A Model for Stock Returns and Volatility

Abstract

We prove that Student's t-distribution provides one of the better fits to returns of S&P component stocks and the generalized inverse gamma distribution best fits VIX and VXO volatility data. We further argue that a more accurate measure of the volatility may be possible based on the fact that stock returns can be understood as the product distribution of the volatility and normal distributions. We find Brown noise in VIX and VXO time series and explain the mean and the variance of the relaxation times on approach to the steady-state distribution.

17 pages, 30 figures, 2 tables

References in corpus (2)

• Stochastic volatility of financial markets as the fluctuating rate of trading: an empirical study
• Distribution Of Wealth In A Network Model Of The Economy

Cited by in corpus (14)

• Switching to non-affine stochastic volatility: A closed-form expansion for the Inverse Gamma model
• Implied and Realized Volatility: A Study of Distributions and the Distribution of Difference
• Correlation and Relaxation Times for a Stochastic Process with a Fat-Tailed Steady-State Distribution
• Combined Mutiplicative-Heston Model for Stochastic Volatility
• Rethinking Generalized Beta Family of Distributions
• Distributions of Historic Market Data - Stock Returns
• Implied and Realized Volatility: A Study of the Ratio Distribution
• Distributions of Historic Market Data -- Implied and Realized Volatility
• Distributions of Historic Market Data -- Relaxation and Correlations
• Generalized Beta Prime Distribution: Stochastic Model of Economic Exchange and Properties of Inequality Indices
• On absence of steady state in the Bouchaud-Mézard network model
• Asymmetry in Distributions of Accumulated Gains and Losses in Stock Returns
• Broken Symmetry of Stock Returns -- a Modified Jones-Faddy Skew t-Distribution
• Broken Symmetry, Conservation Law, and Scaling in Accumulated Stock Returns -- a Modified Jones-Faddy Skew t-Distribution Perspective