I need some clarifications regarding spread options. I have always found them characterized as paying, at maturity, the difference between the prices of two underlying assets: $$ (S_1(T)-S_2(T)-K)^+ $$ I have been presented with the task of pricing a spread option paying, at maturity, the difference between the performance of two underlying assets, as in: $$ \left(\frac{S_1(T)}{S_1(0)} - \frac{S_2(T)}{S_2(0)} - K)^+\right) $$ Since I have not found explicit references to the form above, I am wondering what are the differences in terms of tractability. How does the level of the spot price impact the problem? Does this form belong to the family of models for spread options that is analytically tractable?
1 Answer
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If you are using a model such as BS where the distribution of $S_{j}(T)/S_{j}(0)$ does not depend on $S_{j}(0)$ it really makes very little difference. Just take the initial stock prices to be $1$ and away you go.
