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.