Options play an important part in financial markets. Throughout the years, several pricing theories have been developed to generate fair prices for options of different sorts. In this thesis we investigate the trinomial asset pricing model. After giving an explanation of its properties, we use the trinomial model to derive a fair price of standard European options. We study the trinomial model approximation of the Black-Scholes price and finally apply the trinomial model on six different exotic options. We have found that, under certain conditions on the model parameters, the trinomial price converges to the Black-Scholes price. Furthermore, we have established that pricing American put options works well using the trinomial model. Regarding the investigated exotic options, we conclude that the trinomial model can often be suitable to use when pricing exotic options that are not path dependent. In relation to the less advanced binomial model, the trinomial model has the advantage of converging to the Black-Scholes price faster than the binomial model.