Multiple time scales and the exponential Ornstein-Uhlenbeck stochastic volatility model

Abstract

We study the exponential Ornstein-Uhlenbeck stochastic volatility model and observe that the model shows a multiscale behavior in the volatility autocorrelation. It also exhibits a leverage correlation and a probability profile for the stationary volatility which are consistent with market observations. All these features make the model quite appealing since it appears to be more complete than other stochastic volatility models also based on a two-dimensional diffusion. We finally present an approximate solution for the return probability density designed to capture the kurtosis and skewness effects.

24 pages, 9 colored figures, Workshop Volatility of Financial Markets (Leiden 18-29 October 2004)

References in corpus (12)

• The statistical properties of the volatility of price fluctuations
• A multifractal random walk
• The leverage effect in financial markets: retarded volatility and market panic
• Multifractal stationary random measures and multifractal random walks with log-infinitely divisible scaling laws
• Exponential distribution of financial returns at mesoscopic time lags: a new stylized fact
• Volatility in Financial Markets: Stochastic Models and Empirical Results
• Multiple time scales in volatility and leverage correlations: An stochastic volatility model
• A correlated stochastic volatility model measuring leverage and other stylized facts
• Stochastic volatility and leverage effect
• Clustering of volatility as a multiscale phenomenon
• 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

Cited by in corpus (21)

• Sentiment Correlation in Financial News Networks and Associated Market Movements
• First-passage and risk evaluation under stochastic volatility
• The escape problem under stochastic volatility: the Heston model
• Agent-based model with asymmetric trading and herding for complex financial systems
• On return-volatility correlation in financial dynamics
• Volatility: a hidden Markov process in financial time series
• Extreme times for volatility processes
• A Generalized Fourier Transform Approach to Risk Measures
• Market Imitation and Win-Stay Lose-Shift strategies emerge as unintended patterns in market direction guesses
• Minimal model of financial stylized facts
• Multiple time scales and the empirical models for stochastic volatility
• Probability distribution of returns in the exponential Ornstein-Uhlenbeck model
• Option pricing under Ornstein-Uhlenbeck stochastic volatility: a linear model
• Statistical analysis and stochastic interest rate modelling for valuing the future with implications in climate change mitigation
• Option pricing under stochastic volatility: the exponential Ornstein-Uhlenbeck model
• Distributions of Historic Market Data -- Relaxation and Correlations
• A contribution to the systematics of stochastic volatility models
• Market memory and fat tail consequences in option pricing on the expOU stochastic volatility model
• Maximum likelihood approach for several stochastic volatility models
• Inferring Volatility in the Heston Model and its Relatives -- an Information Theoretical Approach
• New volatility evolution model after extreme events