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Random Timestepping Algorithm with Exponential Distribution for Pricing Various Structures of One-Sided Barrier Options

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Document pages: 15 pages

Abstract: Theexponentially-distributed random timestepping algorithm with boundary test isimplemented to evaluate the prices of some variety of single one-sided barrieroption contracts within the framework of Black-Scholes model, giving efficientestimation of their hitting times. It is numerically shown that this algorithm,as for the Brownian bridge technique, can improve the rate of weak convergencefrom order one-half for the standard Monte Carlo to order 1. The exponential timesteppingalgorithm, however, displays better results, for a given amount of CPU time,than the Brownian bridge technique as the step size becomes larger or thevolatility grows up. This is due to the features of the exponential distributionwhich is more strongly peaked near the origin and has a higher kurtosiscompared to the normal distribution, giving more stability of the exponential timesteppingalgorithm at large time steps and high levels of volatility.

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