APPROXIMATING LEVY PROCESSES WITH COMPLETELY MONOTONE JUMPS

• 成果类型: Article
• 署名作者: Hackmann, Daniel; Kuznetsov, Alexey
• 署名单位: York University - Canada
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/14-AAP1093
• 发表日期: 2016
• 页码: 328-359
• 关键词: wiener-hopf factorization; Asian options; barrier; stieltjes; driven; prices; FAMILY

摘要

Levy processes with completely monotone jumps appear frequently in various applications of probability. For example, all popular stock price models based on Levy processes (such as the Variance Gamma, CGMY/KoBoL and Normal Inverse Gaussian) belong to this class. In this paper we continue the work started in [Int. J. Theor. Appl. Finance 13 (2010) 63-91, Quant. Finance 10 (2010) 629-644] and develop a simple yet very efficient method for approximating processes with completely monotone jumps by processes with hyperexponential jumps, the latter being the most convenient class for performing numerical computations. Our approach is based on connecting Levy processes with completely monotone jumps with several areas of classical analysis, including Pade approximations, Gaussian quadrature and orthogonal polynomials.