蒙特卡洛方法和拟蒙特卡洛方法在期权定价中应用的比较研究

Comparison of Monte Carlo Simulation and Quasi-Monte Carlo Simulation in Option Pricing

在期权的交易中,最关键的问题是期权定价。蒙特卡洛模拟作为期权定价的有效的数值方法之一,近年来发展迅速。然而蒙特卡洛方法产生的随机数为伪随机数有收敛速度慢、计算量大等缺陷。拟蒙特卡洛模拟是采用拟随机数序列代替伪随机数序列的蒙特卡洛模拟。通过考察线性同余发生器;Halton序列、Sobol序列等拟随机数序列的特点,以欧式看涨期权为对象研究了蒙特卡洛方法和拟蒙特卡洛方法的有效性。对比实验显示了拟蒙特卡洛模拟明显优于蒙特卡洛模拟。

In options trading, the most critical problem is the determination of option prices. Monte Carlo simulation, an effective method for option pricing, had rapid development in recent years. However, Monte Carlo method generated pseudo-random numbers, which shows slow convergence rate, large amount of calculation. Quasi-Monte Carlo simulation is proposed to replace the quasi-random numbers sequences of pseudo-random number sequences of Monte Carlo simulation. This method for the improvement of estimated effect depends on the random sequences＇ distribution homogeneity in sample space. A linear congruence generator is studied; Halton sequences, Sobol＇ sequences, and the characteristics of such random number sequences. European-style call option as an example to study the effectiveness of the proposed Monte Carlo method, pseudo-random sequence and random sequence carried out Monte Carlo simulation in financial calculations, as the contrastive experiment shows the Quasi-Monte Carlo simulation has high precision, speed and so on.