Exponential moments of affine processes

Martin Keller‐Ressel · Eberhard Mayerhofer

72 citations0/0 files storedThe Annals of Applied Probability

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Stochastic processes and financial applications Financial Markets and Investment Strategies Probability and Risk Models

Abstract

We investigate the maximal domain of the moment generating function of affine processes in the sense of Duffie, Filipović 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], Filipović 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.

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1993A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options 1985A Theory of the Term Structure of Interest Rates 2003Financial Modelling with Jump Processes 1996A YIELD‐FACTOR MODEL OF INTEREST RATES 1999Option valuation using the fast Fourier transform 2001Non-Gaussian Ornstein–Uhlenbeck-based Models and Some of Their Uses in Financial Economics 2000Specification Analysis of Affine Term Structure Models 2000Post-'87 crash fears in the S&P 500 futures option market

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