Why Smiles Exist in Foreign Exchange Options Markets: Isolating Components of the Risk Neutral Process

Abstract

Prices of foreign exchange options systematically diverge from those consistent with several previous option pricing models. This paper examines whether alternative models better explaining the empirical dynamics of the foreign exchange futures markets can yield implied volatility surfaces similar to those observed for options on Foreign Exchange futures. The most suitable alternative models include jumps and stochastic volatility. The inclusion of both these factors introduces unspanned sources of risk and therefore, the martingale measure will not necessarily be unique. However, it is not the objective of this research to propose which martingale measure is optimal; the aim, instead, is to gain a deeper understanding of the properties (and particularly the order of magnitude) of the risk premium. This is done by choosing a feasible martingale measure (based upon the no arbitrage condition), assuming no market price of jump or stochastic volatility risks, and price options under this measure. The implied volatility biases from model-based option prices are then compared to the actual implied volatility surfaces for options on these markets. The systematic and substantive differences that are found suggest a negative risk premium, which is a relatively more important (and universal) component in FX option pricing than previously reported. Furthermore, it appears that the relative risk premium across strike price and time is similar across four foreign exchange options markets. This may imply that some systematic mechanism causes the risk premium in these markets.