran Building
100 Cathedral Street
Glasgow G4 0LN
United Kingdom
+44 1524 381 172 (Phone)
+44 1524 846874 (Fax)

Marti G. Subrahmanyam (Contact Author)

New York University (NYU) - Leonard N. Stern School of Business ( email )

44 West 4th Street
Suite 9-160
New York, NY NY 10012
United States

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