拟蒙特卡洛模拟方法在期权定价中的应用研究

Quasi-Monte Carlo Method in European Option Pricing

不断变化的市场利率、汇率,难以预测的突发事件,以及各种复杂情形都对金融衍生产品定价方法提出了更高的要求。蒙特卡洛模拟是一种比较有效的衍生品定价方法,它通过伪随机序列模拟标的资产价格的路径,对相应的期权进行定价,但它存在着一定的弊端:收敛速度慢,不能通过增加模拟次数有效地逼近真值。拟蒙特卡洛模拟对蒙特卡洛模拟进行了改进,用低差异序列代替伪随机序列,提高了模拟的准确性。论文利用蒙特卡洛和拟蒙特卡洛模拟方法对欧式期权进行定价,对两种方法进行比较分析,结果表明在低维情况下拟蒙特卡洛模拟方法可以得到更加精确地效果,收敛速度也比较快;在高维情况下通过修正也达到同样的效果。

Varying interest rates, unpredictable cases, and other complications all put forward higher requirements in the financial derivatives pricing methods. Monte Carlo simulation is an appropriate approach for financial derivatives pricing. It uses the pseudorandom sequence to simulate the price path of the underlying asset, then prices the corresponding options But this method has some drawbacks： its convergence speed is slow and It can not approach true value effectively by increasing the number of simulation. Quasi-Monte Carlo method improves the shortcomings of Monte Carlo method., using low-discrepancy sequences instead of pseudorandom sequence, then improves the accuracy of the simulations. This paper prices the European vanilla options using Monte Carlo method and Quasi-Monte Carlo method, then does the comparative analysis for the two methods. The results show that under the condition of low dimensional Quasi- Monte Carlo simulation method can get more precise result, and the convergence speed is faster. Under the condition of high dimension the Quasi- Monte Carlo method can arrive the same results by correction.