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

The Laplace transform approach of [GY] is a celebrated advance in valuing Asian options. Its insights are fundamental from both a mathematical and a nancial perspective. In this paper, we discuss two observations regarding the nancial relevance of its results. First, we show that the [GY] Laplace transform is not that of an Asian option price, as reported in [GY] and other papers. We nonetheless show how the [GY] Laplace transform can be used to obtain the price of an Asian option. Second, we nd that following [GY] 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 nancial applicability of the Laplace transform approach.