In this paper, we develop an efficient lattice algorithm to price European and American options under discrete time GARCH processes. We show that this algorithm is easily extended to price options under generalized GARCH processes, with many of the existing stochastic volatility bivariate diffusion models appearing as limiting cases. We establish one unifying algorithm that can price options under almost all existing GARCH specifications as well as under a large family of bivariate diffusions in which volatility follows its own, perhaps correlated, process.

Unlike most interest rate claim models, the Ho-Lee (1986) model utilizes full information on the current term structure. Unfortunately, the model has a major deficiency in that negative interest rates can occur. This article modifies the model such that interest rates are well behaved.

[We develop a model of nominal and real bond yield curves that has four stochastic drivers but seven factors: three factors primarily determine the cross-section of yields, whereas four volatility factors solely determine risk premia. The model is estimated using nominal Treasury yields, survey inflation forecasts, and inflation swap rates and has attractive empirical properties. Time-varying volatility is particularly apparent in shortterm real rates and expected inflation. Also, we detail the different economic forces that drive short-and long-term real and inflation risk premia and provide evidence that Treasury inflation-protected securities were undervalued prior to 2004 and during the recent financial crisis.]

[We establish Markovian models in the Heath, Jarrow, and Morton (1992) paradigm that permit an exponential affine representation of riskless and risky bond prices while offering significant flexibility in the choice of volatility structures. Estimating models in our family is typically no more difficult than in the workhorse affine family. Besides diffusive and jump-induced default correlations, defaults can impact the credit spreads of surviving firms, allowing for a greater clustering of defaults. Numerical implementations highlight the importance of incorporating interest rate-credit spread correlations, credit spread impact factors, and the full credit spread curve when building a unified framework for pricing credit derivatives.]

This article establishes efficient lattice algorithms for pricing American interest-sensitive claims in the Heath, Jarrow, and Morton paradigm under the assumption that the volatility structure of forward rates is restricted to a class that permits a Markovian representation of the term structure. The class of volatilities that permits this representation is quite large and imposes no severe restrictions on the structure for the spot rate volatility. The algorithm exploits the Markovian property of the term structure and permits the efficient computation of all types of interest rate claims. Specific examples are provided.

ABSTRACT The purpose of this article is to compare the Perrakis and Ryan bounds of option prices in a single‐period model with option bounds derived using linear programming. It is shown that the upper bounds are identical but that the lower bounds are different. A comparison of these bounds, together with Merton's bounds and the Black‐Scholes prices in a lognormal securities market, is presented.

In this paper, we develop an efficient lattice algorithm to price European and American options under discrete time GARCH processes. We show that this algorithm is easily extended to price options under generalized GARCH processes, with many of the existing stochastic volatility bivariate diffusion models appearing as limiting cases. We establish one unifying algorithm that can price options under almost all existing GARCH specifications as well as under a large family of bivariate diffusions in which volatility follows its own, perhaps correlated, process.

ABSTRACT Unlike most interest rate claim models, the Ho‐Lee model utilizes full information on the current term structure. Unfortunately, the model has a major deficiency in that negative interest rates can occur. This article modifies the model such that interest rates are well behaved.

Unlike most interest rate claim models, the Ho-Lee model utilizes full information on the current term structure. Unfortunately, the model has a major deficiency in that negative interest rates can occur. This article modifies the model such that interest rates are well behaved.