We introduce a new representation of the bivariate normal distribution to first give a short derivation of the classic Margrabe exchange-option formula, using elementary integration methods. The second application is a new and simple technique to provide an accurate lower bound for the value of a spread option with a nonzero strike.
The simplified proof of the Margrabe formula, using elementary integration techniques, was developed in the context of a course on energy commodities that the author teaches in the Mathematical Finance Program at the University of Toronto. I thank the anonymous referee for comments and suggestions that helped to improve the presentation, and my wife Marguerite Martindale for a professional line edit.
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