A contribution to the systematics of stochastic volatility models
arXiv:1009.2696 · doi:10.1016/j.physa.2010.03.044
Abstract
We compare systematically several classes of stochastic volatility models of stock market fluctuations. We show that the long-time return distribution is either Gaussian or develops a power-law tail, while the short-time return distribution has generically a stretched-exponential form, but can assume also an algebraic decay, in the family of models which we call ``GARCH''-type. The intermediate regime is found in the exponential Ornstein-Uhlenbeck process. We calculate also the decay of the autocorrelation function of volatility.
15 pages, no figures
References in corpus (26)
- Scaling of the distribution of fluctuations of financial market indices
- The statistical properties of the volatility of price fluctuations
- Scaling of the distribution of price fluctuations of individual companies
- The leverage effect in financial markets: retarded volatility and market panic
- Volatility distribution in the S&P500 Stock Index
- Exponential distribution of financial returns at mesoscopic time lags: a new stylized fact
- Volatility Effects on the Escape Time in Financial Market Models
- Hitting Time Distributions in Financial Markets
- Mean Escape Time in a System with Stochastic Volatility
- Role of Noise in a Market Model with Stochastic Volatility
- Volatility in Financial Markets: Stochastic Models and Empirical Results
- Comparison between the probability distribution of returns in the Heston model and empirical data for stock indexes
- Multiple time scales and the exponential Ornstein-Uhlenbeck stochastic volatility model
- A correlated stochastic volatility model measuring leverage and other stylized facts
- Stochastic volatility and leverage effect
- A comparison between several correlated stochastic volatility models
- Underlying Dynamics of Typical Fluctuations of an Emerging Market Price Index: The Heston Model from Minutes to Months
- Additive-multiplicative stochastic models of financial mean-reverting processes
- Microscopic Origin of Non-Gaussian Distributions of Financial Returns
- Stochastic volatility of financial markets as the fluctuating rate of trading: an empirical study
- Activity autocorrelation in financial markets. A comparative study between several models
- Volatility: a hidden Markov process in financial time series
- Extreme times for volatility processes
- Langevin processes, agent models and socio-economic systems
- Perturbation Expansion for Option Pricing with Stochastic Volatility
- Stochastic model for market stocks with strong resistance