A moment-matching method to generate arbitrage-free scenarios

•The monomial method is applied to build a scenario generator for financial assets.•The scenario generator belongs to the class of the moment-matching methods.•The marginal moments up to the fourth order and correlations are matched.•The generated scenarios satisfy the no-arbitrage condition.•Accuracy and efficiency analysis is carried out when solving financial problems.

We propose a new moment-matching method to build scenario trees that rule out arbitrage opportunities when describing the dynamics of financial assets. The proposed scenario generator is based on the monomial method, a technique to solve systems of algebraic equations. Extensive numerical experiments show the accuracy and efficiency of the proposed moment-matching method when solving financial problems in complete and incomplete markets.