The fractional volatility model: An agent-based interpretation

2007/06/30 by R. Vilela Mendes
Economics, Econometrics and Finance · Physics and Astronomy · #Artificial intelligence #Autoregressive conditional heteroskedasticity #Complex Systems and Time Series Analysis #Computer science #Econometrics #Economics #Finance #Financial Risk and Volatility Modeling #Financial market #Implied volatility #Leverage (statistics) #Leverage effect #Stochastic processes and financial applications #Stochastic volatility #Volatility (finance) #Volatility smile #physics.data-an #physics.soc-ph #q-fin.ST

paper · pdf · doi:10.1016/j.physa.2008.01.052

published as Physica A: Statistical Mechanics and its Applications, 387 (2008) 3987-3994 · 23 pages, 11 figures

arxiv created 2007/08/29 · openalex publication_date 2008/01/16 · arxiv updated 2010/08/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

Based on criteria of mathematical simplicity and consistency with empirical market data, a model with volatility driven by fractional noise has been constructed which provides a fairly accurate mathematical parametrization of the data. Here, some features of the model are discussed and, using agent-based models, one tries to find which agent strategies and (or) properties of the financial institutions might be responsible for the features of the fractional volatility model.

Citations

• Analyzing and modeling 1+1d markets
• Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation
• A long memory property of stock market returns and a new model
• Toward a theory of marginally efficient markets
• Fractional Brownian Motions, Fractional Noises and Applications
• The Pricing of Options and Corporate Liabilities
• Statistical theory of the continuous double auction
• Exponential distribution of financial returns at mesoscopic time lags: a new stylized fact
• Simple model of a limit order-driven market