台指選擇權隱含風險趨避估計

Abstract

我國選擇權市場於民國九十年十二月二十四日正式創立，至今已經過了八個年頭，臺指選擇權目前已經成為股票市場中投機及避險的主力商品，連帶的也使得選擇權的每日成交資料更具有連續性，更具有參考價值。本文即是利用台指選擇權的買權及其標的物的歷史資料，透過一些假設及條件限制，結合隱含波動率及投資人效用函數的方式來估計台灣股票市場的風險趨避測度值，另透過比較不同效用函數，來找出其中的差異性及對於選擇價格資訊的解釋能力到底孰優孰劣，並希望能透過風險趨避測度值的變化，來探討投資人的風險趨避測度值是否會因選擇權履約價的高低、標的物價格的高低、距到期日的長短以及隱含波動率的高低而有所變化，找出其間的相關性，俾能對於金融市場的波動有所掌握。 由本文所觀察到的結果來看，相對風險趨避測度值與其本身的標準差、標的物價格、履約價、距到期日長短都是呈現正向變動的情形，與隱含波動率則是呈現反向波動的情形，顯示影響選擇權價格的這幾項因素均會對於投資人的風險趨避程度產生影響。

Our country option market established officially in December 24, 2001, until now passed through for eight years. The option products already become the main force products in the Taiwan stock market. While applied to the European-style TWSE index options from 21 June 2007 to 16 December 2008, this paper makes an assumption that the underlying asset price follow lognormal distribution to find out the relative risk aversion. Given the daily option closing price, we can transfer it to implied volatility by the B-S option pricing model. By the implied volatility and the utility functions of investors, we can find out the relative risk aversion. Our empirical results reveal significant evidence of positive relation between relative risk aversion and underlying asset price, time to maturity, option strike price, and the standard deviation of itself. The results also reveal the negative relation between relative risk aversion and implied volatility.