Rate of convergence of trinomial formula to Black–Scholes formula

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 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 2013, 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.