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Portfolio analysis in jump-diffusion model with power-law tails

Author

Listed:
  • Pawe? Kliber

    (Poznan University of Economics)

Abstract

The classic portfolio analysis given by Markowitz theory and Capital Asset Pricing Model is based on the assumption that the assets? returns are normally distributed. In this situation one can use only two criteria: expected return and variance of return as the measures of possible gains and risk, respectively. However there is a growing evidence that the assets? returns and in particular returns of shares in the stock markets fail to obey Gaussian distribution. Therefore different measures of risk should be considered.In the paper we analyze the portfolio problem in the situation when stock prices follows jump-diffusion model with the tails of jumps obeying power-law. We consider a portfolio problem with two risk criteria: risk in the situation of normal market circumstances and the risk of jumps. We propose a method for numerical computing the former risk using Fast Fourier Transform (FFT). Finally we present the examples of portfolio analysis with the new method for the shares from Warsaw Stock Market Exchange.

Suggested Citation

  • Pawe? Kliber, 2016. "Portfolio analysis in jump-diffusion model with power-law tails," Proceedings of International Academic Conferences 5306873, International Institute of Social and Economic Sciences.
    • Handle: RePEc:sek:iacpro:5306873
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    File URL: https://iises.net/proceedings/27th-international-academic-conference-prague/table-of-content/detail?cid=53&iid=023&rid=6873
    File Function: First version, 2016
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    More about this item

    Keywords

    portfolio analysis; jump-diffusion models; power-law; risk of extremes; Fast Fourier Transform;
    All these keywords.

    JEL classification:

    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics

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