Probability distribution of returns in the exponential Ornstein-Uhlenbeck model
We analyze the problem of the analytical characterization of the probability distribution of financial returns in the exponential Ornstein-Uhlenbeck model with stochastic volatility. In this model the prices are driven by a Geometric Brownian motion, whose diffusion coefficient is expressed through an exponential function of an hidden variable Y governed by a mean-reverting process. We derive closed-form expressions for the probability distribution and its characteristic function in two limit cases. In the first one the fluctuations of Y are larger than the volatility normal level, while the second one corresponds to the assumption of a small stationary value for the variance of Y. Theoretical results are tested numerically by intensive use of Monte Carlo simulations. The effectiveness of the analytical predictions is checked via a careful analysis of the parameters involved in the numerical implementation of the Euler-Maruyama scheme and is tested on a data set of financial indexes. In particular, we discuss results for the German DAX30 and Dow Jones Euro Stoxx 50, finding a good agreement between the empirical data and the theoretical description.
Year of publication: |
2008-05
|
---|---|
Authors: | Bormetti, Giacomo ; Cazzola, Valentina ; Montagna, Guido ; Nicrosini, Oreste |
Institutions: | arXiv.org |
Saved in:
freely available
Saved in favorites
Similar items by person
-
A Generalized Fourier Transform Approach to Risk Measures
Bormetti, Giacomo, (2012)
-
Accounting for risk of non linear portfolios: a novel Fourier approach
Bormetti, Giacomo, (2010)
-
Option pricing under Ornstein-Uhlenbeck stochastic volatility: a linear model
Bormetti, Giacomo, (2009)
- More ...