Using Simulated Currency Rainbow Options to Evaluate Covariance Matrix Forecasts

When choosing evaluation measures for variance and covariance forecasts one has to consider what the actual purpose of these forecasts is. In this paper we extend the results of Gibson and Boyer (1998) by looking at portfolios of rainbow currency options and how simulated trading of such options portfolios can be used as a preference free evaluation measure for the forecasted covariance matrix. The advantage of using portfolios instead of single options is the possibility it gives of relying on shorter return series. We apply the methodology to a system of four U.S. dollar exchange rates and compare the relative performance of different forecasting models. In doing this, we also apply and evaluate the fairly new Orthogonal GARCH technique to exchange rates, both with the option evaluation technique and with standard statistical measures