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Monte 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)

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)

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)

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)

This paper develops, analyzes, and tests computational procedures for the numerical solution of LIBOR market models with jumps. We consider, in particular , a class of models in which jumps are driven by marked point processes with intensities that depend on the LIBOR rates themselves. While this formulation offers some attractive modeling features, it… (More)

Intimtesirnal perturbation analysis is a technique for estimating derivatives of performance indices from simulation or observation of discrete event systems. Such derivative estimates are useful in performing optimization and sensitivity analysis through simulation. A general formulation of finite-horizon perturbation analysls derivative estimates is… (More)

We investigate and compare two dual formulations of the American option pricing problem based on two decompositions of supermartingales: the and the multiplicative dual of Jamshidian (Minimax optimality of Bermudan and American claims and their Monte-Carlo upper bound approximation. NIB Capital, The Hague, 2003). Both provide upper bounds on American option… (More)

This paper develops methods for relating the prices of discrete-and continuous-time versions of path-dependent options sensitive to extremal values of the underlying asset, including lookback, barrier, and hindsight options. The relationships take the form of correction terms that can be interpreted as shifting a barrier, a strike, or an extremal price.… (More)