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In the paper \ve present a proposal of augmenting portfolio analysis for the infinitely divisible distributions of returns - so that the prices of assets can follow Levy processes. In the classical portfolio analysis (by Markovitz or Sharp) the portfolio is evaluated according to two criteria: mean return and variance of returns. Such an approach is cumbersome second moments of assets' returns do not exist or if the interdependence between the returns of different assets can not be described only by covariation. In this article we propose a model in which asset prices follow multidimensional Levy process and the interdependence between assets are described by covariance (Gaussian part) and multidimensional jump measure (Poisson pan). Then we propose to choose the optimal portfolio based on three criteria: mean return, total variance of diffusion and a measure of jump risk. We also consider augmenting this multi-criteria choice setup for the costs of possible portfolio adjustments.
Słowa kluczowe
Rocznik
Tom
Strony
43--52
Opis fizyczny
Bibliogr. 20 poz.
Twórcy
autor
- Poznań University of Economics, Department of Mathematical Economics, al. Niepodległości 10, 60-967 Poznań, Poland
Bibliografia
- [1]Andersen L., Andereasen J., Jump-diffusion models: Volatility smile fitting and numerical methods for pricing, Rev. Derivatives Research 4, 2000, 231-262.
- [2]Appelbaum D., Levy Processes and Stochastic Calculus, Cambridge University Press, 2004.
- [3]Campbell J.Y., Lo A.W., MacKinlay A.C., The Econometrics of Financial Markets, Princeton University Press, 1997.
- [4]Cont R., Tankov P., Financial Modelling with Jump Processes, Chapman & Hall, 2004.
- [5]Cont R., Tankov P., Calibrating of jump-diffusion option pricing models: A robust non-parametric approach, Raport Interne 490, Ecole Polytechnique, 2002.
- [6]Fama E.F., Portfolio Analysis in a Stable Paretian Market, Management Science 11, 1965,404-419.
- [7]Feller W., An introduction to probability theory and its application, Wiley, 1967.
- [8]Gamba A., Portfolio Analysis with Symmetric Stable Paretian Returns, in: Current Topics in Quantitative Finance, E. Canestrelli (ed.), Springer-Verlag, 1999.
- [9]Kallsen J., Optimal portfolios for exponential Levy processes, Mathematical Methods of Operational Research 51, 2000, 357-374.
- [10]Kou S., A jump-diffusion model for option pricing, Management Science 48, 2002, 1086-1101.
- [1l]Kyprianou A.E., Introductory Lectures on Fluctuations of Levy Processes with Applications, Springer, 2006.
- [12]Mandelbrot B.B., Fractals and Scaling in Finance, Springer, 1997.
- [13]Mandelbrot B.B., Hudson R.L., Fraktale undFinanzen, Piper, Miinchen, 2005.
- [14]Markowitz H.M, Portfolio Selection, Journal of Finance, 7, 1952, 77-91.
- [15]Merton R., Option pricing when underlying stock returns are discontinuous, Journal of Financial Economics 3, 1976, 125-144.
- [16]Mittnik S., Svetlozar R., Toker D., Portfolio Selection in the Presence of Heavy-tailed Asset Returns, w: Contributions to Modern Econometrics, From Data Analysis to Economic Policy, (S. Mittnik, I. Klein, ed.), Springer-Verlag, 2002.
- [17]Sato K., Levy Processes and Infinitely Divisible Distributions, Cambridge University Press, 1999.
- [18]Schoutens W., Levy Processes in Finance: Pricing Financial Derivatives, John Wiley & Sons, 2003.
- [19]Sharpe W.F., A Simplified Model for Portfolio Analysis, Management Science 9, 1963, 277-293.
- [20]Schiryaev A.N., Essentials of Stochastic Finance: Facts, Models, Theory, World Scientific Publishing Company, 1999.
Typ dokumentu
Bibliografia
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bwmeta1.element.baztech-article-BPP1-0082-0029