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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.
A. Definition of change of numeraire.
B. Useful calculation.
C. Transformation of SDE based on change of measure results.
D. Transformation of SDE in two asset situation.
E. Transformation of SDE based on term matching.
F. Invariant representation for drift modification.
G. Transformation of SDE based on delta hedging.
H. Example. Change of numeraire in Black-Scholes economy.
I. Other ways to look at change of numeraire.
3. Basics of derivative pricing II.
4. Market model.
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.

Useful calculation.

he previous section hints that we are going to work with ratios of stochastic processes. We will repeatedly perform the ( Ito_formula )-based evaluation of MATH and MATH MATH MATH Hence,

MATH (Useful formula)
Suppose the stochastic processes $X_{t}$ and $Y_{t}$ are given by the SDEs MATH MATH where the $\sigma$ and $dW$ are columns. In terms of the SDE's coefficients we obtain MATH Note, if $dW_{t}$ is a Brownian motion in a $Y_{t}$ -numeraire measure then the above drift is zero and MATH It is informative to compare the last relationship with the ( Market prices of risk ).

Notation. Index. Contents.

Copyright 2007