Market model for forward interest rates
Question
Describe the LIBOR Market Model (also called BGM) and the kinds of products it is typically used for.
Short answer
The LMM (BGM) models a set of discrete, observable forward rates directly, each lognormal under its own forward measure. That makes it consistent with Black's formula for caplets, so it calibrates to caps and swaptions. Drifts follow from no-arbitrage when switching measures, and it is usually implemented by Monte Carlo. It is used for pricing and hedging path-dependent and exotic interest rate products such as Bermudan swaptions and callable range accruals.
Adapted from Wilmott, Frequently Asked Questions in Quantitative Finance, FAQ 39, p.183; question and answer rewritten by SelfMadeQuant.com.
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- Expectations, Volatility, and the Shape of the Term Structure
- Exponential Growth, Decay, and Continuous Compounding
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