Convergence of trinomial formula for European option pricing

Yuttana Ratibenyakool and Kritsana Neammanee

Communications in Statistics - Theory and Methods, 2022, vol. 51, issue 18, 6227-6249

Abstract: The binomial formula which was given by Cox et al. is a tool for valuating the European call option. We know that it converges to the Black–Scholes formula which was given by Black and Scholes as the number of periods (n) converges to infinity. In 1988, Boyle introduced the trinomial formula to be another tool for calculating the European call option. In 2013, Entit et al. considered the trinomial formula in case that the rate of a stock price rising is u=eλσTn and the rate of a stock price falling is d=u−1, where T is maturity time, σ is volatility and λ>1. They gave examples to show that the value of European option from their model is closed to the value from the Black–Scholes formula. In this paper, we give the rigorous proof of this conjecture by showing that the trinomial formula converges to the Black–Scholes formula.

Date: 2022
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DOI: 10.1080/03610926.2020.1860221

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