We study the information content of implied volatility from several volatility specifications of the Heath-Jarrow-Morton (1992) (HJM) models relative to popular historical volatility models in the Eurodollar options market. The implied volatility from the HJM models explains much of the variation of realized interest rate volatility over both daily and monthly horizons. The implied volatility dominates the GARCH terms, the Glosten et al. (1993) type asymmetric volatility terms, and the interest rate level. However, it cannot explain that the impact of interest rate shocks on the volatility is lower when interest rates are low than when they are high.

We develop an arbitrage-free discrete time model to price American-style claims for which domestic term structure risk, foreign term structure risk, and currency risk are important. This model combines a discrete version of the Heath, Jarrow, and Morton (1992) term structure model with the binomial model of Cox, Ross, and Rubinstein (1979). It converges (weakly) to the continuous time models in Amin and Jarrow (1991, 1992). The general model is “path dependent” and can be implemented with arbitrary volatility functions to value claims with maturity up to five years. The model is illustrated with applications to long-dated American currency warrants and a cross-rate swap from the quanto class.

[We develop an arbitrage-free discrete time model to price American-style claims for which domestic term structure risk, foreign term structure risk, and currency risk are important. This model combines a discrete version of the Heath, Jarrow, and Morton (1992) term structure model with the binomial model of Cox, Ross, and Rubinstein (1979). It converges (weakly) to the continuous time models in Amin and Jarrow (1991, 1992). The general model is "path dependent" and can be implemented with arbitrary volatility functions to value claims with maturity up to five years. The model is illustrated with applications to long-dated American currency warrants and a cross-rate swap from the quanto class.]

We study the information content of implied volatility from several volatility specifications of the Heath–Jarrow–Morton (1992) (HJM) models relative to popular historical volatility models in the Eurodollar options market. The implied volatility from the HJM models explains much of the variation of realized interest rate volatility over both daily and monthly horizons. The implied volatility dominates the GARCH terms, the Glosten et al. (1993) type asymmetric volatility terms, and the interest rate level. However, it cannot explain that the impact of interest rate shocks on the volatility is lower when interest rates are low than when they are high.