以模擬法為路徑相依新奇選擇權訂價

Abstract

本研究主要在探討與比較使用蒙地卡羅模擬法對路徑相依新奇選擇權訂價時，各種效率改善的技巧所能夠提供的效率與精確性的改善效果。 在效率改善方面，本研究是比較一般的蒙地卡羅模擬法與使用效率改善技巧的蒙地卡羅模擬所得的價格，在變異數上的改善程度作為效率改善的指標。而在精確度改善方面，本研究透過比較使用各種效率改善技巧，並經過收斂以後所得的模擬價格與理論價格的差異，作為精確度改善的指標。 經由上述的方法，本研究比較了不同的效率改善技巧之間在速度、效率與精確度的改善效果。同時在評價障礙選擇權與回顧選擇權時，加入條件機率的概念來降低蒙地卡羅模擬過程中的偏誤。

This paper studies how different efficiency improvement techniques can improve efficiency and accuracy when we use Monte Carlo simulation in pricing path-dependent exotic options. In this paper, we compare the variances of simulation prices obtained by using naïve Monte Carlo simulation with those obtained by using Monte Carlo simulation with different efficiency improvement techniques. The results represent improvement in effieciency. We also compare the simulation price obtained by using Monte Carlo simulation with different efficiency improvement techniques with analytical solutions to check improvement in accuracy. Through the approaches mentioned above, we compare improvements in speed, efficiency, and accuracy of different efficiency improvement techniques.Besides, this paper also use the concept of conditional probability to improve accuracy in pricing barrier options and lookback options