What Is the Brace Gatarek Musiela (BGM) Model?

The Brace Gatarek Musiela Model (BGM) is a nonlinear financial model that uses the London Interbank Offered Rate (LIBOR) to price interest rate derivatives. The Brace Gatarek Musiela (BGM) model prices securities by examining market-quoted rates. It is used most frequently when pricing swaptions and caplets (a call on LIBOR) on the LIBOR market.

The Brace Gatarek Musiela Model is also known as the LIBOR market model.

Understanding the Brace Gatarek Musiela (BGM) Model

Unlike the Hull-White model, which uses the instantaneous short rate, or the Heath-Jarrow-Morton (HJM) model, which uses the instantaneous forward rate, the Brace Gatarek Musiela Model (BGM) model only uses rates that are observable: forward LIBOR rates. The BGM model is also consistent with Black’s model, which is a variant of the widely used Black-Scholes derivative model.

The Intercontinental Exchange, the authority responsible for LIBOR, will stop publishing one-week and two-month USD LIBOR after Dec. 31, 2021. All other LIBOR will be discontinued after June 30, 2023.

Uses of BGM Model

The BGM model can determine a price for an investment if the payoff can be broken down into forward rates (yields), since forward rates apply to a specific time frame and correlate with other forward rates. Investors can run simulations using the various volatilities and correlations, and then determine the fair value by discounting coupons.

The London Interbank Offered Rate is the average of interest rates estimated by each of the leading banks in London that it would be charged were it to borrow from other banks. It is usually abbreviated to Libor or LIBOR.