Empirical evidence has shown that subordinated processes represent well the price changes of stocks and futures. Using either transaction counts or trading volume as a proxy for information arrival, it supports the contention that volatility is stochastic in calendar-time because of random...

Discrepancies between the Black-Scholes value of Japanese equity warrants and their observed prices are explained in part by the stochastic volatility of changes in prices of the underlying stocks. We fit GARCH and EGARCH models to the stochastic volatility and briefly compare their performance...

Quasi-Monte Carlo (QMC) methods are important numerical tools in the pricing and hedging of complex financial instruments. The effectiveness of QMC methods crucially depends on the discontinuity and the dimension of the problem. This paper shows how the two fundamental limitations can be...

In many of the numerical methods for pricing American options based on the dynamic programming approach, the most computationally intensive part can be formulated as the summation of Gaussians. Though this operation usually requiresO(NN') work when there areN' summations to compute and the...

The valuation of Asian, or a average price, options and of European options on portfolios in a "Black-Scholes" environment has given researchers trouble. The difficulty with these problems is that the probability distribution of the variable which determines the option payoff at expiration, a...

We develop a model for valuing revenue streams from innovations. The stochastic properties of revenue from innovations create a more difficult environment in which to value options than when the underlying is a security. There is no initial revenue, and cumulative revenue cannot decrease....

The authors develop a new Monte Carlo-based method for pricing path-dependent options under the variance gamma (VG) model. The gamma bridge sampling method proposed by Avramidis et al. (Avramidis, A. N., P. L'Ecuyer, P. A. Tremblay. 2003. Efficient simulation of gamma and variance-gamma...

Pricing European-style Asian options based on the arithmetic average, under the Black and Scholes model, involves estimating an integral (a mathematical expectation) for which no easily computable analytical solution is available. Pricing their American-style counterparts, which provide early...

This article considers the pricing of interest-rate-sensitive claims when the underlying interest rate is driven by a two-state-variable GARCH process. Analytical solutions are established for the case when the innovations in the short rate are normal and/or chi-squared random variables and the...

Simulation has proved to be a valuable tool for estimating security prices for which simple closed form solutions do not exist. In this paper we present two direct methods, a pathwise method and a likelihood ratio method, for estimating derivatives of security prices using simulation. With the...