Lattice structures for the stochastic comparison of call ratio backspread derivatives with an application

Abstract

The comparison of investments in fnancial derivatives is an appealing topic in the optimization of resources. A relevant derivative is the call ratio backspread. Motivated by the need to compare investments in such derivatives, a new family of stochastic orders is introduced. That permits to reach decisions on the allocations of funds in those derivatives under general conditions and without assuming specifc probability distributions of the asset prices. Characterizations of the orders are developed. Special emphasis is placed on the existence of infma and suprema in such dominance criteria, which leads to lattice structures on some special spaces and to the reduction of some optimization problems with stochastic dominance constraints. The method is illustrated with an application using real data from fnancial markets.