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Pricing European options on instruments with a constant dividend yield: The randomized discrete-time approach

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  • Rafal Weron

Abstract

Due to the well known fact that market returns are not normally distributed, we use generalized hyperbolic distributions for pricing options in a randomized discrete-time setup. The obtained formulas can be used for pricing options on stock indexes, currencies and futures contracts. We test them on options written on the Nikkei 225 index futures and conclude that a proper calibration scheme could give us an advantage in the financial market.

Suggested Citation

  • Rafal Weron, 2002. "Pricing European options on instruments with a constant dividend yield: The randomized discrete-time approach," HSC Research Reports HSC/02/04, Hugo Steinhaus Center, Wroclaw University of Science and Technology.
    • Handle: RePEc:wuu:wpaper:hsc0204
    as

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    File URL: http://www.im.pwr.wroc.pl/~hugo/RePEc/wuu/wpaper/HSC_02_04.pdf
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    File URL: http://www.math.uni.wroc.pl/~pms/files/22.2/Article/22.2.15.pdf
    File Function: Final printed version, 2002
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    References listed on IDEAS

    as
    1. Aleksander Janicki & Aleksander Weron, 1994. "Simulation and Chaotic Behavior of Alpha-stable Stochastic Processes," HSC Books, Hugo Steinhaus Center, Wroclaw University of Science and Technology, number hsbook9401, December.
    2. Eberlein, Ernst & Keller, Ulrich & Prause, Karsten, 1998. "New Insights into Smile, Mispricing, and Value at Risk: The Hyperbolic Model," The Journal of Business, University of Chicago Press, vol. 71(3), pages 371-405, July.
    3. Harrison, J. Michael & Pliska, Stanley R., 1981. "Martingales and stochastic integrals in the theory of continuous trading," Stochastic Processes and their Applications, Elsevier, vol. 11(3), pages 215-260, August.
    4. Krzysztof Burnecki & Agnieszka Marciniuk & Aleksander Weron, 2002. "On annuities under random rates of interest," HSC Research Reports HSC/02/01, Hugo Steinhaus Center, Wroclaw University of Technology.
    5. Benoit Mandelbrot, 2015. "The Variation of Certain Speculative Prices," World Scientific Book Chapters, in: Anastasios G Malliaris & William T Ziemba (ed.), THE WORLD SCIENTIFIC HANDBOOK OF FUTURES MARKETS, chapter 3, pages 39-78, World Scientific Publishing Co. Pte. Ltd..
    6. Black, Fischer, 1976. "The pricing of commodity contracts," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 167-179.
    7. Cox, John C. & Ross, Stephen A. & Rubinstein, Mark, 1979. "Option pricing: A simplified approach," Journal of Financial Economics, Elsevier, vol. 7(3), pages 229-263, September.
    8. Joanna Nowicka-Zagrajek & Rafal Weron, 2002. "Modeling electricity loads in California: ARMA models with hyperbolic noise," HSC Research Reports HSC/02/02, Hugo Steinhaus Center, Wroclaw University of Technology.
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    More about this item

    Keywords

    Option pricing; Dividends; Randomization; Alternative models;
    All these keywords.

    JEL classification:

    • C16 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Econometric and Statistical Methods; Specific Distributions
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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