Algebraic Form of Malliavin Calculus: Creation-Annihilation Operators, Conserved Currents and All That

Abstract: The extremely useful method of Malliavin calculus has not yet gained adequate popularity because of the complicated analytic apparatus of this method. The author attempts here to propose a simplified algebraic formalism similar to Malliavin calculus, but based on the notion of creation-annihilation operators instead of Malliavin derivative to replace analytic theorems with algebraic computations. Three test problems: the valuation of portfolio with stochastic payoff function, the expression of the terminal payoff through stochastic integral and the approximate equation for the high-frequency market measure are discussed in Appendices.