Rough volatility in foreign exchange markets

Absztrakt (kivonat)

In recent years the application of fractional Brownian motion in financial modelling has become widespread both in theoretical finance and financial econometrics. In their seminal paper Gatheral et al (2014) have shown that, their fractional Brownian motion-based model performs better, than standard econometric models at predicting realized volatility of different equity indexes. In this study we will analyze the evolution of the volatility of different liquid and illiquid foreign exchange rates. Our hypothesis is that FX volatilities exhibit the same smoothness feature as equity volatilities. Despite the different characteristics of the volatility on currency markets we expect the Rough Fractional Volatility model to perform well in predicting the realized variances. In order to test our hypothesis we used high-frequency datasets for 6 currencies. Our results are encouraging, because our model proved to be a superior forecasting tool of realized variance compared to other econometric models.