6533b837fe1ef96bd12a1e4c
RESEARCH PRODUCT
Mean Escape Time in a System with Stochastic Volatility
Giovanni BonannoBernardo SpagnoloDavide Valentisubject
Physics - Physics and SocietyMean escape timeFOS: Physical sciencesPhysics and Society (physics.soc-ph)Heston modelFOS: Economics and businessEconometricsEconophysics; Mean escape time; Heston model; Stochastic modelStatistical physicsCondensed Matter - Statistical MechanicsMathematicsGeometric Brownian motionStatistical Finance (q-fin.ST)Statistical Mechanics (cond-mat.stat-mech)Stochastic volatilityStochastic processEconophysicQuantitative Finance - Statistical FinanceDisordered Systems and Neural Networks (cond-mat.dis-nn)Brownian excursionCondensed Matter - Disordered Systems and Neural NetworksSettore FIS/07 - Fisica Applicata(Beni Culturali Ambientali Biol.e Medicin)Heston modelStochastic modelReflected Brownian motionVolatility (finance)Rendleman–Bartter modeldescription
We study the mean escape time in a market model with stochastic volatility. The process followed by the volatility is the Cox Ingersoll and Ross process which is widely used to model stock price fluctuations. The market model can be considered as a generalization of the Heston model, where the geometric Brownian motion is replaced by a random walk in the presence of a cubic nonlinearity. We investigate the statistical properties of the escape time of the returns, from a given interval, as a function of the three parameters of the model. We find that the noise can have a stabilizing effect on the system, as long as the global noise is not too high with respect to the effective potential barrier experienced by a fictitious Brownian particle. We compare the probability density function of the return escape times of the model with those obtained from real market data. We find that they fit very well.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2007-01-01 |