全局自适应拟Monte Carlo技术在数字期权中的运用

Applying an Adaptive Monte Carlo Integration Algorithm with General Division Approach to Hedge Digital Option

运用优化分层Monte Carlo模拟和比例分层Monte Carlo模拟两种方法计算数字期权的Δ值,结果表明优化分层Monte Carlo模拟计算的效果优于比例分层Monte Carlo模拟。针对优化分层Monte Carlo不能有效地配置模拟样本点资源以及计算速度较慢的缺点,采用全局自适应拟Monte Carlo模拟方法计算数字期权的Δ值,并对优化分层Monte Carlo模拟方法和全局自适应拟Monte Carlo模拟方法的计算结果进行比较。结果表明,在期权定价方面,全局自适应拟Monte Carlo模拟方法比优化分层Monte Carlo的计算精度和效率更高、计算方差和误差更小。

The Delta values of hedging digital option were calculated by Monte Carlo model with optimal stratified sampling（OSS-MC） and Monte Carlo model with proportional stratified sampling（PSS-MC）.The results show that OSS-MC is more efficient than PSS-MC in calculating the Delta value.However,OSS-MC allocates simulation resources ineffectively and computes at slow speed.Considering the disadvantage of OSS-MC,adaptive Monte Carlo integration algorithm with general division was introduce to simulate the Delta value,and the results simulated by adaptive Monte Carlo integration algorithm were compared with general division and OSS-MC.It shows that the simulation results computed by the adaptive Monte Carlo integration algorithm are more accurate,more efficient with less variance and less error than that computed by OSS-MC.