Unlike a short-rate model, which moves the unobservable instantaneous short rate, the LIBOR market model moves the observable forward rate for a given period directly1. If volatility is a function of time only, caplet prices match Black's formula2.

Although the name contains LIBOR, the same form also applies to Euribor rates1. A paper from the Institute for Monetary and Economic Studies of the Bank of Japan says that modeling LIBOR directly with a lognormal distribution in this way makes the model easy to handle and that it is often implemented by Monte Carlo simulation3. The forward rate equation and how the drift is determined are in the related article (valuation/lmm).

Notes

  1. Martin Haugh, "Market Models" (Columbia University, Term Structure Models: IEOR E4710, 2010), page 1 (the opening and footnote 2). ↩ ↩2

  2. Haugh, "Market Models", page 8, around equations (25) and (26). ↩

  3. Haruyasu Ota, "マルコフ関数モデルによる金利オプションの価格付けの実用化" (Putting the Markov-functional model into practice for pricing interest rate options), Kinyu Kenkyu, Institute for Monetary and Economic Studies, Bank of Japan (October 2010), "1. はじめに" (1. Introduction), page 132 (in Japanese). ↩