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High-dimensional problems frequently arise in the pricing of derivative securities – for example, in pricing options on multiple underlying assets and in pricing term structure derivatives. American versions of these options, ie, where the owner has the right to exercise early, are particularly challenging to price. We introduce a stochastic mesh method for… (More)

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 direct methods, the information from a single simulation can be… (More)

M onte Carlo simulation is widely used to measure the credit risk in portfolios of loans, corporate bonds, and other instruments subject to possible default. The accurate measurement of credit risk is often a rare-event simulation problem because default probabilities are low for highly rated obligors and because risk management is particularly concerned… (More)

The payoff of a barrier option depends on whether or not a specified asset price, index, or rate reaches a specified level during the life of the option. Most models for pricing barrier options assume continuous monitoring of the barrier; under this assumption, the option can often be priced in closed form. Many (if not most) real contracts with barrier… (More)

This paper develops a variance reduction technique for Monte Carlo simulations of path-dependent options driven by high-dimensional Gaussian vectors. The method combines importance sampling based on a change of drift with stratified sampling along a small number of key dimensions. The change of drift is selected through a large deviations analysis and is… (More)

The views expressed here are those of the author(s) and not necessarily those of the Federal Deposit Insurance Corporation Abstract We consider the problem of decomposing the credit risk in a portfolio into a sum of risk contributions associated with individual obligors or transactions. For some standard measures of risk — including value-at-risk and… (More)

1 Motivation The estimation of rare event probabilities poses some of the of the most diicult computational challenges for Monte Carlo simulation and, at the same time, some of the greatest opportunities for eeciency improvement through the use of variance reduction techniques. Current i n terest in rare events stems primarily from developments in computer… (More)

We analyze the performance of an importance sampling estimator for a rare-event probability in tandem Jackson networks. The rare event we consider corresponds to the network population reaching <italic>K</italic> before returning to ø, starting from ø, with <italic>K</italic> large. The estimator we study is based on interchanging the arrival rate… (More)

This paper presents an adjoint method to accelerate the calculation of Greeks by Monte Carlo simulation. The method calculates price sensitivities along each path; but in contrast to a forward pathwise calculation, it works backward recursively using adjoint variables. Along each path, the forward and adjoint implementations produce the same values, but the… (More)

An approach to rare event simulation uses the technique of splitting. The basic idea is to split sample paths of the stochastic process into multiple copies when they approach closer to the rare set; this increases the overall number of hits to the rare set for a given amount of simulation time. This paper analyzes the bias and efficiency of some simple… (More)