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Probability distribution of returns in the Heston model with stochastic volatility | | Adrian A. Dragulescu
; Victor M. Yakovenko
; | | Date: |
4 Mar 2002 | | Journal: | Quantitative Finance 2, 443 (2002) | | Subject: | Statistical Mechanics | cond-mat.stat-mech | | Abstract: | We 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. | | Source: | arXiv, cond-mat/0203046 | | Services: | Forum | Review | PDF | Favorites | |
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