Option valuation and hedging using multinomial lattices with cumulants

In this paper, we analyze some properties of multinomial lattices that model the underlying stock dynamics by taking into account any given cumulants. A parameterization of multinomial lattices is provided, where we show that mean, variance, skewness, and kurtosis of the underlying may be matched using five branches. We also investigate the convergence of the multinomial lattice when the basic time period approaches zero, and prove that the limiting distribution of the multinomial lattice that matches annualized mean, variance, skew ness and kurtosis is given by that of a compound Poisson process