Recovering Risk-Neutral Implied Probability Distributions of the Taiwan Stock Index Options

[[abstract]]本篇研究可分為兩部分，第一部分為利用台指選擇權與台指期貨的收盤價，藉由Black-Scholes公式，求算指數選擇權的隱含波動率，以探討台灣指數選擇權市場是否存在波動微笑現象。第二部份為依循Rubinstein的『最適方法』，利用台指選擇權與台指期貨的收盤價與最後買賣價，找出台指選擇權之風險中立隱含機率分配。本文選取的資料為2003年台灣期貨交易所所交易的台灣發行量加權股價指數選擇權與台灣發行量加權股價指數期貨的每日收盤價與最後買賣價格，得到的主要結果如下： 1.台指選擇權的隱含波動率呈現類似美國外匯選擇權市場的波動微笑(volatility smile)現象，而較不類似美國權益選擇權市場的波動偏態(volatility skew)現象。 2.台指選擇權的風險中立隱含機率分配非常近似於對數常態分配，並不存在Rubinstein(1994)的駝峰(hump)現象。 3.2003上下半年之間的隱含機率沒有顯著差異，顯示投資人在2003年並沒有顯著的學習效果存在。[[abstract]]This article contains two major parts. The first is to calculate the implied volatilities of the Taiwan Stock Index Options using Blank-Scholes model and the daily last prices of the Taiwan Stock Index Options and Futures. And then, we can find if there exists volatility smile in Taiwan’s stock index options market. The second is to find the risk-neutral implied probability of the Taiwan Stock Index by Rubinstein’s “Optimization Method” and the daily last bid prices, ask prices, and exchange prices of the Taiwan Stock Index Options and Futures. We used the daily data in 2003 and found: 1.The implied volatility plot of the Taiwan Stock Index Options is similar to the one of currency options in America, which we call “volatility smile”, and is not similar to the one of equity options in America, which we call “volatility skew”. 2.The risk-neutral implied probability distribution of the Taiwan Index Options is really close to the lognormal distribution. We can not find any hump just like in Rubinstein(1994). 3.The risk-neutral implied probability distribution of the second half of the year has no remarkable difference from the one of the first half. It seems there is no learning effect in Taiwan Stock Index Option Market during 2003