Comparison between the probability distribution of returns in the Heston model and empirical data for stock indexes

Abstract

We compare the probability distribution of returns for the three major stock-market indexes (Nasdaq, S&P500, and Dow-Jones) with an analytical formula recently derived by Dragulescu and Yakovenko for the Heston model with stochastic variance. For the period of 1982-1999, we find a very good agreement between the theory and the data for a wide range of time lags from 1 to 250 days. On the other hand, deviations start to appear when the data for 2000-2002 are included. We interpret this as a statistical evidence of the major change in the market from a positive growth rate in 1980s and 1990s to a negative rate in 2000s.

Elsevier style (enclosed), 7.5 pages, 7 figures with 14 eps files. Submitted to Physica A, Proceedings of International Econophysics Conference in Bali, 28-31 August 2002

Cited by in corpus (11)

• Exponential distribution of financial returns at mesoscopic time lags: a new stylized fact
• Volatility Effects on the Escape Time in Financial Market Models
• First-passage and risk evaluation under stochastic volatility
• The escape problem under stochastic volatility: the Heston model
• Underlying Dynamics of Typical Fluctuations of an Emerging Market Price Index: The Heston Model from Minutes to Months
• A path integral approach to closed-form option pricing formulas with applications to stochastic volatility and interest rate models
• Epstein-Zin Utility Maximization on a Random Horizon
• Properties of a simple bilinear stochastic model: estimation and predictability
• Multiple time scales and the empirical models for stochastic volatility
• A geometrical imaging of the real gap between economies of China and the United States
• A contribution to the systematics of stochastic volatility models