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 rate. anilla swap agreement has positive cashflows at times  calculated as and negative cashflows at times calculated as where . The number is some predetermined fixed rate. The swap rate is the particular value of the parameter that makes such contract of zero value at the time . Hence, the is defined by the relationship Since is a martingale with respect to the -forward measure we continue Hence, Observe that Therefore, (Swap rate)

It is useful to express price of swap with any parameter through the swap rate. Similarly to the above computations we have    Notation. Index. Contents.