This paper focuses on constructing an optimal hedge ratio for exchange rate hedging by using future contracts. We use the returns of British and American stock markets and the returns of their respective domestic currencies to construct hedge ratios. We consider an extension of Gaussian copula theory by allowing its correlation parameter to vary over the time, thus enabling us to observe how the correlation parameter moves over the time. Patton’s evolution equation for Gaussian copula and the Dynamic Conditional Correlation models are used in order to model the correlation, allowing it to vary over the time. In the end they will be compared as to which method produces hedge ratio with higher utility.