What is the LIBOR Market Model?

Danielle DeLee

The LIBOR market model is a model of the interest rate market. It predicts the behavior of interest rates based on certain assumptions of which factors influence their movement. The model is often used for its method of pricing financial derivatives, most notably interest rate swaps, and determining a hedging strategy for investors who hold them.

Man climbing a rope
Man climbing a rope

The exact origin of the model is unknown, but it was probably in use for several years before its formal publication in an economic paper. It was published in three papers in 1997: one by Alan Brace, Dariusz Gatarek and Marek Musiela; one by Farshid Jamshidian; and one by Kristian Miltersen, Klaus Sandmann and Dieter Sondermann. These authors’ names inspired alternative names for the model. It is sometimes known as the BGM model or the BGM/J model. The most common name for the model, however, is the LIBOR market model, or the LMM.

The LIBOR in LIBOR market model is a commonly used abbreviation for the London Interbank Offered Rate. LIBOR is the interest rate that banks offer each other for overnight loans that demand no collateral from the borrowing bank. This interest rate is a widely accepted benchmark rate that serves as a basis for many of the interest rate swaps sold on the market.

The LIBOR market model uses stochastic processes to predict the movement of LIBOR rates. Other models predict short-term interest rates, but the LIBOR market model gives a set of forward rates. These rates are all predictions of future LIBORs, so the accuracy of the model may be tested by comparing its predictions with observed LIBORs in the market.

Having a set of forward interest rates enables investors to perform various calculations to determine pricing and investment strategies. They can use the forward rates to discount the expected cash flows from derivatives so they can more accurately decide what to pay for them in the present. Expectations of interest rates also help them to determine how to construct their portfolios to guard against risk using a combination of derivatives.

The LIBOR is the basis for a variety of derivatives, which means the LIBOR market model can be used to price complicated derivatives that include interest rate swaps in their structures. Its uses include calculating the prices of Bermudan swaptions, an option to enter into an interest rate swap that is complicated by its limitations on the dates on which the options may be exercised. The LIBOR market model is also instrumental in determining prices for a range of other derivatives.

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