I use forward-looking information available in stock market volatility indices to predict forex returns. In particular, I find that equity variance risk premiums (VRPs) -- the difference between the risk-neutral and statistical expectations of market return variation -- predict forex returns at a one-month horizon, both in-sample and out-of-sample. Moreover, compared to the major currency carry predictors, global VRP has more predictive power for currency carry trade returns, bilateral forex returns, and excess equity return differentials. To formalize the link between equity VRPs and forex returns, I provide a long-run risk model with stochastic volatility and complete markets, where the expected forex returns are a function of consumption growth variances and equity VRPs.

Sellers of variance swaps earn time-varying risk premia for their exposure to realized variance, the level of variance swap rates, and the slope of the variance swap curve. To measure risk premia, we estimate a dynamic term structure model that decomposes variance swap rates into expected variances and term premia. Empirically, we document a strong global factor structure in variance term premia across the U.S., U.K., Europe, and Japan. We further show that variance term premia are negatively correlated with the risk appetite of hedge funds, broker-dealers, and mutual funds. Our results support the hypothesis that financial intermediaries are marginal investors in the variance swap market.

This book mainly addresses the general equilibrium asset pricing method in two aspects: option pricing and variance risk premium. First, volatility smile and smirk is the famous puzzle in option pricing. Different from no arbitrage method, this book applies the general equilibrium approach in explaining the puzzle. In the presence of jump, investors impose more weights on the jump risk than the volatility risk, and as a result, investors require more jump risk premium which generates a pronounced volatility smirk. Second, based on the general equilibrium framework, this book proposes variance risk premium and empirically tests its predictive power for international stock market returns.