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The Libor Market Model (LMM) is a mathematical model for pricing and risk management of interest rate derivatives and has been built on the framework of modelling forward rates. For the conceptual understanding of the model a strong background in the fields of mathematics, statistics, finance and, especially for implementation, computer science is necessary. The book provides the necessary groundwork to understand the LMM and delivers a framework to implement a working model where possible calibration and parameterization methods for volatility and correlation are explained. Special emphasis lies also on the tradeoff of speed and correctness where differences in choosing random number generators and the advantages of factor reduction are shown.

The Libor Market Model (LMM) is a mathematical model for pricing and risk management of interest rate derivatives and has been built on the framework of modelling forward rates. For the conceptual understanding of the model a strong background in the fields of mathematics, statistics, finance and, especially for implementation, computer science is necessary. The book provides the necessary groundwork to understand the LMM and delivers a framework to implement a working model where possible calibration and parameterization methods for volatility and correlation are explained. Special emphasis lies also on the tradeoff of speed and correctness where differences in choosing random number generators and the advantages of factor reduction are shown. Contents Libor Market Model implementation framework Speed vs. correctness Application examples and possible extensions Target Groups Researchers and advanced master degree students in a quantitative field (Mathematics, Quant. Finance, Statistics, Physics) Practitioners in the quantitative area of the financial services industry The Author Christoph Hackl, MA obtained his master's degree at the UAS bfi Vienna in the programme "Quantitative Asset and Risk Management"

Interest rate traders have been using the SABR model to price vanilla products for more than a decade. However this model suffers however from a severe limitation: its inability to value exotic products. A term structure model à la LIBOR Market Model (LMM) is often employed to value these more complex derivatives, however the LMM is unable to capture the volatility smile. A joint SABR LIBOR Market Model is the natural evolution towards a consistent pricing of vanilla and exotic products. Knowledge of these models is essential to all aspiring interest rate quants, traders and risk managers, as well an understanding of their failings and alternatives. SABR and SABR Libor Market Models in Practice is an accessible guide to modern interest rate modelling. Rather than covering an array of models which are seldom used in practice, it focuses on the SABR model, the market standard for vanilla products, the LIBOR Market Model, the most commonly used model for exotic products and the extended SABR LIBOR Market Model. The book takes a hands-on approach, demonstrating simply how to implement and work with these models in a market setting. It bridges the gap between the understanding of the models from a conceptual and mathematical perspective and the actual implementation by supplementing the interest rate theory with modelling specific, practical code examples written in Python. .

In this article, we review the construction and properties of some popular approaches to modeling LIBOR rates. We discuss the following frameworks: classical LIBOR market models, forward price models and Markov‐functional models. We close with the recently developed affine LIBOR models.

The Lévy Libor or market model which was introduced in Eberlein and Özkan (2005) is extended to a multi-currency setting. As an application we derive closed form pricing formulas for cross-currency derivatives. Foreign caps and floors, cross-currency swaps and quanto caplets are studied in detail. Numerically efficient pricing algorithms based on bilateral Laplace transforms are derived. A calibration example is given for a two-currency setting (EUR, USD).