2012/04/30 by Jordi Camprodon, Josep Perelló
Economics, Econometrics and Finance · Physics and Astronomy · #Complex Systems and Time Series Analysis #Forward volatility #Heston model #Implied volatility #SABR volatility model #Stochastic processes and financial applications #Stochastic volatility #Stylized fact #Theoretical and Computational Physics #Volatility (finance) #Volatility smile #cond-mat.stat-mech #physics.data-an #q-fin.CP
paper · pdf · doi:10.1088/1742-5468/2012/08/p08016
published as J. Stat. Mech. (2012) P08016 · 26 pages, 15 figures
arxiv created 2012/07/02 · openalex publication_date 2012/08/31 · arxiv updated 2012/09/03 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/06
Volatility measures the amplitude of price fluctuations. Despite it being one of the most important quantities in finance, volatility is not directly observable. Here we apply a maximum likelihood method which assumes that price and volatility follow a two-dimensional diffusion process where volatility is the stochastic diffusion coefficient of the log-price dynamics. We apply this method to the simplest versions of the expOU, the OU and the Heston stochastic volatility models and we study their performance in terms of the log-price probability, the volatility probability, and its Mean First-Passage Time. The approach has some predictive power on the future returns amplitude by only knowing the current volatility. The assumed models do not consider long-range volatility autocorrelation and the asymmetric return-volatility cross-correlation but the method still yields very naturally these two important stylized facts. We apply the method to different market indices and with a good performance in all cases.