Probability distribution of returns in the Heston model with stochastic volatility

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dc.creatorDragulescu, Adrian A.
dc.creatorYakovenko, Victor M.
dc.date2002-03-03
dc.date2002-11-05
dc.date.accessioned2026-07-07T12:06:39Z
dc.date.available2026-07-07T12:06:39Z
dc.descriptionWe study the Heston model, where the stock price dynamics is governed by a geometrical (multiplicative) Brownian motion with stochastic variance. We solve the corresponding Fokker-Planck equation exactly and, after integrating out the variance, find an analytic formula for the time-dependent probability distribution of stock price changes (returns). The formula is in excellent agreement with the Dow-Jones index for the time lags from 1 to 250 trading days. For large returns, the distribution is exponential in log-returns with a time-dependent exponent, whereas for small returns it is Gaussian. For time lags longer than the relaxation time of variance, the probability distribution can be expressed in a scaling form using a Bessel function. The Dow-Jones data for 1982-2001 follow the scaling function for seven orders of magnitude.
dc.description11 pages, 7 figures, RevTeX 4. V.2: substantial revision - new figures, sections, and references; V.3: accepted to Quantitative Finance, minor corrections
dc.identifierhttps://arxiv.org/abs/cond-mat/0203046
dc.identifierhttp://arxiv.org/abs/cond-mat/0203046
dc.identifierQuantitative Finance 2, 443 (2002)
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/208717
dc.subjectStatistical Mechanics
dc.subjectStatistical Finance
dc.titleProbability distribution of returns in the Heston model with stochastic volatility
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