The Valuation of American-Style Swaptions in a Two-Factor Spot-Futures Model1

40 Pages Posted: 11 Nov 2008

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

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 and 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 Libor 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. These prices are shown to be highly sensitive to the existence of the second factor and its volatility characteristics.

Suggested Citation

Peterson, Sandra and Stapleton, Richard C. and Subrahmanyam, Marti G., The Valuation of American-Style Swaptions in a Two-Factor Spot-Futures Model1 (December 1999). NYU Working Paper No. FIN-99-078, Available at SSRN: https://ssrn.com/abstract=1299449

Sandra Peterson (Contact Author)

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

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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