論文主要使用以選擇權為未來交割商品的期貨的概念，架構出遠期選擇權的訂價方法，在假設市場上存在可交易的期貨商品，且滿足無套利的情況下，利用兩個不同到期日的選擇權價格，得到遠期選擇權的訂價公式。並且透過Black-Scholes訂價公式，使用S&P500指數選擇權的價格資料，在假設股價走勢符合幾何布朗運動下，計算出遠期選擇權價格，並且進一步計算得到隱含遠期波動率。
使用芝加哥期權交易所（CBOE）發行的波動率指數商品VIX期貨，作為未來的隱含波動率，並和使用遠期選擇權價格計算出的隱含遠期波動率比較，驗證其預測效果。

We introduce a new pricing formula on forward options, and we add the concept of futures whose underlying asset is an option. Under the assumption of no-arbitrage, we use two options of different maturities to get the price of the forward option. Then, we put relative parameters into Black-Scholes pricing formula, getting the volatility which is so-called the implied forward volatility.
After computing the implied forward volatility from the formula of forward options, we will use data of VIX futures to make comparison. We also compare with forward volatility and examine the predictability of it.

第一章 緒論 1
1.1 研究背景 1
1.2 研究動機 2
第二章 文獻回顧 5
第三章 研究方法 7
3.1 遠期選擇權訂價公式 7
3.2 Black-Scholes 訂價公式 10
3.3 隱含遠期波動率 12
3.4 VIX 期貨 13
第四章 實證分析 14
4.1 資料 14
4.1.1 S&P500 指數選擇權 15
4.1.2 VIX期貨 18
4.2 波動率預測比較 20
4.2.1 平均絕對誤差與均方誤差 20
4.2.2 迴歸分析 23
4.2.3 Fama 迴歸分析 28
第五章 結論 32
參考文獻 33

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