基于贝叶斯MCMC算法的美式期权定价

鉴于美式期权的定价具有后向迭代搜索特征,本文结合Longstaff和Schwartz提出的美式期权定价的最小二乘模拟方法,研究基于马尔科夫链蒙特卡洛算法对回归方程系数的估计,实现对美式期权的双重模拟定价.通过对无红利美式看跌股票期权定价进行大量实证模拟,从期权价值定价误差等方面同著名的最小二乘蒙特卡洛模拟方法进行对比分析,结果表明基于MCMC回归算法给出的美式期权定价具有更高的精确度.模拟实证结果表明本文提出的对美式期权定价方法具有较好的可行性、有效性与广泛的适用性.该方法的不足之处就是类似于一般的蒙特卡洛方法,会使得求解的计算量有所加大.

Pricing American-Style Options Based on Bayesian Markov Chain Monte Carlo Algorithm

Based on the backward feature of iterative search of American-style options pricing, and combining with the idea of least-squares Monte-Carlo pricing American-style options by Longstaff and Schwartz, we proposed a new method, in which the coefficient of the regression equation was estimated by the Markov Chain Monte-Carlo method to price American-style options by double simulation. The methodology is extensively tested on simulated data of pricing American-style stock put option with no dividend. Comparing the option value and relative error with the well-known least-squares Monte Carlo algorithm for pricing American-style options, the precision based on MCMC regression method is better than it. It can be concluded that MCMC regression method for pricing American-style options is much more feasible and effective by empirical simulation. This method has extensive applicability as well. The drawback of the method is potentially heavy computation demand, which is the same as the general Monte Carlo method.