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Rate of convergence of trinomial formula to Black–Scholes formula

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  • Ratibenyakool, Yuttana
  • Neammanee, Kritsana

Abstract

The Black–Scholes formula which was introduced by three economists, Black et al. (1973) has been widely used to calculate the theoretical price of the European call option. In 1979, Cox, Ross and Rubinstein (Cox et al., 1979) gave the binomial formula which is a tool to find the price of European option and showed that this formula converges to the Black–Scholes formula as the number of periods (n) converges to infinity. In 1988, Boyle investigated another formula that is used to find the price of European option, that is the trinomial formula. In 2015, Puspita et al. gave examples to show that the trinomial formula is closed to the Black–Scholes formula. After that, Ratibenyakool and Neammanee (2020) gave the rigorous proof of this convergence. In this paper, we show that the rate of convergence is of order 1n.

Suggested Citation

  • Ratibenyakool, Yuttana & Neammanee, Kritsana, 2024. "Rate of convergence of trinomial formula to Black–Scholes formula," Statistics & Probability Letters, Elsevier, vol. 213(C).
    • Handle: RePEc:eee:stapro:v:213:y:2024:i:c:s0167715224001366
    DOI: 10.1016/j.spl.2024.110167
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    References listed on IDEAS

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    1. Boyle, Phelim P., 1988. "A Lattice Framework for Option Pricing with Two State Variables," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 23(1), pages 1-12, March.
    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. Lo-Bin Chang & Ken Palmer, 2007. "Smooth convergence in the binomial model," Finance and Stochastics, Springer, vol. 11(1), pages 91-105, January.
    4. 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.
    5. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    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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