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The Convergence Rate of Option Prices in Trinomial Trees
Leduc, Guillaume Palmer, Kenneth
Leduc, Guillaume
Palmer, Kenneth
Date
2023-03-26
Author
Advisor
Type
Article
Peer-Reviewed
Published version
Peer-Reviewed
Published version
Degree
Description
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.