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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 measure.

he expression MATH 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 ), MATH may be taken as a numeraire. The probability measure associated with the numeraire MATH is called the "swap measure". The numerator of the formula ( Swap rate ) is also a price of a traded instrument. Therefore, the quantity MATH 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 MATH MATH MATH MATH We arrived to the Black-Scholes situation if MATH is assumed to be log-normal.

Notation. Index. Contents.

Copyright 2007