Decision, Operations & Information Technologies

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Prior to January 4, 2009, this unit was named Decision & Information Technologies.

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Author: search.filters.author.Fu, Michael C.Subject: search.filters.subject.simulation

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Now showing 1 - 3 of 3
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    A Large Deviations Analysis of Quantile Estimation with Application to Value at Risk
    (2005-07-01T12:31:49Z) Jin, Xing; Fu, Michael C.
    Quantile estimation has become increasingly important, particularly in the financial industry, where Value-at-Risk has emerged as a standard measurement tool for controlling portfolio risk. In this paper we apply the theory of large deviations to analyze various simulation-based quantile estimators. First, we show that the coverage probability of the standard quantile estimator converges to one exponentially fast with sample size. Then we introduce a new quantile estimator that has a provably faster convergence rate. Furthermore, we show that the coverage probability for this new estimator can be guaranteed to be 100% with sufficiently large, but finite, sample size. Numerical experiments on a VaR example illustrate the potential for dramatic variance reduction.
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    Sensitivity Analysis for Monte Carlo Simulation of Option Pricing
    (1995) Fu, Michael C.; Hu, Jian-Qiang
    Monte Carlo simulation is one alternative for analyzing options markets when the assumptions of simpler analytical models are violated. We introduce techniques for the sensitivity analysis of option pricing which can be efficiently carried out in the simulation. In particular, using these techniques, a single run of the simulation would often provide not only an estimate of the option value but also estimates of the sensitivities of the option value to various parameters of the model. Both European and American options are considered, starting with simple analytically tractable models to present the idea and proceeding to more complicated examples. We then propose an approach for the pricing of options with early exercise features by incorporating the gradient estimates in an iterative stochastic approximation algorithm. The procedure is illustrated in a simple example estimating the option value of an American call. Numerical results indicate that the additional computational effort required over that required to estimate a European option is relatively small.
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    Stochastic Gradient Estimation
    (2005-07-01T12:31:02Z) Fu, Michael C.
    We consider the problem of efficiently estimating gradients from stochastic simulation. Although the primary motivation is their use in simulation optimization, the resulting estimators can also be useful in other ways, e.g., sensitivity analysis. The main approaches described are finite differences (including simultaneous perturbations), perturbation analysis, the likelihood ratio/score function method, and the use of weak derivatives.