Static Hedging of Asian Options under Lévy Models

The Asian option pricing problem is a lot like the American put problem in the 1970s. An Asian payoff is a rather simple, and common, option feature, but it messes up our clean, closed-form valuation equations. This situation is apparently a persistent source of annoyance to mathematicians and other quants, who respond with an outpouring of creativity, in the form of theory, algorithms, and approximate solutions. Although this may seem like overkill for the specific problem at hand, it produces useful new ideas and techniques for our general derivatives valuation toolkit. In this article, Albrecher et al, introduce a new approach to pricing Asian options, based on the principle of comonotonicity and the “stop-loss transform.” They derive tight bounds on the value, even when the underlying asset's price follows a Lévy process, rather than a Gaussian diffusion. As with many of the solutions to the American put problem, this technique can potentially be applied to a much broader class of valuation problems.