2008/07/14 by G. L. Buchbinder, Buchbinder, G. L., K. M. Chistilin +1
Economics, Econometrics and Finance · #Complex Systems and Time Series Analysis #Data Analysis #FOS: Economics and business #FOS: Physical sciences #Financial Risk and Volatility Modeling #Physics and Society (physics.soc-ph) #Statistical Finance (q-fin.ST) #Statistics and Probability (physics.data-an) #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.0807.2083
openalex publication_date 2008/07/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The model describing market dynamics after a large financial crash is considered in terms of the stochastic differential equation of Ito. Physically, the model presents an overdamped Brownian particle moving in the nonstationary one-dimensional potential U under the influence of the variable noise intensity, depending on the particle position x. Based on the empirical data the approximate estimation of the Kramers-Moyal coefficients D1,2 allow to predicate quite definitely the behavior of the potential introduced by D1 = - ∂ U /∂ x and the volatility ∼ √(D2). It has been shown that the presented model describes well enough the best known empirical facts relative to the large financial crash of October 1987. \