Multivariate distribution of returns in financial time series

Article type: Research Article

Authors: Krivoruchenko, M.I.^{a; b; c; *} | Alessio, E.^a | Frappietro, V.^a | Streckert, L.J.^a

Affiliations: [a] Metronome-Ricerca sui Mercati Finanziari, C. so Vittorio Emanuele 84, 10121 Torino, Italy | [b] Institute for Theoretical and Experimental Physics, B. Cheremushkinskaya 25, 117259 Moscow, Russia | [c] Institut für Theoretische Physik, Universität Tübingen, Auf der Morgenstelle 14, D-72076 Tübingen, Germany

Correspondence: [*] Corresponding author. E-mail: [email protected].

Abstract: Multivariate probability density functions of returns are constructed in order to model the empirical behavior of returns in a financial time series. They describe the well-established deviations from the Gaussian random walk, such as an approximate scaling and heavy tails of the return distributions, long-ranged volatility-volatility correlations (volatility clustering) and return-volatility correlations (leverage effect). Free parameters of the model are fixed over the long term by fitting 100+ years of daily prices of the Dow Jones 30 Industrial Average. The multivariate probability density functions which we have constructed can be used for pricing derivative securities and risk management.

Keywords: Financial time series, scaling, heavy tails, volatility clustering, leverage effect

DOI: 10.3233/JCM-2006-65-605

Journal: Journal of Computational Methods in Sciences and Engineering, vol. 6, no. 5-6, pp. 315-324, 2006