Berlin 2008 – wissenschaftliches Programm
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AKSOE: Arbeitskreis Physik sozio-ökonomischer Systeme
AKSOE 3: Financial Markets and Risk Management I
AKSOE 3.3: Vortrag
Montag, 25. Februar 2008, 11:15–11:45, EW 203
The hidden volatility process in financial time series — •Josep Perelló1, Jaume Masoliver1, and Zoltán Eisler2 — 1Departament de Física Fonamental, Universitat de Barcelona, Diagonal, 647, E-08028 Barcelona, Spain — 2Department of Theoretical Physics, Budapest University of Technology and Economics, Budafoki út 8., H-1111, Budapest, Hungary
Volatility characterizes the amplitude of log-price fluctuations. Despite its popularity on trading floors, volatility is unobservable and only the price is known. Diffusion theory has many common points with the research on volatility, the key of the analogy being that volatility is a time-dependent diffusion coefficient of a random walk. We present a formal procedure to extract volatility from price data by assuming that it is described by a hidden Markov process which together with the price forms a two-dimensional diffusion process [1]. We derive an alternative maximum-likelihood estimate valid for a wide class of processes. We apply it to the exponential Ornstein-Uhlenbeck stochastic volatility model [2] since studies have shown its good performance in several aspects [3-5] and observe that it is able infer the hidden state of volatility [1]. The formalism is applied to the Dow Jones daily index.
[1] Z. Eisler, J. Perelló, J. Masoliver, Phys. Rev. E 76, 056105 (2007)
[2] J. Masoliver, J. Perelló, Quant. Finance 6, 423 (2006)
[3] J. Perelló, J.Masoliver, Phys. Rev. E 67, 037102 (2003)
[4] J. Perelló, J. Masoliver, Phys. Rev. E 75, 046110 (2007)
[5] T. Qiu, B. Zheng, F. Ren, S. Trimper, Phys. Rev. E 73, 065103 (2006)