控制變數法運用於蒙地卡羅模擬法計算選擇權價格

Applying Control Variate Technique to the Monte Carlo Simulation of Option

本文討論如何將控制變數法運用於蒙地卡羅模擬法來計算奇異式選擇權價格，以減少選擇權價格估計值的標準誤，本文建議採用具有封閉解的控制變數選擇權，其邊界條件應盡量接近被評價奇之異式選擇權的邊界條件，本文建議可以採用Derman, Ergener and Kani （1995）的靜態複製法來尋找控制變數選擇權投資組合。本文的數值分析考慮了美式選擇權、障礙式選擇權、亞式選擇權及價差選擇權，數值分析的結果顯示好的控制變數選擇權可以有效地降低定價的標準誤。

Monte Carlo simulation is an important numerical approach for pricing complex options without closed-form solutions. In its basic form, however, Monte Carlo simulation is computationally inefficient and thus the control variate technique can be used to improve the efficiency. This paper presents a principle for finding good control variates, i.e. the boundary condition for the control variate should be as close to the boundary condition for the target option as possible. To do so, one can apply the static option replication portfolio approach proposed by Derman, Ergener and Kani (1995). In the numerical analyses, we price American put options, barrier options, Asian options, and spread options. The result shows that a good control variate can improve the efficiency of the simulation dramatically in a Monte Carlo simulation.