Asian options: European American Arithmetic and Geometric Averaging

Abstract

First, we demonstrate a recursive integration technique for pricing European-style Asian options, whereby a multidimensional integral in the pricing formula is replaced by a recursive sequence of one-dimensional integrals involving the univariate normal distribution. Second, we analyze American-style Asian options by deriving a canonical optimal stopping problem from which early exercise boundaries can be obtained, and developing a decomposition approach to evaluate American-style Asian option values as the sum of European-style Asian option values and a corresponding early exercise premium. We show how the recursive integration technique can be used on the computation of this premium. Asian options based on both arithmetic and geometric averaging are discussed in this talk. (This is joint work with T.L. Lai.)