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

作　　者：Hasan Alzubaidi 

机构地区：[1]Department of Mathematics, Al-Qunfudah University College, Umm Al-Qura University, Mecca, KSA

出　　处：《American Journal of Computational Mathematics》2017年第3期228-242,共15页美国计算数学期刊（英文）

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

关 键 词：BARRIER OPTION with REBATE Payment Binary BARRIER OPTION Partial BARRIER OPTION Hitting Time Error Exponential Time-Stepping ALGORITHM 

分 类 号：O1[理学—数学]