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 I. Basic math.
 II. Pricing and Hedging.
 1 Basics of derivative pricing I.
 2 Change of numeraire.
 3 Basics of derivative pricing II.
 4 Market model.
 A. Forward LIBOR.
 B. LIBOR market model.
 C. Swap rate.
 D. Swap measure.
 5 Currency Exchange.
 6 Credit risk.
 7 Incomplete markets.
 III. Explicit techniques.
 IV. Data Analysis.
 V. Implementation tools.
 VI. Basic Math II.
 VII. Implementation tools II.
 VIII. Bibliography
 Notation. Index. Contents.

## LIBOR market model. e are considering a debt structure with payment dates  We introduce the following notation (Libor2)
We introduce the probability measure associated with the price taken as a numeraire, . The is an increment of the th standard Brownian motion under the . It is the assumption of the model that the process is lognormal under for any , where the are some deterministic functions. The increment , , has a drift under  The calculation of is our next task. According to the formula ( Change of drift recipe 1 ) By the definition ( Libor definition ), Hence, for ,  We use the formula ( Change_of_drift_recipe_1 ), Therefore  where the are correlations and are volatilities of the forward rates Similarly, for , LIBOR market model introduces a curve-dependent drift. Hence, it has a state variable (=description of filtration) of high dimensionality.

 Notation. Index. Contents.