关于算术平均值亚式期权的估值：Laguerre级数和Theta积分
On the valuation of arithmetic-average Asian options: Laguerre series and Theta integrals
摘要：
在最近的一个重大进展中，使用Laguerre级数，亚式期权的估值已经被Dufresne减少到计算Yor累积过程的负矩。对于这些，他给出了功能递归规则的概率结构一直是对象的密集最近的研究Yor和同事。强调θ函数的作用，本文现在解决这些递归规则，并表示这些负矩为某些Theta积分的线性组合。利用Jacobi变换公式，导出了它们的非常快速且非常稳定的收敛级数.用这种方法得到了亚式期权的Black-Scholes价格的可计算序列，并给出了数值例子。此外，Laguerre级数的方法的Dufresne是严格的，并讨论了扩展和修改。这里的关键是分析Yor的1992年亚洲密度的可积性和增长特性，这些基本问题似乎是第一次在这里讨论。
英文摘要：
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.
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