Within the Heath-Jarrow-Morton model and given the geometric Brownian motion processes for all currency exchange rates, this paper studies: (1) the pricing and hedging of diff swap which notional principal is denominated in the 3rd country currency, and (2) the concept of pricing duality. A pricing formula for such a diff swap is derived under a unique equivalent martingale measure Q. This pricing formula includes that derived in Turnbull (1993), Wei (1994), and Chang, Chung and Yu (2001) as a special case. Moreover, simulations are performed to study the constant spread rate and correlation parameters. Finally, this paper discusses the concept of pricing duality. With this concept, diff swaps with notional principal denominated in foreign and the 3rd country currencies can be easily priced.
