We develop a class of discrete, path-independent models to compute prices of American options within the Black-Scholes (1973) framework, including models in which state variables have time-varying volatility functions and models with multiple state variables. Time-varying volatility functions are illustrated with applications to term structure models developed by Vasicek (1977) and Heath, Jarrow, and Morton (1988), (1990). Distinct from previous work in the literature, the multivariate models suggested in this paper are consistent with arbitrarily large, though constant, covariance functions. Finally, we compare and contrast the numerical accuracy of a large number of models with simulation results.

The author develops a simple, discrete time model to value options when the underlying process follows a jump diffusion process. Multivariate jumps are superimposed on the binomial model of J. C. Cox, S. A. Ross, and M. Rubinstein (1979) to obtain a model with a limiting jump diffusion process. This model incorporates the early exercise feature of American options as well as arbitrary jump distributions. It yields an efficient computational procedure that can be implemented in practice. As an application of the model, the author illustrates some characteristics of the early exercise boundary of American options with certain types of jump distributions.

We develop a simple, discrete time model to value options when the underlying process follows a jump diffusion process. Multivariate jumps are superimposed on the binomial model of Cox, Ross, and Rubinstein (1979) to obtain a model with a limiting jump diffusion process. This model incorporates the early exercise feature of American options as well as arbitrary jump distributions. It yields an efficient computational procedure that can be implemented in practice. As an application of the model, we illustrate some characteristics of the early exercise boundary of American options with certain types of jump distributions.

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.]

The authors use an extension of the equilibrium framework of M. Rubinstein (1976) and M. Brennan (1979) to derive an option valuation formula when the stock return volatility is both stochastic and systematic. Their formula incorporates a stochastic volatility process as well as a stochastic interest rate process in the valuation of options. If the 'mean,'volatility, and 'covariance' processes for the stock return and the consumption growth are predictable, the authors' option valuation formula can be written in 'preference-free'form. Further, many popular option valuation formulae in the literature can be written as special cases of their general formula.

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.

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.