第30卷第2期 经济数学 Vol.30,No.2 2013年6月 JOURNAL OF QUANTITATIVE ECONOMICS Jun.2013 基于贝叶斯MCMC算法的美式期权定价 熊炳忠，马柏林 (嘉兴学院数理与信息工程学院，浙江嘉兴314000) 摘要鉴于美式期权的定价具有后向选代搜索特征，本文结合L,ongstaff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。 关键词美式期权；MCMC回归；方差减少技术；蒙特卡洛模拟 中图分类号F830 文献标识码A Pricing American-Style Options Based on Bayesian Markov Chain Monte Carlo Algorithm XIONG Bing-zhong,MA Bo-lin (Institute of Mathematics,Physics and Information Engineering,JiaXing University,ZheJiang,JiaXing 314001,China) Abstract Based on the backward feature of iterative search of American-style options pricing,and combining with the i- dea 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 algo- rithm 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. Key words American-style option:MCMC regression;variance reduction techniques;Monte Carlo simulation 重要且最具活力的方向之一·美式期权的显著特点 1引言 是合约在有效期内的任意时刻都可以执行该合约， 使得投资者可以更加方便地处理其投资组合，受到 对美式期权的合理定价一直是数量金融中最为 广大投资者的欢迎，因此它在金融衍生品市场中使 收稿日期：2013-04-05 基金项目：渐江省教育厅2012年度科研计划项目(Y201225300):浙江省自然科学基金(Y6100810):2010年嘉兴学院科研重点项目 (70110096) 作者简介：熊炳忠(1971一)，男，江西玉山人，讲师，硕士 E-mail xiongbzh@mail.zjxu.edu.cn 万方数据第30卷 2 O l 3 第2期 年6月 经 济 数 学 JOURNAL 0F QUANTITATIVE ECONOMICS Vol-30，No．2 Jun．2 O l 3 基于贝叶斯MCMC算法的美式期权定价+ 熊炳忠，马柏林 (嘉兴学院数理与信息工程学院，浙江嘉兴314000) 摘要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． 关键词 美式期权；MCMC回归；方差减少技术；蒙特卡洛模拟 中图分类号F830 文献标识码A Pricing American—Style options Based on Bayesian MarkoV Chain Monte Carlo Algorithm X10NG Bing—zhong，MA Bo—lin (J挖盯如“把。厂』垭2￡^棚fics，P^j塔if5 n以d J行，0，7，硷fi伽Ekgi埘碧一ng，．，缸Xi玎g Uhit肥巧缸y。Zh已．，谊行g．．，谊Xi以g 314001。(冼i，搬) Abstract Based on the backward feature of iterative search of American—style options pricing，and combining with the i— dea of least—squares Mont}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 Mont}Carlo method to price Americanf 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 reIative error with the well—known least—squares IⅥonte Carlo algo— rithm 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 p“cing Ame“can-styIe 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． Key words American—style option；MCMC regression；variance reduction techniques；Monte Carlo simulation 引 言 对美式期权的合理定价一直是数量金融中最为 重要且最具活力的方向之一．美式期权的显著特点 是合约在有效期内的任意时刻都可以执行该合约， 使得投资者可以更加方便地处理其投资组合，受到 广大投资者的欢迎，因此它在金融衍生品市场中使 收稿日期：2013一04一05 基金项目：浙江省教育厅2012年度科研计划项目(Y201225300)；浙江省自然科学基金(Y6100810)；2010年嘉兴学院科研重点项且 (70110096) 作者简介：熊炳忠(1971一)，男，江西玉山人，讲师，硕士 E—mail：xiongbzh@mail．zjxu．edu．cn 万方数据