數位選擇權避險參數之蒙地卡羅法估計

Monte Carlo Estimation of Digital Option Greeks

陳俊傑(Chiun-Chieh Chen) ； 張曉欽(Hsiao-Chin Chang) ； 楊晴雯(Cing-Wun Yang)

《建國科大社會人文期刊》 35卷1期 (2016/01) Pp. 1-20

摘要

自從Black-Scholes 公式於1973 年被發表後，使得選擇權市場發展蓬勃，連帶其他相關金融商品交易也日漸活絡。面對這麼多金融商品的競爭，爲能減低避險成本，其中如何做出正確的評價以及避險，自然是每一位投資者所關注的焦點。數位選擇權普遍被應用於結構型商品中，加上其避險參數所具有的特殊性質，導致避險部位的估計需更加留意，有鑑於張森林(2005)所述類似歐式選擇權MCBS法之償付平滑函數的效果，亦可適用於數位選擇權之推論，本研究修正MCBS法，另外提出結合數位選擇權公式解之MCD 法，藉以檢視相關避險參數估計的可靠性。研究結果顯示，MCD 法對數位選擇權避險參數的估計皆比蒙地卡羅法更加準確，且較不易受擾動量大小的影響；然而MCD 法雖可有效改善Delta 值的模擬，但對於Gamma 值之估計，其所得結果則依舊是不甚理想，亦即有關償付平滑函數在歐式選擇權的作用，並無法完全適用於數位選擇權上。

關鍵字

數位選擇權 ； 避險參數 ； 蒙地卡羅法

並列摘要

Since the Black-Scholes Model has been issued in 1973, the options market has become more flourishing, consequently revitalizing the growth of financial instruments trade. Faced with such great competition, how to decrease hedging cost, especially including how to make correct evaluations and risk-hedging decisions, has drew the attention from each of investors nowadays. Digital options are widely applied to structured products, and its hedge parameters are so unusual that we need to be more careful about the estimation of risk hedging. In view of what Chung(2005) mentioned that the effect of the smooth convex function from a method similar to Monte Carlo with Black Scholes (MCBS) method can be applied to the inference of digital options. This study revises MCBS method and suggests MCD method, which is the solution to combine Monte Carlo simulation with the digital option formula, so it can survey the reliability of related hedge ratio estimates. The findings indicate that MCD method is more accurate than Monte Carlo method in calculating the hedge ratios of digital options, and additionally it is not sensitive to the perturbation h. Although MCD method can effectively improve the simulation of the Delta estimates, it still can not improve the accuracy of the Gamma estimates, which means that the effect of the smooth convex function on MCBS method cannot be applied to digital options at all.

並列關鍵字

Digital Options ； Hedge Ratios ； Monte Carlo Method