Trinomial Option Pricing Model with Yang-Zhang Volatility

Binomial and Trinomial option pricing models are popular because they can be used for many types of options. Both models produce the same results for a vanilla option on a stock that does not pay a dividend and the main advantage of the trinomial model for pricing this type of option is, therefore, only in the number of time steps as it requires half the number of steps compared to the binomial model. This paper is focused on pricing of the American options where the underlying stock pays several dividends during the life of an option. Special attention is paid to the estimation of the volatility. The trinomial model with the Yang-Zhang volatility that handles both opening jumps and drift is used in this paper to estimate the price of options for several stocks that pay dividends and results are compared to the market price of the options.