Implementing the Implied Volatility Tree for S&P 500 Options: Evidence from the Kernel-Regression Volatility Surface with an Algorithm for Dealing with Bad Transition Probabilities

隱含波動樹在核迴歸波動度曲面上定價：史丹普500指數選擇權之實證演算法設計

10.6545/JFS.2009.17(2).2

林月能(Yueh-Neng Lin)

隱含波動樹 ； 核迴歸 ； 隱含波幅曲面 ； Implied Volatility Tree ； Kernel Regression ； Implied Volatility Surface

財務金融學刊

17卷2期（2009 / 06 / 30）

35 - 70

英文

本文使用核迴歸方法計算隱含波幅曲面，並建構演算法對史丹普500指數選擇權刻釗出隱含在該核迴歸波幅曲面中的隱含波動樹。該隱含波幅曲面與隱含波動樹皆有相對應的風險中立機率分配，給由比較核二分自己之相似性，可得知隱含波動樹是否能提供合理的史丹普500指數選擇權價格。本文使用三個統計撿定量、樣本外預測與避險績效來測試兩分配是否相似之議題。實證結果發現隱含波動樹對短期與中期史丹普500指數選擇權較長期選擇權於樣本期間內（1990至1995）能提供較佳的自己適度。

This paper implements an algorithm to infer. from the implied volatility tree, the risk-neutral density that is comparable to the one implicit in the kernel-regression volatility surface on which the tree is constructed. The equality between these two densities becomes an empirical issue on the validity of the tree model in option pricing. Three statistical tests, out-of-sample fit and hedging effectiveness are investigated for the S&P 500 index options from January 1990 to December 1995. The matches between these two densities for 30-day and 100-day options are found, while the inaccuracy for 300-day options is remarkably stable for different periods.

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