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Pricing of basket options I

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  • Alexander Kushpel

Abstract

Pricing of high-dimensional options is a deep problem of the Theoretical Financial Mathematics. In this article we present a new class of L\'{e}vy driven models of stock markets. In our opinion, any market model should be based on a transparent and intuitively easily acceptable concept. In our case this is a linear system of stochastic equations. Our market model is based on the principle of inheritance, i.e. for the particular choice of parameters it coincides with known models. Also, the model proposed is effectively numerically realizable. For the class of models under cosideration, we give an explicit representations of characteristic functions. This allows us us to construct a sequence of approximation formulas to price basket options. We show that our approximation formulas have almost optimal rate of convergence in the sense of respective n-widths.

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  • Alexander Kushpel, 2014. "Pricing of basket options I," Papers 1401.1856, arXiv.org.
    • Handle: RePEc:arx:papers:1401.1856
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    References listed on IDEAS

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    1. Lord, Roger & Fang, Fang & Bervoets, Frank & Oosterlee, Kees, 2007. "A fast and accurate FFT-based method for pricing early-exercise options under Lévy processes," MPRA Paper 1952, University Library of Munich, Germany.
    2. Li, Minqiang, 2008. "Closed-Form Approximations for Spread Option Prices and Greeks," MPRA Paper 6994, University Library of Munich, Germany.
    3. Mandelbrot, Benoit B, 1972. "Correction of an Error in "The Variation of Certain Speculative Prices" (1963)," The Journal of Business, University of Chicago Press, vol. 45(4), pages 542-543, October.
    4. Svetlana I Boyarchenko & Sergei Z Levendorskii, 2002. "Non-Gaussian Merton-Black-Scholes Theory," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 4955, September.
    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. Margrabe, William, 1978. "The Value of an Option to Exchange One Asset for Another," Journal of Finance, American Finance Association, vol. 33(1), pages 177-186, March.
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    Cited by:

    1. Alexander Kushpel, 2015. "Pricing of high-dimensional options," Papers 1510.07221, arXiv.org.

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