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European Option General First Order Error Formula

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  • Leduc, Guillaume

Abstract

We study the value of European security derivatives in the Black-Scholes model when the underlying asset ξ is approximated by random walks ξ⁽ⁿ⁾. We obtain an explicit error formula, up to a term of order O(n^{-(3/2)}), which is valid for general approximating schemes and general payoff functions. We show how this error formula can be used to find random walks ξ⁽ⁿ⁾ for which option values converge at a speed of O(n^{-(3/2)}).

Suggested Citation

  • Leduc, Guillaume, 2012. "European Option General First Order Error Formula," MPRA Paper 42015, University Library of Munich, Germany, revised 01 Oct 2012.
    • Handle: RePEc:pra:mprapa:42015
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    File URL: https://mpra.ub.uni-muenchen.de/42015/1/MPRA_paper_42015.pdf
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    References listed on IDEAS

    as
    1. Dietmar Leisen & Matthias Reimer, 1996. "Binomial models for option valuation - examining and improving convergence," Applied Mathematical Finance, Taylor & Francis Journals, vol. 3(4), pages 319-346.
    2. Carbone, Raffaella, 2004. "Binomial approximation of Brownian motion and its maximum," Statistics & Probability Letters, Elsevier, vol. 69(3), pages 271-285, September.
    3. 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.
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    Cited by:

    1. Guillaume Leduc & Merima Nurkanovic Hot, 2020. "Joshi’s Split Tree for Option Pricing," Risks, MDPI, vol. 8(3), pages 1-26, August.
    2. Jean-Christophe Breton & Youssef El-Khatib & Jun Fan & Nicolas Privault, 2021. "A q-binomial extension of the CRR asset pricing model," Papers 2104.10163, arXiv.org, revised Feb 2023.

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    More about this item

    Keywords

    European options; approximation scheme; error formula; Black-Scholes;
    All these keywords.

    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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