Mean square optimal hedges using higher order moments

The authors pose and solve a mean square optimal hedging problem that takes higher order moments (or cumulants) into account. They first provide a discrete stochastic dynamics model using a general multinomial lattice, where the first m cumulants are matched over each time step. They then analyze the effect of higher order moments in the underlying asset process on the price of derivative securities. The relationship between the term structure of the volatility smile and smirk and higher order cumulants is illustrated through numerical experiments.