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Interest-Rate Models and the Pricing of Derivatives:
Practical implementation and calibration methods

The outline for the course is to develop an understanding of multi-factor models that can be applied to the valuation of interest-rate derivatives, such as European-style and Bermudan-style swaptions. The course will begin by reviewing various approaches that have been suggested and used and will then concentrate on the practical implementation of the LIBOR Market Model (LMM). A new approach to building a two-factor, recombining LMM will be explained and illustrated. This approach uses the Ho, Stapleton and Subrahmanyam recombining binomial tree method. Methods of calibrating the model to market prices of caps and swaptions will be discussed.
  1. Review of interest-rate models: Purpose of the models, Spot-rate vs. forward-rate models, single-factor vs. multi-factor models. Standard models for valuation of caps, floors and swaptions. The Black model for pricing LIBOR futures options.

  2. Development and proof of The LIBOR market model (Brace, Gatarek, Musiela model (BGM)). Main features of the LMM: consistency with the Black model for caplets.The forward rate drift in the LMM.

  3. Inputs for the LMM. Steps required for building a one-factor LMM. Building a spreadsheet version of the LMM. The difference between the LMM prices and BK prices for caplets and floorlets. Exercise: build a spreadsheet version of a one-factor two-factor model, 'bushy tree' case.

  4. Calibrating and implementing a 2-factor LMM. Calibration to forward rates, caplet volatilities. Fitting the correlation of forward rates. Calibrating to swaption volatilities.Pricing of Bermudan-style swaptions using the LMM. A recombining binomial version of the 2-factor LMM. A comparison with the 2-factor spot rate approaches of Hull-White and Peterson, Stapleton and Subrahmanyam.
All teaching is delivered by Professor Richard Stapleton.

If you would like to register an interest in participating in any future courses on the Libor Market Model, or if you would like us to perform a course on your behalf, then please register your interest here.

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