2008/04/02 by Attilio L. Stella, Fulvio Baldovin
Economics, Econometrics and Finance · Physics and Astronomy · #Autoregressive model #Complex Systems and Time Series Analysis #Econophysics #Financial Risk and Volatility Modeling #Probabilistic logic #Probability density function #Scaling #Series (stratigraphy) #Stochastic process #Stochastic volatility #Theoretical and Computational Physics #Volatility (finance) #Volatility clustering #cond-mat.stat-mech #physics.soc-ph #q-fin.ST
paper · pdf · doi:10.1007/s12043-008-0167-0
published as Pramana - Journal of Physics 71, 341 (2008) · Based on the Key Note lecture by A.L. Stella at the Conference on ``Statistical Physics Approaches to Multi-Disciplinary Problems'', IIT Guwahati, India, 7-13 January 2008
arxiv created 2008/04/02 · openalex publication_date 2008/08/01 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
Modeling the evolution of a financial index as a stochastic process is a problem awaiting a full, satisfactory solution since it was first formulated by Bachelier in 1900. Here it is shown that the scaling with time of the return probability density function sampled from the historical series suggests a successful model. The resulting stochastic process is a heteroskedastic, non-Markovian martingale, which can be used to simulate index evolution on the basis of an auto-regressive strategy. Results are fully consistent with volatility clustering and with the multi-scaling properties of the return distribution. The idea of basing the process construction on scaling, and the construction itself, are closely inspired by the probabilistic renormalization group approach of statistical mechanics and by a recent formulation of the central limit theorem for sums of strongly correlated random variables.