蒙地卡羅模擬法在美式選擇權評價之應用

Pricing American Options Using Monte Carlo Simulation

張森林(San-Lin Chung) ； 何振文(Chen-Wen Ho)

《財務金融學刊》 10卷3期 (2002/12) Pp. 33-61

https://doi.org/10.6545/JFS.2002.10(3).2

摘要

文獻上已有學者利用蒙地卡羅模擬法來評價美式選擇權，其中Barraquand and Martmeau（BM, 1995）將資產價格之狀態空間予以分隔，並觀察每條路徑在不同區域間移動的機率，再以類似二項式的方式回推加以求解。Raymar and Zwecher（RZ, 1997）則修正BM的模型，將資產價格之狀態空間分隔成兩個維度以提高估計值的準確性。在本文中，我們發現BM及RZ兩模型對於持有價值的估計有所偏誤，並進一步提出修正模型，模擬分析的結果顯示：（1）、修正模型較BM模型或RZ模型而言，可以增加對於美式選擇權價值估計的準確程度；（2）、不同的區塊分隔方式以及不同的區塊分隔因子會影響到估計值的準確程度和收斂速速度；（3）、修正模型對於五種美式選擇權評價均有不錯的效果。

關鍵字

蒙地卡羅模擬法 ； 選擇權評價 ； 美式選擇權 ； 持有價值

並列摘要

This paper modifies Barraquand and Martineau (BM, 1995) and Raymar and Zwecher (RZ, 1997) models to value American options using Monte Carlo simulation. The contribution of this article is threefold. First, we point out that the holding values in the BM and RZ models are biased. We then propose a correction model and show that the point estimate, low estimate, and high estimate of American option values calculated from our model are more accurate than those obtained from the BM and RZ models. Second, we investigate how the bucket formation method and the number of buckets will affect the accuracy and convergence of price estimates Third, we show that our model is appropriate for valuing many American-style options such as barrier. lookback, and Asian options etc.

並列關鍵字

Monte Carlo simulation ； option valuation ； American option ； holding value

參考文獻

Barraquand, J.,Martineau, D.(1995).Numerical Valuation of High Dimensional Multivariate American Securities.Journal of Financial and Quantitative Analysis.30(3)

Barraquand, J.,Pudet, T.(1996).Pricing of American Path-Dependent Contingent Claims.Mathematical Finance.6

Black, F.,Scholes, M. S.(1973).The Pricing of Options and Corporate Liabilities.Journal of Political Economy.81(3)

Boyle, P.(1977).Options: A Monte Carlo Approach.Journal of Financial Economics.4

Broadie, M.,Glasserman, P.(1997).Pricing American-Style Securities Using Simulation.Journal of Economic Dynamics and Control.21(8/ 9)