Comparative Analysis of Lattice Based Option Pricing Models

Binomial and trinomial option pricing models are very popular numerical methods for pricing American option. In general, there is unfortunately no analytical solution to the American option problem. Since, no closed form solution is derived, lattice based models as binomial and trinomial model can be used in order to obtain approximate solutions. The binomial option pricing model was developed in 1979. This model involves the construction of binomial tree to represent the various probabilities for the future price over the life of the option. However, the binomial model assumes that the option price can either go up or down over a time step. It does not assume that the option price may remain unchanged. In 1986 Boyle proposed the trinomial option pricing model. Under the model, in each period, the prices can go up, down or remain unchanged ant that‘s the reason why author of trinomial model present it as an improvement of binominal model. However, trinomial model have never achieved popularity of binominal model. This phenomenon inspired authors of this paper to research rate of convergence of previously mentioned models. In this paper authors will generalize research of M. Horasali (2007) in which he research rate of convergence of binominal and trinomial model for “in the money” options. In this paper we research rate of convergence for “in the money”, “at the money” and “out of the money” options. Furthermore, authors will be, also, determined time which computer spends to calculate value of options with given precision.