CMBS Tranche Valuation Framework: Correlated
Geometric Brownian Motions Simulation

Abstract

This article proposes a Monte Carlo simulation framework for valuation of commercial mortgage-backed securities (CMBS) based on loan level net operating income (NOI) and market capitalization rate. By using geometric Brownian motions (GBM) to create stochastic paths for NOI and cap rate, one can simulate credit defaults and loss severity. Correlation is introduced between loan NOIs to allocate losses along the capital structure of the CMBS. Stochastic months-to-recovery variables are also generated through a Poisson process to capture equity tranche interest-only option value. The model offers a framework to systematically evaluate CMBS tranche prices by decomposing principal prepayment risk as well as credit default risk, which offers potential trading opportunities in the market.