Implied volatility functions in arbitrage-free term structure models

Abstract

We test six term structure models in the Heath, Jarrow, and Morton (1992) class using Eurodollar futures and options data from 1987*1992. We study the time series of implied interest rate volatilities from these models. Using one-day lagged implied volatilities, our one-and two-parameter models simultaneously price an average of 18.5 options each day with an average absolute error of one-and-a-half to two basis points. Although the models fit well, we document systematic strike- price and time-to-maturity biases for all models. We also implement simple trading strategies to test whether the models identify genuine biases.