EXPONENTIAL MOMENTS OF AFFINE PROCESSES

• 成果类型: Article
• 署名作者: Keller-Ressel, Martin; Mayerhofer, Eberhard
• 署名单位: Technical University of Berlin; Dublin City University
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/14-AAP1009
• 发表日期: 2015
• 页码: 714-752
• 关键词: stochastic volatility; term structure; models; Explosions; options; jumps

摘要

We investigate the maximal domain of the moment generating function of affine processes in the sense of Duffle, Filipovie and Schachermayer [Ann. AppL Probab. 13 (2003) 984-1053], and we show the validity of the affine transform formula that connects exponential moments with the solution of a generalized Riccati differential equation. Our result extends and unifies those preceding it (e.g., Glasserman and Kim [Math. Finance 20 (2010) 1-33], Filipovie and Mayerhofer [Radon Ser. Comput. Appl. Math. 8 (2009) 1-40] and Kallsen and Muhle-Karbe [Stochastic Process Appl. 120 (2010) 163-181]) in that it allows processes with very general jump behavior, applies to any convex state space and provides both sufficient and necessary conditions for finiteness of exponential moments.