Introducing the Citi LMM Term Structure Model for Mortgages

Abstract

Valuation of mortgage-backed securities pairs a prepayment model with a term-structure model of interest rates. While the prepayment model is crucial, the choice of the term-structure model matters as well. The article presents Citigroup’s Libor Market Model for MBS valuation and compares it to the short-rate term-structure model currently in production. The new LMM term-structure model improves control over the volatility and correlations structure of forward LIBORs. This leads to more realistic correlations of swap rates. The new model achieves a more accurate calibration to the entire volatility surface. The authors discuss consequences for serial correlation of swap rates and mortgage option volatility. The Mortgage Option-Adjusted Term Structure (MOATS) model, Citi’s approach to arbitrage-free mortgage rate modeling, has been re-implemented to work with LMM, retaining all desirable properties. The LMM produces wider OASs and longer durations than in the current model; the partial durations and vegas are comparable.