Hybrid Brownian motion: a model for price feedback and volatility explosion
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Mon, 30/11/2009 15:45 |
William Shaw (King’s College London) |
Stochastic Analysis Seminar  |
Eagle House |
| Numerous studies of asset returns reveal excess kurtosis as fat tails, often characterized by power law behaviour. A hybrid of arithmetic and geometric Brownian motion is proposed as a model for short-term asset returns, and its equilibrium and dynamical properties explored. Some exact solutions for the time-dependent behaviour are given, and we demonstrate the existence of a stochastic bifurcation between mean- reverting and momentum-dominated markets. The consequences for risk management will be discussed. | |||