The Importance of Forward Rate Volatility Structures in Pricing Interest Rate-Sensitive Claims

Abstract

Studies of the sensitivity of the prices of interest rate claims to alternative specifications of the volatility of spot and forward interest rates have drawn different conclusions. One possible explanation for this is that it is difficult to adjust the volatility structure without disturbing the initial set of bond prices. In this chapter we use a term structure-constrained model that lets us change the volatility structure for spot and forward rates without altering either their initial values or the set of initial bond prices. Consequently, any differences in prices of interest rate-sensitive claims can be attributed solely to alternative assumptions on the structure of spot and forward-rate volatilities rather than to variations in the initial conditions. We show that even when the initial conditions are common, option prices on interest rates and on bonds are sensitive to the specification of the volatility structure of spot rates. Further, we find that using a simple generalised Vasicek model to price claims can lead to significant mispricings if interest rate volatilities do indeed depend on their levels.