Beliefs and stochastic modelling of interest rate scenario risk
Allfonds-BKG Asset Management, Arabellastr. 27, 81925 Munich, Germany
2 Institute of Physics, Humboldt-University, Invalidenstr. 110, 10115 Berlin, Germany
Corresponding author: a firstname.lastname@example.org
Published online: 15 April 2001
We present a framework that allows for a systematic assessment of risk given a specific model and belief on the market. Within this framework the time evolution of risk is modeled in a twofold way. On the one hand, risk is modeled by the time discrete and nonlinear garch(1,1) process, which allows for a (time-)local understanding of its level, together with a short term forecast. On the other hand, via a diffusion approximation, the time evolution of the probability density of risk is modeled by a Fokker-Planck equation. Then, as a final step, using Bayes theorem, beliefs are conditioned on the stationary probability density function as obtained from the Fokker-Planck equation. We believe this to be a highly rigorous framework to integrate subjective judgments of future market behavior and underlying models. In order to demonstrate the approach, we apply it to risk assessment of empirical interest rate scenario methodologies, i.e. the application of Principal Component Analysis to the the dynamics of bonds.
PACS: 05.45.Tp – Time series analysis / 02.50.Ey – Stochastic processes
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2001