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A Joint Framework for Consistently Pricing Interest Rates and Interest Rate Derivatives

Published online by Cambridge University Press:  01 June 2009

Massoud Heidari  and
Liuren Wu
Massoud Heidari
Affiliation:
Caspian Capital Management, LLC, 745 5th Ave., 28th floor, New York, NY 10151. [email protected]
Liuren Wu
Affiliation:
Baruch College, Zicklin School of Business, 1 Bernard Baruch Way, Box B10-225, New York, NY 10010. [email protected]
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Abstract

Dynamic term structure models explain the yield curve variation well but perform poorly in pricing and hedging interest rate options. Most existing option pricing practices take the yield curve as given, thus having little to say about the fair valuation of the underlying interest rates. This paper proposes an m + n model structure that bridges the gap in the literature by successfully pricing both interest rates and interest rate options. The first m factors capture the yield curve variation, whereas the latter n factors capture the interest rate options movements that cannot be effectively identified from the yield curve. We propose a sequential estimation procedure that identifies the m yield curve factors from the LIBOR and swap rates in the first step and the n options factors from interest rate caps in the second step. The three yield curve factors explain over 99% of the variation in the yield curve but account for less than 50% of the implied volatility variation for the caps. Incorporating three additional options factors improves the explained variation in implied volatilities to over 99%.

Type
Research Articles
Information
Journal of Financial and Quantitative Analysis , Volume 44 , Issue 3 , June 2009 , pp. 517 - 550
Copyright
Copyright © Michael G. Foster School of Business, University of Washington 2009

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