Real-world forward rate dynamics with affine realizations

Abstract

We investigate the existence of affine realizations for Lévy driven interest rate term structure models under the real-world probability measure, which so far has only been studied under an assumed risk-neutral probability measure. For models driven by Wiener processes, all results obtained under the risk-neutral approach concerning the existence of affine realizations are transferred to the general case. A similar result holds true for models driven by compound Poisson processes with finite jump size distributions. However, in the presence of jumps with infinite activity we obtain severe restrictions on the structure of the market price of risk; typically, it must even be constant.

31 pages

References in corpus (5)

• Bilateral Gamma distributions and processes in financial mathematics
• Tempered stable distributions and processes
• Existence of Lévy term structure models
• An alternative approach on the existence of affine realizations for HJM term structure models
• Existence of affine realizations for Lévy term structure models

Cited by in corpus (3)

• Invariance of closed convex cones for stochastic partial differential equations
• Affine realizations with affine state processes for stochastic partial differential equations
• Existence of affine realizations for stochastic partial differential equations driven by Lévy processes