Asset 1: Put Option on Asset 2 in terms of Asset 1 Formula: H1 = max( X1 - S12, 0)

Asset 2: Call Option on Asset 1 in terms of Asset 2

Asset 3: Spread Option on Asset 1 and Asset 2 in terms of Asset 3

Please compare charts for assets 1 and 2 in this diagram with the one in the "PAT in Two-Asset Environment" section. You will see that the payoffs are the same - this is again the case of a put-call pairing in a two-asset environment: every put or call option on one side of the market has a financially equivalent call or put option on the other side of the market.

The chart for Asset 3, however, is different. This is a logical result to expect because the Asset 3 payoff has to take into account the two different payoffs of Asset 1 and Asset 2. From the shape of the Asset 3 payoff we can see that it is a well-known exotic option — a Spread Option on Assets 1 and 2.