Differences in beliefs and currency risk premiums

This paper studies the importance of heterogeneous beliefs for the dynamics of asset prices. We focus on currency markets, where the absence of short-selling constraints allows us to perform sharper tests of theoretical predictions. Using a unique data set with detailed information on foreign-exchange forecasts, we construct an empirical proxy for differences in beliefs. We show that this proxy has a strong effect on the implied volatility of currency options beyond the volatility of macroeconomic fundamentals. We document that differences in beliefs impact also on the shape of the implied volatility smile, on the volatility risk-premiums, and on future currency returns.     

The price of a smile: hedging and spanning in option markets

The volatility smile changed drastically around the crash of1987, and new option pricing models have been proposed to accommodatethat change. Deterministic volatility models allow for moreflexible volatility surfaces but refrain from introducing additionalrisk factors. Thus, options are still redundant securities.Alternatively, stochastic models introduce additional risk factors,and options are then needed for spanning of the pricing kernel.We develop a statistical test based on this difference in spanning.Using daily S&P 500 index options data from 1986-1995, ourtests suggest that both in- and out-of-the-money options areneeded for spanning. The findings are inconsistent with deterministicvolatility models but are consistent with stochastic modelsthat incorporate additional priced risk factors, such as stochasticvolatility, interest rates, or jumps.