Bulls vs Bears: a Trinomial Model of a Financial Asset

Abstract: We present a variation of the well-known binomial model of asset prices. This variation incorporates a bound to short-selling, inspired by a model from Gunduz Caginalp[2]. We formalize this model and prove a formula for all the moments of the logarithmic returns. We also derive a formula for the case with infinitely many investors. As an application of the model, we show how to compute parameters in order to approximate given moments, enabling the modeling of skewness and excess kurtosis. Finally, we generalize the model and give the corresponding formula for the moments of the logarithmic returns, and the algorithm for fitting given moments.