Semivariance and Semiskew Risk Premiums in Currency Markets

Abstract

Using the model-free methodology proposed in the literature, variance and skew swaps are extracted from currency options for several foreign exchange rates. Moreover, these variables are decomposed into semivariance and semiskew swaps, which are conditional to the evolution of the foreign exchange rate, and it is shown to have higher explanatory power for currency excess return. These semivariances enable the definition of a variance-skew swap that also possesses a strong explanatory power for currency excess return. From these variables, higher moment semi-risk premiums can be computed and measure how tail risks are priced. These semivariance and semiskew swaps better explain the currency excess return than the standard or undecomposed ones. For semivariance swaps, both the up and down contracts are equally informative while for semiskew swaps only the down tail related one is. Down semivariance and semiskew swaps carry complementary information regarding the currency excess return. Trimming these variables enables us to show that extreme movements affecting the currency option market contain no information on the evolution of the currency. Lastly, forecasting tests further illustrate the importance of decomposing the variance and skew swaps into semi components as it improves significantly the results.