選擇權隱含風險中立機率密度函數之解釋能力與預測能力的檢驗──以外幣選擇權為例

Explanatory and Predictive Powers of Option Implied Risk Neutral Density: Evidence from FX Options

本研究乃探討由選擇權價格所隱含之風險中立機率密度函數（Risk Neutral Density）的資訊內涵，透過2006年1月至2016年7月的四種貨幣（歐元、日圓、南非幣以及人民幣）兌換美元的選擇權市場資料（共計552筆週資料），我們獲得新的研究發現。首先是風險中立機率密度函數比隱含波動率（Implied Volatility）能涵蓋更多資訊。其次，風險中立機率密度函數的三階動差與外幣交換曲線（Foreign Exchange Swap Curve）有很高的相關。另外，本研究亦發現風險中立機率密度函數的動差對災難性事件比隱含波動率有更高的敏感度。最後，本研究亦發現用中立機率密度函數所衡量的三、四階動差對於預測匯率變動的能力會比隱含波動率來得高。

In this paper, we study information contents of the risk neutral densities (RND) implied by option prices. Using weekly options data of multiple currencies (Euro, JPY, ZAR, and RMB) during the period from January 4, 2006 till July 27, 2016 (total of 552 weeks), we have the following innovative findings: (1) RND moments contain more information than implied volatility; (2) the third moment of the RND has substantially high correlation with FX swap curves; (3) the moments of the RNDs are much more sensitive to catastrophic events than the implied volatility; and (4) the third and fourth moments have higher predictive powers for exchange rate movement than the implied volatility does.