Abstract
Recently differential swaps have become a popular financial instrument because it could mitigate the exchange rate risk. Although the market of differential swaps develops quickly, there has been little literature on the valuation of differential swaps. According to the observation of economic phenomenon and proof of many theses, we find that the interest rate might “jump” when certain events suddenly happen. As a result, we use affine jump diffusion model to capture the effect of shocks caused by the events. Because differential swaps are private contracts between two parties, the counterparty whose contract value is negative may default when the interest rate jumps. Thus, differential swaps may be very sensitive to the default risk. In the past, the default risk has not been heavily considered in other studies; therefore we added the element related to credit risk into our model. Using this model, we can derive the pricing formula of differential swaps and simulate the result. Most importantly, we find a more effective way to value differential swaps to assist the academic community to understand more about this financial instrument.