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.

This paper examines the properties of the variance risk premium (VRP). We propose a flexible asset pricing model that captures co-jumps in prices and volatility, and self-exciting jump clustering. We estimate the model on equity returns and variance swap rates at different horizons. The total VRP is negative and has a downward-sloping term structure, while its jump component displays an upward-sloping term structure. The abrupt and persistent response of the short-term jump VRP to extreme events makes this specific premium a proxy for investors' fear of a market crash. Furthermore, the use of the VRP level and slope, and of its components, helps improve the short-run predictability of equity excess returns.

Variance risk premium is arguably one of the most important and robust risk premia documented in the academic finance. The first chapter of this thesis deals with variance risk on the FX market: therein, I recover risk-neutralized covariance matrices of currency returns and combine them with ex post realized covariance matrices to determine the sign of the premium, associate portfolios ranked from highest to lowest premium values with popular currency factors, study the determinants of the FX variance risk and its explore asset pricing properties. I find evidence for an overall negative FX variance risk premium, but also document existence of strategies with a significantly positive one. Among portfolios with the most negative premium estimates, the US dollar index and Carry trade familiarly emerge. I report that portfolios of negative spot return momentum and high recently realized variance exhibit more negative FX variance risk premium. As far as the asset pricing properties are concerned, the Carry trade variance risk dominates the US dollar variance risk as a priced factor, contributing to resolution of the differential pricing of "good and bad'' carry portfolios. The second chapter studies the dynamics of currency spot and excess returns before policy rate announcements of central banks in developed economies. Therein, Dmitry Borisenko and I show that currencies depreciate before target rate cuts and appreciate before rate hikes. What makes the finding surprising is the fact that the fixed income derivatives market allows to forecast monetary policy decisions accurately enough to make the above drift exploitable by investors: our baseline specification of the trading strategy constructed by going long and short currencies before predicted local rate hikes and cuts earns a significant average return which would be only marginally higher if the forecast quality were perfect. In the third chapter, Nikola Mirkov, Paul Söderl.

I extend the evidence on the basic stylized facts documented for the U.S. variance risk premium (VP) and show that, while VPs in other countries are also positive and time varying, they do not have predictive power for domestic stock returns, in contrast to the implications of existing single-country models. I also provide new empirical evidence that the U.S. VP has predictive power for international stock returns. To rationalize these results, I propose a two-country general equilibrium model and show that my model explains the predictive power of U.S. VP for international stock returns and the domestic predictability puzzle.