The Information Content Of Option Implied Risk Neutral Density

Volatility smile has been widely used for studying the information content of the option markets.If the assumption of the Black-Scholes model is correct,the implied volatility of each strike price should have the same value.However,the implied volatility from the market price of a series of options is different with respect to different strike price,which constitute the phenomenon of volatility smile.Breeden and Litzenberger(1978)think one can retrieve Risk Neutral Density(RND)from the volatility smile.Recent asset pricing literature has focused on "crash risk".In particular,Gabaix et.al.(2008)and Farhi and Gabaix(2016)study the crash risk in the currency market.Gabaix et.al.(2016)uncover that since the Fall of 2008,"crash risk" has increased dramatically,implied by the FX options data.Motivated by Gabaix et.al.and the literature,and furthermore the recent troubles in the Euro zone(since 2008),we use the EUR/USD exchange rate to study the information contents of its RNDs since the crisis.We study the EUR/USD exchange rate risk-neutral density(RND)that results in a number of novel findings.Using daily data from EUR/USD FX options during the period from January 2,2008 till March 18,2015,we discover that RND(especially higher moments)has superior explanatory powers in predicting and explaining crash risk and its risk premiums.Furthermore,our empirical results show that the higher moments of RND co-move closely with macroeconomic variables.In all cases,we find moments outperform the implied volatility from the Black-Scholes model.This research has some findings.(1)The third and fourth moments in this paper show constantly better than implied volatility in explaining FX swap spread,which been treated as a proxy of risk premium.(2)The third and fourth moments can successfully explain crash risk,like Lehman crisis,flash risk,and euro sovereign risk.(3)The third and fourth moments can also preditct spot level.(4)Shorter maturity(less than 3 months)fourth moments is driven by speculation behavior from the market participants,and longer maturity is driven by the physical export/import activities.(5).Higher order moments can predit economic policy index and USD influence index.(6).The fourth moments have better power in predicting future realized variance/volatility.