Scenario tree generation and multi-asset financial optimization problems

We compare two popular scenario tree generation methods in the context of financial optimization: moment matching and scenario reduction. Using a simple problem with a known analytic solution, moment matching–when ensuring absence of arbitrage–replicates this solution precisely. On the other hand, even if the scenario trees generated by scenario reduction are arbitrage-free, the solutions are biased and highly variable. These results hold for correlated and uncorrelated asset returns, as well as for normal and non-normal returns.