Decision, Operations & Information Technologies Research Works

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Browsing Decision, Operations & Information Technologies Research Works by Subject "gradient estimation"

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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.