On the Information in the Interest Rate Term Structure and Option Prices

Abstract

Cap and swaption prices contain information on interest rate volatilities and correlations. In this paper, we examine whether this information in cap and swaption prices is consistent with realized movements of the interest rate term structure. To extract an option-implied interest rate covariance matrix from cap and swaption prices, we use Libor market models or discrete-tenor string models as modeling framework. We propose a flexible parameterization of the interest rate covariance matrix, which cannot be generated by standard low-factor term structure models. The empirical analysis is based on weekly US data from 1995 to 1999. Our empirical results show that the option prices imply a covariance matrix of interest rates that is significantly different from the covariance matrix implied by realized interest rate changes. In particular, if one uses the latter covariance matrix to price caps and swaptions, one significantly underprices these options. We discuss and analyze several explanations for our findings.

Keywords: Term Structure Models, Interest Rate Derivatives, Volatility Hump, Caps and Swaptions

JEL Classification: G12, G13, E43