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 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.

Master the new edge in options trades: the hidden volatility risk premium that exists in options for every major asset class. One of the most exciting areas of recent financial research has been the study of how the volatility implied by option prices relates to the volatility exhibited by their underlying assets. Here, I’ll explain the concept of the volatility risk premium, present evidence for its presence in options on every major asset class, and show how to estimate, predict, and trade on it....

I derive the volatility risk premium in FX market from a consumption based model. High volatility corresponds to low consumption growth of professional FX market participants, so they are ready to pay a premium for holding assets correlated with volatility shocks. This premium is not decreased to zero by households, because they can only participate in FX market through asset managers. Asset managers optimize their utility from performance-based compensation. This makes them behave as if they are owners of the funds deriving all their income from investment activities and they require a compensation for the risks that they take. The size of risk premium is determined by the asset manager's risk aversion and their compensation structure. I test the model prediction that the volatility risk premium is different in FX and stock market and find that the difference in estimates is highly statistically significant.