Asset 1: Square-Root function Formula: H1 = SQRT (S12)

Asset 2: Square-Root function

Asset 3: unidentified

When comparing this payoff with the one in the "PAT In Two-Asset Environment" section, we again notice that as our original payoff is dependent on S12 only (the "exchange rate" of Asset 1 vs. Asset 2), payoffs for assets 1 and 2 represent the two-asset case. The payoff for Asset 3, however, is quite different again. As we said in the previous section, the square-root function is one of the very few cases when the payoffs on both sides of the market are exactly the same. This is clearly not the case in a three-asset environment.