On the valuation of arithmetic-average Asian options: the Geman-Yor Laplace transform revisited

Abstract

The 1993 Laplace transform approach of Geman and Yor is a celebrated advance in valuing Asian options. Its insights are fundamental from both a mathematical and a financial perspective. In this paper, we discuss two observations regarding the financial relevance of its results. First, we show that the Geman and Yor Laplace transform is not that of an Asian option price, as reported in Geman and Yor and other papers. We nonetheless show how the Geman and Yor Laplace transform can be used to obtain the price of an Asian option. Second, we find that following Geman and Yor these Laplace transfoms are available only if the risk-neutral drift is not less than half the squared volatility. Using complex analytic techniques, we lift this restriction, thus extending the financial applicability of the Laplace transform approach.