Document Type : Research Article
Authors
Department of Mathematics, Amir Kabir University of Technology, Tehran, Iran
Abstract
Identifying the structures of dependence between financial assets is one of the interesting topics to researchers. However, there are challenges to this purpose. One of them is the modelling of heavy tail distributions. Distributions of financial assets generally have heavier tails than other distributions, such as exponential distributions. Also, the dependence of financial assets in crashes is stronger than in booms and consequently the skewed parameter in the left tail is more. To address these challenges, there is a function called Copula. So, copula functions are suggested for modelling dependency structure between multivariate data without any assumptions on marginal distributions, which they solve the problems of dependency measures such as linear correlation coefficient. Also, tail dependency measures have analytical formulas with copula functions. In general, the copula function connects the joint distribution functions to the marginal distribution of every variables. With regard, we have introduced a factor copula model that is useful for models where variables are based on latent factor structures. Finally, we have estimated the parameters of factor copula by Simulated method of Moment, Newton-Raphson method and Robbins-Monroe algorithm and have compared the results of these methods to each other.
Keywords
[2] Oh, Dong Hwan and Patton, Andrew J Simulated method of moments estimation for copula-based multivariate models Journal of the American Statistical Association,Taylor & Francis, 108(502):689{700, 2013.
[3] Gelman, Andrew Method of moments using Monte Carlo simulation Journal of Computational and Graphical Statistics,Taylor & Francis, 4(1):36{54, 1995.
[4] Avriel, Mordecai Nonlinear programming: analysis and methods Courier Corporation, 220{221 ,2003.
[5] Allen III, Myron B and Isaacson, Eli L Numerical analysis for applied science John wiley & sons, 35:188{195, 2011.
[6] Dennis Jr, John E and Schnabel, Robert B Numerical methods for unconstrained optimization and nonlinear equations SIAM, 168{193, 1996.
[7] Kvaalen, Eric A faster Broyden method BIT Numerical Mathematics, Springer, 31(2):369{372, 1991.
[8] Robbins, Herbert and Monro, Sutton A stochastic approximation method Theannals of mathematical statistics ,JSTOR, 22(3):400{407, 1951.
[9] Blum, Julius R and others Approximation methods which converge with probability one The Annals of Mathematical Statistics, Institute of Mathematical Statistics, 25(2):382{386, 1954.
[10] Chamberlain, Gary Funds, factors, and diversi cation in arbitrage pricing models Econometrica: Journal of the Econometric Society, JSTOR, 1305{1323, 1983.
[11] French, Craig W. "The Treynor capital asset pricing model." Journal of Investment Management 1.2 (2003): 60-72.
[12] Cherubini, Umberto et al. Copula methods in nance. (2004).
)