PAT - The Payoff Advantage Tool
Call Options on Asset 2 and Asset 3

Asset 1: Call options on Asset 2 and Asset 3 in terms of Asset 1.

Formula: H1 = max(s12 - X1, 0) + max(s13 - X2, 0)

Asset 2: unidentified Asset 3: unidentified

Here we have a case where our original payoff in terms of Asset 1 is dependent on both Asset 2 and Asset 3. Clearly the level of complexity has increased. Still we can notice clear signs of symmetry between all of the payoffs, which helps us to understand how all of them can be financially equivalent and hence interchangeable.

When analyzing the payoffs in terms of Asset 2 and Asset 3, we notice elements known to us already from before. We will see that this case of two options on different assets is just an extension of a previous case, which was an option on one asset viewed from a three-asset perspective.

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