STOCHASTIC MODELS AND ESCAPE TIMES OF FINANCIAL MARKETS

We shortly review three stochastic models of financial markets, namely the geo-metric Brownian motion, the GARCH model and the Heston model. We focus on the statistical properties of the escape time to reach a barrier or a given threshold. We compare the probability density function (PDF) of these models with that obtained from real market data. We point out the limitations and the peculiarities of each model. We report also the PDF of escape times for intraday price returns obtained from real market data. PACS: 89.65.Gh, 05.40.-a, 02.50.-r, 89.75-