Convergence of trinomial formula for call option prices

Abstract

The binomial formula given by Cox, Ross and Rubinstein (1979) is a tool for valuating the call option price. It is well known that the price from binomial formula converges to the price from Black-Scholes formula which was given by Black, Scholes and Merton (1973) as the number of periods (n) converges to infinity. In 1988, Boyle introduced the trinomial formula which is another tool for calculating call option price. He considered the trinomial formula in the case that the rising rate of a stock price is u = e λσ√T n and the falling rate of the stock price is d = u −1 , where T is maturity time, σ is volatility and λ > 1. After that, Entit et al. (2013) gave examples which show that the call option price from trinomial formula is closed to the call option price from the Black-Scholes formula. In this thesis, we give the rigorous proof of this conjecture by showing that the trinomial formula converges to the Black-Scholes formula. Moreover, we prove that the rate of this convergence is 1 √ n .