The exponentially-distributed random timestepping algorithm with boundary\ntest is implemented to evaluate the prices of some variety of single one-sided\nbarrier option contracts within the framework of Black-Scholes model, giving\nefficient estimation of their hitting times. It is numerically shown that this algorithm,\nas for the Brownian bridge technique, can improve the rate of weak\nconvergence from order one-half for the standard Monte Carlo to order 1.\nThe exponential timestepping algorithm, however, displays better results, for\na given amount of CPU time, than the Brownian bridge technique as the step\nsize becomes larger or the volatility grows up. This is due to the features of the\nexponential distribution which is more strongly peaked near the origin and\nhas a higher kurtosis compared to the normal distribution, giving more stability\nof the exponential timestepping algorithm at large time steps and high levels\nof volatility.
Loading....