從選擇權價格萃取風險中立下的機率分佈

Abstract

本文展示數種方法，如何從金融資產價格中推導出市場隱含的風險 中立機率。我們選擇聯邦利率期貨與歐洲美元選擇權進行研究，又因 兩者都與美國利率有直間關係，我們認為兩個市場應彼此連結在一起， 不會脫鉤。為了證明我們的想法，我們進行事件研究，研究訊息是如 何影響市場對2016 年底的利率的看法。藉由5/19/2016 與6/6/2016 兩 天的資料，我們可以推導出市場對遠期利率在風險中立下的機率分布， 進而證實我們的想法，即是無論從哪個市場出發都能得到一致的結論。 因此，本文展示的方法的確合理且有效。

This article shows the methodology of extracting risk-neutral probability density distributions (denote RNDs) from two financial instruments, the Fed Fund futures and the options on Eurodollar futures. Since both of them are related to U.S. interest rate, we believe they share same properties. To confirm this idea, we do the event study for how the information impacting the expected forward rate in the end of 2016. We derived RNDs from the data in 5/19/2016 and 6/6/2016. The influences of the impact are similar in all of the results. In conclusion, the Fed fund futures market and options on Eurodollar futures are consistent with each other. Therefore, it shows the methods are reasonable and reliable.