以往的文獻中，在計算選擇權的價值時，對於波動度的估計，大部份是假設其波動度為一固定常數，不然就是一些對波動度的變化做模型假設，如：GARCH、隨機波動度。但上述的模型都沒有考慮到景氣的變化與股票市場波動度的變化。在美國的實證資料中，表示股票市場波動度應該是跟著總體的經濟相關的，當經濟狀況較佳時，股票市場的波動度會較小，反之，當經濟狀況較差時，股票市場的波動度則會較大，此現象稱之為股票市場波動度的反循環變動。而上述的模型都沒有考慮到這點，故本論文的目的是希望結合Campbell and Cochrane (1999)，以考慮了習慣塑造的一般均衡模型，結合三元樹來評價選擇權，將股票市場的波動度與景氣循環的關係考慮進去，另外亦將無風險利率與景氣循環的函數關係也考慮進來，進而影響指數選擇權的價值。而以S&P500指數選擇權(SPX)實證結果顯示，本論文的模型顯然較單純使用固定常數波動度的Black-Scholes模型所計算的選擇權價值更為貼近實際市場價值。

When evaluating index options, most literatures assume the volatility to be constant, the GARCH process, the stochastic volatility process, etc. However, there is no one considering the relationship between the volatility and the stock market is closely related with the macroeconomic, for example, the volatility of stock market is relatively low in a boom and becomes relatively high in a recession. This phenomenon is the countercyclical variation of stock market volatility. For this reason, the goal of this paper is to develop a model to evaluate index options based on the consumption-based asset pricing model with habit formation in Campbell and Cochrance (1999), in which the relationship between the volatility of the stock market and the business cycle is considered. Moreover, the relationship between the risk-free interest rate and the business cycle is also taken into account, thereby affecting the value of index options. Empirical results on S&P500 index option shows that the option value derived in our model are more close to the actual market price than the Black-Scholes model which employs the constant volatility assumption.

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