Asymmetric skew Bessel processes and their applications to finance

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:186

Article

Decamps, M ; Goovaerts, M ; Schoutens, W

关键词: Bessel processes;    local time;    perpetuities;    Asian options;   

DOI  :  10.1016/j.cam.2005.03.067

来源: Elsevier

【 摘 要 】

In this paper, we extend the Harrison and Shepp's construction of the skew Brownian motion (1981) and we obtain a diffusion similar to the two-dimensional Bessel process with speed and scale densities discontinuous at one point. Natural generalizations to multi-dimensional and fractional order Bessel processes are then discussed as well as invariance properties. We call this family of diffusions asymmetric skew Bessel processes in opposition to skew Bessel processes as defined in Barlow et al. [On Walsh's Brownian motions, Seminaire de Probabilities XXIII, Lecture Notes in Mathematics, vol. 1372, Springer, Berlin, New York, 1989, pp. 275-293]. We present factorizations involving (asymmetric skew) Bessel processes with random time. Finally, applications to the valuation of perpetuities and Asian options are proposed. (c) 2005 Elsevier B.V. All rights reserved.

【 授权许可】

Free