Some theoretical and practical aspects antithetic and common random numbers for variance reduction in simulation of stochastic systems with dependent elements are considered. A proof of their optimality in estimating the expected value of the response sum or the response difference of a pair of...

This paper describes a simulation procedure for estimating the distribution function of the shortest path length in a network with random arc lengths. The method extends the concept of conditional Monte Carlo utilizing special properties of the Uniformly Directed Cutsets and the unique arcs. The...

In a recent paper, Longstaff and Schwartz (2001) suggest a method to American option valuation based on simulation. The method is termed the Least Squares Monte Carlo (LSM) method, and although it has become widely used, not much is known about the properties of the estimator. This paper...

The main goal of this paper is to describe a new multistage Monte Carlo (MMC) simulation method for solving influence diagrams using local computation. Global methods have been proposed by others that sample from the joint probability distribution of all the variables in the influence diagram....

The point estimator used in naive Monte Carlo sampling weights all the computed function evaluations equally, and it does not take into account the precise locations at which the function evaluations are made. In this note, we consider one-dimensional integration problems in which the integrand...

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...

We consider the problem of pricing a contingent claim whose payoff depends on several sources of uncertainty. Using classical assumptions from the Arbitrage Pricing Theory, the theoretical price can be computed as the discounted expected value of future cash flows under the modified risk-neutral...

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...