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Abstract: An efficient conditioning technique, the so-called Brownian Bridgesimulation, has previously been applied to eliminate pricing bias that arisesin applications of the standard discrete-time Monte Carlo method to evaluateoptions written on the continuous-time extrema of an underlying asset. It isbased on the simple and easy to implement analytic formulas for thedistribution of one-dimensional Brownian Bridge extremes. This paper extendsthe technique to the valuation of multi-asset options with knock-out barriersimposed for all or some of the underlying assets. We derive formula for theunbiased option price estimator based on the joint distribution of themulti-dimensional Brownian Bridge dependent extrema. As analytic formulas arenot available for the joint distribution in general, we develop upper and lowerbiased option price estimators based on the distribution of independent extremaand the Fr\-echet lower and upper bounds for the unknown distribution. Allestimators are simple and easy to implement. They can always be used to bindthe true value by a confidence interval. Numerical tests indicate that ourbiased estimators converge rapidly to the true option value as the number oftime steps for the asset path simulation increases in comparison to theestimator based on the standard discrete-time method. The convergence ratedepends on the correlation and barrier structures of the underlying assets.



Autor: P. V. Shevchenko

Fuente: https://arxiv.org/







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