针对障碍期权的定价问题,给出了一种高效的蒙特卡罗(Monte Carlo,MC)模拟方法——基于布朗桥构造路径的随机化拟蒙特卡罗(Brownian bridge path randomization quasi Monte Carlo,BBPR-QMC)方法.首先,用Faure序列代替MC方法中的随机序列...针对障碍期权的定价问题,给出了一种高效的蒙特卡罗(Monte Carlo,MC)模拟方法——基于布朗桥构造路径的随机化拟蒙特卡罗(Brownian bridge path randomization quasi Monte Carlo,BBPR-QMC)方法.首先,用Faure序列代替MC方法中的随机序列,得到了Faure序列的拟蒙特卡罗(quasi Monte Carlo,QMC)模拟方法;其次,应用Moro算法得到了随机化拟蒙特卡罗(randomization quasi Monte Carlo,R-QMC)模拟方法;最后,将QMC方法和R-QMC方法结合,利用布朗桥技术来降低有效维,得到障碍期权定价的BBPR-QMC方法.数值试验表明,与MC方法和R-QMC方法相比较,BBPR-QMC方法模拟的价格与真实价格更接近、收敛速度更快.数值试验证实,BBPR-QMC方法是一种高效求解障碍期权定价的数值方法.展开更多
The problem o f analytically pricing the discrete monitored European barrier options is studied under the assumption of the Black-Scholes market.First,using variable transformation,the mean vector and covariance matri...The problem o f analytically pricing the discrete monitored European barrier options is studied under the assumption of the Black-Scholes market.First,using variable transformation,the mean vector and covariance matrix of multi-dimensional marginal distribution are given.Secondly,the analytica pricing formulas of the discrete monitored upknock-out European call option and the discrete monitored down-knock-out European put option a e obtained by using the conditional probability and the characteristics o f the multidimensional normal distribution.Finally,the effects of the discrete monitoring barriers on the prices of the barrier optionsare discussed and analyzed.The research results state that the price o f the discrete monitored up-knock-out European call option mcreases with the increase in the up barrier,a d the price o f the discrete monitored down-knock-out European put option decreases with the increase in the down barrier.展开更多
文摘针对障碍期权的定价问题,给出了一种高效的蒙特卡罗(Monte Carlo,MC)模拟方法——基于布朗桥构造路径的随机化拟蒙特卡罗(Brownian bridge path randomization quasi Monte Carlo,BBPR-QMC)方法.首先,用Faure序列代替MC方法中的随机序列,得到了Faure序列的拟蒙特卡罗(quasi Monte Carlo,QMC)模拟方法;其次,应用Moro算法得到了随机化拟蒙特卡罗(randomization quasi Monte Carlo,R-QMC)模拟方法;最后,将QMC方法和R-QMC方法结合,利用布朗桥技术来降低有效维,得到障碍期权定价的BBPR-QMC方法.数值试验表明,与MC方法和R-QMC方法相比较,BBPR-QMC方法模拟的价格与真实价格更接近、收敛速度更快.数值试验证实,BBPR-QMC方法是一种高效求解障碍期权定价的数值方法.
基金The National Natural Science Foundation of China(No.71273139)the Soft Science Foundation of China(No.2010GXS5B147)the National Public Sector(Weather)Special Fund(No.GYHY201106019)
文摘The problem o f analytically pricing the discrete monitored European barrier options is studied under the assumption of the Black-Scholes market.First,using variable transformation,the mean vector and covariance matrix of multi-dimensional marginal distribution are given.Secondly,the analytica pricing formulas of the discrete monitored upknock-out European call option and the discrete monitored down-knock-out European put option a e obtained by using the conditional probability and the characteristics o f the multidimensional normal distribution.Finally,the effects of the discrete monitoring barriers on the prices of the barrier optionsare discussed and analyzed.The research results state that the price o f the discrete monitored up-knock-out European call option mcreases with the increase in the up barrier,a d the price o f the discrete monitored down-knock-out European put option decreases with the increase in the down barrier.
