The Maximum and Minimum Price in Trinomial Model

In this work, we discussed the problem of the trinomial model which is also called the trinomial tree model. This research is based on the binomial model, but it is much more complicated and realistic than the binomial model because it contains the situation that the stock price does not change. In this work, how asset option pricing is made, the time when the trinomial model can be replicated, the value of probabilities for the increased, unchanged, and decreased strike respectively, the maximum and minimum price in the trinomial model, and the option pricing formula are discussed. Basic financial knowledge of non-arbitrage and statistics knowledge for probabilities are covered in this work to fulfill our goal.