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A Multifactor Spot Rate Model for the Pricing of Interest Rate Derivatives

Published online by Cambridge University Press:  06 April 2009

Sandra Peterson ,
Richard C. Stapleton  and
Marti G. Subrahmanyam
Sandra Peterson
Affiliation:
drsjp@btopenworld.com, Scottish Institute for Research in Investment and Finance, Strathclyde University, Glasgow, UK;
Richard C. Stapleton
Affiliation:
richard.stapleton@btinternet.com, Manchester School of Accounting and Finance, University of Manchester, Manchester, UK, and University of Melbourne, Australia;
Marti G. Subrahmanyam
Affiliation:
msubrahm@stern.nyu.edu, Stern School of Business, New York University, Management Education Center, New York, NY 10012.
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Abstract

We propose a multifactor model in which the spot rate, LIBOR, follows a lognormal process, with a stochastic conditional mean, under the risk-neutral measure. In addition to the spot rate factor, the second factor is related to the premium of the first futures rate over the spot LIBOR. Similarly, the third factor is related to the premium of the second futures rate over the first futures rate. We calibrate the model to the initial term structure of futures rates and to the implied volatilities of interest rate caplets. We then apply the model to price interest rate derivatives such as European and Bermudan-style swaptions, and yieldspread options. The model can be employed to price more complex interest rate derivatives such as path-dependent derivatives or multi-currency-dependent derivatives because of its Markovian property.

Type
Research Article
Information
Journal of Financial and Quantitative Analysis , Volume 38 , Issue 4 , December 2003 , pp. 847 - 880
Copyright
Copyright © School of Business Administration, University of Washington 2003

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