On Arithmetic-Average Asian Power Options: Closed Forms and Explicit Methods for Valuation

The article considers arithmetic-averageAsian power options whose underlying follows geometric Brownian motion. Integral representations and consequent explicit methods for valuation are developed, with the former obtained by analytic inversion of a Laplace transform of Yor's. Principal methods for the replication of contingent claims on averages by Asian power options portfolios are derived. The results are numerically demonstrated in the case of Asian option valuation.