The Convergence Rate of Option Prices in Trinomial Trees

Guillaume Leduc () and Kenneth Palmer ()
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Guillaume Leduc: Department of Mathematics and Statistics, American University of Sharjah, Sharjah P.O. Box 26666, United Arab Emirates
Kenneth Palmer: Department of Mathematics, National Taiwan University, Taipei 10617, Taiwan

Risks, 2023, vol. 11, issue 3, 1-33

Abstract: We study the convergence of the binomial, trinomial, and more generally m -nomial tree schemes when evaluating certain European path-independent options in the Black–Scholes setting. To our knowledge, the results here are the first for trinomial trees. Our main result provides formulae for the coefficients of 1 / n and 1 / n in the expansion of the error for digital and standard put and call options. This result is obtained from an Edgeworth series in the form of Kolassa–McCullagh, which we derive from a recently established Edgeworth series in the form of Esseen/Bhattacharya and Rao for triangular arrays of random variables. We apply our result to the most popular trinomial trees and provide numerical illustrations.

Keywords: option pricing; trinomial tree; asymptotic expansion; Edgeworth series (search for similar items in EconPapers)
JEL-codes: C G0 G1 G2 G3 K2 M2 M4 (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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