标题： 关于算术平均亚式期权的定价：拉盖尔级数和Theta积分 显示英文标题

标题： On the valuation of arithmetic-average Asian options: Laguerre series and Theta integrals

摘要： 最近的重大进展中，Dufresne 使用拉盖尔级数将亚式期权的定价问题简化为计算Yor积累过程的负矩。 对于这些过程，他给出了功能递归规则，其概率结构已成为Yor及其同事近期深入研究的对象。 本文强调了Theta函数的作用，现在解出了这些递归规则，并将这些负矩表示为某些Theta积分的线性组合。 利用雅可比变换公式，得出了它们的收敛速度非常快且数值非常稳定的级数。 这样得到了可用于计算亚式期权Black--Scholes价格的可计算级数，并进行了数值说明。 此外，使Dufresne的拉盖尔级数方法严格化，并讨论了扩展和修改。 关键在于对Yor 1992年提出的亚洲密度的可积性和增长性质的分析，这些问题似乎首次在此得到解决。 显示英文摘要

摘要： In a recent significant advance, using Laguerre series, the valuation of Asian options has been reduced by Dufresne to computing the negative moments of Yor's accumulation processes. For these he has given functional recursion rules whose probabilistic structure has been the object of intensive recent studies of Yor and co-workers. Stressing the role of Theta functions, this paper now solves these recursion rules and expresses these negative moments as linear combinations of certain Theta integrals. Using the Jacobi transformation formula, very rapidly and very stably convergent series for them are derived. In this way computable series for Black--Scholes price of the Asian option result which are numerically illustrated. Moreover, the Laguerre series approach of Dufresne is made rigorous, and extensions and modifications are discussed. The key for this is the analysis of the integrability and growth properties of Yor's 1992 Asia density, basic problems which seem to be addressed here for the first time.