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, 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