Determining The Optimal Number of Periods to Evaluate Option Price Using the Binomial and Trinomial Model A Case Study of Set50 Options

Abstract

The valuation of derivatives, which is the financial instruments, has garnered significant interest from investors, particularly in pricing option derivatives. This study investigates the valuation of options using both binomial and trinomial models. The objective is to determine the appropriate number of steps or intervals (N) for these models to evaluate option values and compare them with the widely used Black-Scholes valuation method. Six different options contracts were selected for this study, with the underlying assets being the SET50 index from the Stock Exchange of Thailand. Historical volatility and implied volatility of the underlying assets were used for comparative valuation.

The research revealed that options valued using the binomial model exhibited more oscillatory behavior compared to those valued using the trinomial model. Ultimately, for the optimal N, both call and put options tended to converge towards the reference price, with errors typically not exceeding ±0.5×10^(-4). This precision corresponds to four decimal places in market prices. The study observed that the trinomial model demonstrated greater stability in its convergence characteristics compared to the binomial model and required fewer intervals for valuation.