Another look at the integral of exponential Brownian motion and the pricing of Asian options

作者：Lyasoff Andrew^*

来源：Finance and Stochastics, 2016, 20(4): 1061-1096.

DOI：10.1007/s00780-016-0307-1

• Exponential Brownian motion
• Random environment
• Asian options

It is shown that Marc Yor's formula (Adv. Appl. Probab. 24:509-531, 1992) for the density of the integral of exponential Brownian motion taken over a finite time interval is an extremal member of a family of previously unknown integral formulae for the same density. The derivation is independent from the one by Yor and obtained from a simple time-reversibility feature, in conjunction with a Fokker-Planck type argument. Similar arguments lead to an independent derivation of Dufresne's result (Scand. Actuar. J. 90:39-79, 1990) for the law of the integral taken over an infinite time interval. The numerical aspects of the new formulae are developed, with concrete applications to Asian options.

• 出版日期2016-10