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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.

## Forward LIBOR. et be observation time. We consider an agreement to invest at time , , a fixed amount of cash and collect at , , one unit of reference currency. We denote the simple compounding rate during the time interval implied by such a contract. We replicate this contract by selling units of bond and purchasing one unit of bond . If the implied rate is fair then the contract should not worth anything at time : The cash flow at time is . According to the contract, the investment will grow at the rate up to the time when it pays 1 unit of currency. Therefore We conclude that the fair rate for the contract is given by the relationship (Libor)

By definition, this is the "forward LIBOR". The structure of the last formula is such that the rate is a martingale with respect to the forward probability measure Prob Prob .

 Notation. Index. Contents.