LIBOR market model

The LIBOR market model (also BGM model after its authors Brace, Gatarek and Musiela) is an interest structure model for evaluating interest rate derivatives , especially complex interest rate derivatives. In contrast to other models, it uses LIBOR rates and volatilities that can be observed on the market (cap volatilities which are broken down into caplet volatilities).

model

In the LIBOR market model is for forward rates , a dynamic of form ${\displaystyle n}$ ${\displaystyle L_{i}}$ ${\displaystyle i=1,\ldots ,n}$

${\displaystyle {\frac {dL_{i}(t)}{L_{i}(t)}}=\mu _{i}(t)\ dt\ +\ \sigma _{i}(t)\ dW_{i}{\text{,}}\qquad i=1,\ldots ,n}$

accepted. Here is the term for the period . The model therefore corresponds to the Black model for a single term . Compared to the Black model, the LIBOR market model considers the dynamics of an entire family of forward rates under a uniform measure. ${\displaystyle L_{i}}$ ${\displaystyle [T_{i},T_{i+1}]}$

literature

Original work

• Alan Brace, Dariusz Gatarek, Marek Musiela: The Market Model of Interest Rate Dynamics . In: Mathematical Finance . tape 7 , 1997, pp. 127-147 (English).
• Farshid Jamshidian: LIBOR and Swap Market Models and Measures . In: Finance and Stochastics . tape 1 , 1997, p. 293-330 (English).
• Kristian R. Miltersen, Klaus Sandmann, Dieter Sondermann: Closed Form Solutions for Term Structure Derivatives with Lognormal Interest Rates . In: Journal of Finance . tape 52 , 1997, pp. 409-430 (English).

Books

• Damiano Brigo, Fabio Mercurio: Interest Rate Models - Theory and Practice . Springer, Berlin 2001, ISBN 3-540-41772-9 (English).
• Christian P. Fries: Mathematical Finance: Theory, Modeling, Implementation . Wiley, 2007, ISBN 0-470-04722-4 (English, table of contents ).
• Marek Musiela, Marek Rutkowski: Martingale methods in financial modeling: theory and applications . Springer, 1997, ISBN 3-540-61477-X (English).
• Riccardo Rebonato: Modern Pricing of Interest-Rate Derivatives: The Libor Market Model and Beyond . Princeton University Press, 2002, ISBN 0-691-08973-6 (English).
• John Schoenmakers: Robust Libor Modeling and Pricing of Derivative Products . Chapman and Hall, 2005, ISBN 1-58488-441-X (English).
• Johannes Wernz: Bank Management and Control . Springer Nature, 2020, ISBN 978-3-03042866-2 (English).

Web links

• Java applets for valuation with the LIBOR market model and Monte Carlo methods