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.