Learning Bermudans

Abstract

American and Bermudan-type financial instruments are often priced with specific Monte Carlo techniques whose efficiency critically depends on the effective dimensionality of the problem and the available computational power. In our work we focus on Bermudan Swaptions, well-known interest rate derivatives embedded in callable debt instruments or traded in the OTC market for hedging or speculation purposes, and we adopt an original pricing approach based on Supervised Learning (SL) algorithms. In particular, we link the price of a Bermudan Swaption to its natural hedges, i.e. the underlying European Swaptions, and other sound financial quantities through SL non-parametric regressions. We test different algorithms, from linear models to decision tree-based models and Artificial Neural Networks (ANN), analyzing their predictive performances. All the SL algorithms result to be reliable and fast, allowing to overcome the computational bottleneck of standard Monte Carlo simulations; the best performing algorithms for our problem result to be Ridge, ANN and Gradient Boosted Regression Tree. Moreover, using feature importance techniques, we are able to rank the most important driving factors of a Bermudan Swaption price, confirming that the value of the maximum underlying European Swaption is the prevailing feature.

Keywords: Bermudan, Swaptions, Pricing, Interest Rates, Derivatives, Least Square, Monte Carlo, Hull-White model, G1++, Machine Learning, Supervised Learning, Neural Networks, Ridge, Support Vector Machine, Decision Tree, Random Forest, Gradient Boosted Regression Tree, K-Nearest Neighbours, Regression, Hedgi

JEL Classification: C45, C53, C63, G12