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Outperformance Options

To me, outperformance options1 are especially interesting because of the alternating layers of complexity and simplicity you discover as you probe more deeply into their valuation.

This note describes a journey through these layers. First we describes the outperformance option’s payoff, a simple function of two underlyers. But valuing a two-underlyer options seems compli- cated; each underlyer has to be hedged. It turns out that, if you think about it the right way, a gen- eral principle lets you find the correct and simple formula for its value. Even an options novice, who understands only single-underlyer options and the Black-Scholes formula, already knows everything necessary to value it, European- or American-style. We then examine the simple for- mulat for the outperformance option value, and notice a surprising, elegant and at first puzzling relation among its two hedge ratios. Finally, we explain the origin of this result.

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