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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.

Example. Change of numeraire in Black-Scholes economy.

e consider an economy with one deterministic asset $\beta_{t}$ given by the equation MATH and one stochastic asset $S_{t}$ evolving according to MATH The $r$ and $\sigma$ are some real numbers. The $\beta_{t}$ is the numeraire. Indeed, MATH MATH and the $dt$ term cancels out MATH We select $S_{t}$ as a new numeraire. We compute MATH MATH MATH MATH where MATH Hence, under the numeraire $S_{t}$ , the set of defining SDEs has the following form MATH MATH

Notation. Index. Contents.

Copyright 2007