Asset 1: Gap Put option on Asset 3 Formula: H1 = (X1 - s13) * heavy (X2 - s13)

Asset 2: unidentified

Asset 3: Gap Option Call

Again we have a situation where we can look at two of these payoffs as a two-asset scenario in the "PAT in Two-Asset Environment" section. But as we have a three-asset environment here, with the help of PAT, we can find a payoff in terms of our third asset (Asset 2) on assets 1 and 3 which is financially equivalent to the either one of the other two payoffs.

Next we would like to take some more complicated cases where our original payoffs can be dependent on more than just one asset.