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The optimal-drift model: an accelerated binomial scheme

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  • Ralf Korn
  • Stefanie Müller

Abstract

We introduce the optimal-drift model for the approximation of a lognormal stock price process by an accelerated binomial scheme. This model converges with order o(1/N), which is superior compared to today’s benchmark methods. Our approach is based on the observation that risk-neutral binomial schemes converge to the lognormal limit independently of the choice of the drift parameter. We verify the improved order of convergence by an asymptotic expansion of the binomial distribution function. Further, we show that the above result on drift invariance implies weak convergence of the binomial schemes suggested by Tian (in J. Futures Mark. 19, 817–843, 1999 ) and Chang and Palmer (in Finance Stoch. 11, 91–105, 2007 ). Copyright Springer-Verlag 2013

Suggested Citation

  • Ralf Korn & Stefanie Müller, 2013. "The optimal-drift model: an accelerated binomial scheme," Finance and Stochastics, Springer, vol. 17(1), pages 135-160, January.
    • Handle: RePEc:spr:finsto:v:17:y:2013:i:1:p:135-160
    DOI: 10.1007/s00780-012-0179-y
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    References listed on IDEAS

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    1. Francine Diener & MARC Diener, 2004. "Asymptotics of the price oscillations of a European call option in a tree model," Mathematical Finance, Wiley Blackwell, vol. 14(2), pages 271-293, April.
    2. 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.
    3. Leisen, Dietmar P. J., 1998. "Pricing the American put option: A detailed convergence analysis for binomial models," Journal of Economic Dynamics and Control, Elsevier, vol. 22(8-9), pages 1419-1444, August.
    4. Kaushik Amin & Ajay Khanna, 1994. "Convergence Of American Option Values From Discrete‐ To Continuous‐Time Financial Models1," Mathematical Finance, Wiley Blackwell, vol. 4(4), pages 289-304, October.
    5. Lo-Bin Chang & Ken Palmer, 2007. "Smooth convergence in the binomial model," Finance and Stochastics, Springer, vol. 11(1), pages 91-105, January.
    6. 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. Alona Bock & Ralf Korn, 2016. "Improving Convergence of Binomial Schemes and the Edgeworth Expansion," Risks, MDPI, vol. 4(2), pages 1-22, May.
    3. 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

    Binomial model; Black–Scholes model; Option pricing; Accelerated convergence; Weak convergence; 91G20; 91G60; G13;
    All these keywords.

    JEL classification:

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

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