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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)
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 &#248;, starting from &#248;, with <italic>K</italic> large. The estimator we study is based on interchanging the arrival rate(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)
This paper develops efficient methods for computing portfolio value-at-risk (VAR) when the underlying risk factors have a heavy-tailed distribution. In modeling heavy tails, we focus on multivariate t distributions and some extensions thereof. We develop two methods for VAR calculation that exploit a quadratic approximation to the portfolio loss, such as(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)