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, 2006

"... On the efficient application of the repeated Richardson extrapolation technique to option pricing ..."

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On the efficient application of the repeated Richardson extrapolation technique to option pricing

### A New Adaptive Mesh Approach for Pricing the American Put Option

"... Various options are now popularly traded all over the world. Thus, the e cient accurate pricing of options is of substantial practical importance. If we assume that the underlying security of an option follows the Black-Scholes dynamics, the price of a European option is given by the general formula ..."

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Various options are now popularly traded all over the world. Thus, the e cient accurate pricing of options is of substantial practical importance. If we assume that the underlying security of an option follows the Black-Scholes dynamics, the price of a European option is given by the general formula, i.e., the expectation of the premium at the maturity date with respect to the equivalent Martingale measure. In the case of American call option, the price is equal to that of corresponding European options, while in the case of American put option, it is known that the pricing is substantially more complicated. Up to now lots of numerical approximation procedures were proposed for pricing American put options. Because of various di culties in calculating the price of American options, however, intensive e orts are still needed for developing new approaches to this problem. In the present paper, based on a trinomial tree approximation, we propose an improved version for pricing the American put option on one underlying asset which follows the Black-Scholes dynamics. We then compare the accuracy of our method with various existing approaches by simulations. The results show that our approach is the most accurate in the case of out-of-the-money. i Acknowledgement This article is the result of research carried out in my second year at the Doctoral Program

### An efficient application of the repeated Richardson extrapolation technique to option pricing

"... In financial engineering one has frequently to deal with approximate results that are obtained by iterative methods or computational procedures depending on some parameter (e.g. the time-step). Often the convergence of numerical schemes is slow and this may be a serious problem to their use in pract ..."

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In financial engineering one has frequently to deal with approximate results that are obtained by iterative methods or computational procedures depending on some parameter (e.g. the time-step). Often the convergence of numerical schemes is slow and this may be a serious problem to their use in practice. For this reason, acceleration techniques, such