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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.

## Swap measure. he expression located in the denominator of the ( Swap rate ) is a linear combination of prices of traded instruments. It is always positive. According to formula ( Suitable numeraire ), may be taken as a numeraire. The probability measure associated with the numeraire is called the "swap measure". The numerator of the formula ( Swap rate ) is also a price of a traded instrument. Therefore, the quantity is a martingale under the swap measure.

One may justify use of Black-Scholes formula for pricing of swaption using the notion of swap measure. Indeed, price of swaption is given by    We arrived to the Black-Scholes situation if is assumed to be log-normal.

 Notation. Index. Contents.