Abstract
We investigate the maximal domain of the moment generating function of affine processes in the sense of Duffie, Filipovíc 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], Filipovic 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.
Original language | English |
---|---|
Pages (from-to) | 714-752 |
Number of pages | 39 |
Journal | Annals of Applied Probability |
Volume | 25 |
Issue number | 2 |
DOIs | |
Publication status | Published - 1 Apr 2015 |
Externally published | Yes |
Keywords
- Affine process
- Exponential moment
- Financial modeling
- Riccati equation