Ordering Garch processes with financial applications

Motivated by simple comparison results between the exponential Esscher and the minimal entropy martingale measures in one period and multiperiod i.i.d. models, we investigate the problem of stochastic ordering of Garch processes. Viewing the process as a stochastic recurrence we find that the natural orderings that are propagated from the innovations to the logreturns are the peakedness ordering and a kurtosis ordering defined by the convex ordering of squared innovations. We present also a numerical example of stochastic comparison of final prices stemming from ordered innovations from the Ged and the t family.