Quantitative Analysis
Parallel Processing
Numerical Analysis
C++ Multithreading
Python for Excel
Python Utilities
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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 rate.

anilla swap agreement has positive cashflows at times $T_{k+1},$ MATH calculated as MATH and negative cashflows at times $T_{k+1}$ calculated as $\Delta_{k}K$ where MATH . The number $K$ is some predetermined fixed rate. The swap rate MATH is the particular value of the parameter $K$ that makes such contract of zero value at the time $t$ . Hence, the MATH is defined by the relationship MATH Since MATH is a martingale with respect to the $T_{k}$ -forward measure we continue MATH Hence, MATH Observe that MATH Therefore,

MATH (Swap rate)

It is useful to express price of swap with any parameter $K$ through the swap rate. Similarly to the above computations we have MATH MATH MATH MATH

Notation. Index. Contents.

Copyright 2007