The convergence of binomial and trinomial option pricing models

We can get the fair value of any financial derivative either analytically, by simulation or applying suitable numerical technique. For example, when we solve the American option valuation problem, the lattice models can be very useful. The procedure is based on modeling of the underlying asset price evolution (in discrete time with discrete price increments) and subsequent evaluation of the payoff function for all scenarios. Next, the initial fair value is obtained by backward procedure. The evolution of the underlying asset can be modeled e.g. by binomial model, trinomial model, etc. In this paper we study the principles of binomial and trinomial models and, since we can treat them as an approximation of the continuous time model, their convergence. More particularly, we examine the convergence of European call and American put options. The application possibilities of lattice models are connected to the firm management through the broad field of real options.