随机波动率下美式期权定价的对偶LSM法
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摘要
当股票价格满足Hull-White随机波动率模型时,应用对偶最小二乘蒙特卡罗(LSM)方法研究美式期权的定价.首先,采用对偶蒙特卡罗(MC)法模拟出股票价格,并利用这些股票价格计算美式期权在不同时刻对应的现金流.其次,利用改进后的最小二乘蒙特卡罗(LSM)法计算美式期权的价格.最后,进行数值模拟计算,得到了随机波动率对美式期权定价的影响,并验证了该方法的准确性.
This paper uses the antithetic variable least-squares Monte Carlo(LSM) method to price the American option under Hull-White stochastic volatility model. First, we simulate the price of the stock by the antitheticvariable Monte Carlo(MC) method. Then, we use the price of the stock to calculate the cash flow of Americanoption at different time. And we improve the least-squares Monte Carlo simulation method which can be used to cal-culate the price of American option. Finally, we illustrate our results with the numerical calculation of the price ofthe American option. Our numerical investigation shows the impact of the stochastic volatility on the American options and the accuracy of the antithetic variable LSM method.
This paper uses the antithetic variable least-squares Monte Carlo(LSM) method to price the American option under Hull-White stochastic volatility model. First, we simulate the price of the stock by the antitheticvariable Monte Carlo(MC) method. Then, we use the price of the stock to calculate the cash flow of Americanoption at different time. And we improve the least-squares Monte Carlo simulation method which can be used to cal-culate the price of American option. Finally, we illustrate our results with the numerical calculation of the price ofthe American option. Our numerical investigation shows the impact of the stochastic volatility on the American options and the accuracy of the antithetic variable LSM method.
引文
[1] HULL J,WHITE A. The pricing of options on assets with stochastic volatilities[J]. Journal of Finance,1987,42(2):281-300.
[2]江良,林鸿熙.随机波动率Hull-White模型参数估计方法[J].系统工程学报,2016,31(5):633-642.
[3]邓国和.随机波动率跳跃扩散模型下复合期权定价[J].数理统计与管理,2015,34(5):910-922.
[4]温鲜.非仿射随机波动率的欧式回望期权定价[J].广西科技大学学报,2018,29(2):132-136.
[5] TILLY J A.Valuing American options in a path simulation model[J].Transactions of the Society of Actuaries,1993,45:55-67.
[6] BROADIE M,GLASSERMAN P. Pricing American style securities using simulation[J]. Journal of Economics Dynamics andControl,1997,21(8-9):1323-1352.
[7] LONGSTAFF F A,SCHWARTZ E S. Valuing American options by simulation:A simple least-squares approach[J]. The Re‐view of Financial Studies,2001,14(1):113-147.
[8] STENTOFT L. Assessing the least squares monte carlo approach to American option valuation[J]. Reviewof Derivatives Re‐search,2004,7(2):129-168.
[9] CORTAZAR G,GRAVET M,URZUA J. The valuation of multidimensional American real options using the LSM simulationmethod[J]. Computers and Operations Research,2008:113-129.
[10] ALONSO S,AZOFRA V,FUENTE G D L. What do you do when the binomial cannot value real options? The LSM model[J].Documentos De Trabajo Funcas,2014,2(1):942338.
[11]刘坚,马超群.随机利率下美式期权的LSM方法定价[J].系统工程,2013,31(10):10-14.
[12]曹小龙,胡云姣.美式期权定价的拟蒙特卡罗模拟及其方差减小技术[J].北京化工大学学报(自然科学版),2014,41(3):119-124.
[13]熊维玲,甘桦源.(3+1)维Jimbo-Miwa方程的非行波解[J].广西科技大学学报,2017,28(1):12-18.
[2]江良,林鸿熙.随机波动率Hull-White模型参数估计方法[J].系统工程学报,2016,31(5):633-642.
[3]邓国和.随机波动率跳跃扩散模型下复合期权定价[J].数理统计与管理,2015,34(5):910-922.
[4]温鲜.非仿射随机波动率的欧式回望期权定价[J].广西科技大学学报,2018,29(2):132-136.
[5] TILLY J A.Valuing American options in a path simulation model[J].Transactions of the Society of Actuaries,1993,45:55-67.
[6] BROADIE M,GLASSERMAN P. Pricing American style securities using simulation[J]. Journal of Economics Dynamics andControl,1997,21(8-9):1323-1352.
[7] LONGSTAFF F A,SCHWARTZ E S. Valuing American options by simulation:A simple least-squares approach[J]. The Re‐view of Financial Studies,2001,14(1):113-147.
[8] STENTOFT L. Assessing the least squares monte carlo approach to American option valuation[J]. Reviewof Derivatives Re‐search,2004,7(2):129-168.
[9] CORTAZAR G,GRAVET M,URZUA J. The valuation of multidimensional American real options using the LSM simulationmethod[J]. Computers and Operations Research,2008:113-129.
[10] ALONSO S,AZOFRA V,FUENTE G D L. What do you do when the binomial cannot value real options? The LSM model[J].Documentos De Trabajo Funcas,2014,2(1):942338.
[11]刘坚,马超群.随机利率下美式期权的LSM方法定价[J].系统工程,2013,31(10):10-14.
[12]曹小龙,胡云姣.美式期权定价的拟蒙特卡罗模拟及其方差减小技术[J].北京化工大学学报(自然科学版),2014,41(3):119-124.
[13]熊维玲,甘桦源.(3+1)维Jimbo-Miwa方程的非行波解[J].广西科技大学学报,2017,28(1):12-18.