The Valuation of American-style Swaptions in a Two-factor Spot Futures Model

40 Pages Posted: 15 Jan 2000  

Sandra Peterson

affiliation not provided to SSRN

Richard C. Stapleton

University of Strathclyde - Department of Accounting and Finance

Marti G. Subrahmanyam

New York University - Stern School of Business

Date Written: December 1999

Abstract

We build a no-arbitrage model of the term structure of interest rates using two stochastic factors, the short-term interest rate and the premium of the futures rate over the short-term interest rate. The model provides an extension of the lognormal interest rate model of Black and Karasinski (1991) to two factors, both of which can exhibit mean-reversion. The method is computationally efficient for several reasons. First, the model is based on futures prices, enabling us to satisfy the no-arbitrage condition without resorting to iterative methods. Second, we modify and implement the binomial approximation methodology of Nelson and Ramaswamy (1990) and Ho, Stapleton and Subrahmanyam (1995) to compute a multiperiod tree of rates with the no-arbitrage property. The method uses a recombining two-dimensional binomial lattice of interest rates that minimizes the number of states and term structures over time. In addition to these computational advantages, a key feature of the model is that it is consistent with the observed term structure of futures rates as well as the term structure of volatilities implied by the prices of interest rate caps and floors. We use the model to price European-style, Bermudan-style, and American-style swaptions. These prices are shown to be highly sensitive to the existence of the second factor and its volatility characteristics.

JEL Classification: E43, G12, G13, G15

Suggested Citation

Peterson, Sandra and Stapleton, Richard C. and Subrahmanyam, Marti G., The Valuation of American-style Swaptions in a Two-factor Spot Futures Model (December 1999). Available at SSRN: https://ssrn.com/abstract=199899 or http://dx.doi.org/10.2139/ssrn.199899

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 - Stern School of Business ( email )

Stern School of Business,
44 West 4th Street, Suite 9-68
New York, NY 10012-1126
United States
212-998-0348 (Phone)
212-995-4233 (Fax)

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