Content of present website is being moved to . Registration of will be discontinued on 2020-08-14.
Quantitative Analysis
Parallel Processing
Numerical Analysis
C++ Multithreading
Python for Excel
Python Utilities
Printable PDF file
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.

Transformation of SDE based on change of measure results.

reviously (see the formula ( General change of Brownian motion )) we calculated generic change of measure for Brownian motion $dW_{t}$ . If $a_{t}$ is given by the SDE MATH in the original measure then the change MATH results in MATH where the $d\tilde{W}_{t}$ is a standard Brownian motion with respect to the new probability $E_{a}$ .

According to the formula ( Change of numeraire kernel ), when the change of numeraire is performed, the process $a\left( t\right) $ is given by the expression MATH Thus, MATH for Brownian motion $dW^{M}$ in $M$ -measure. Therefore, MATH or

MATH (Change of Brownian motion)

Notation. Index. Contents.

Copyright 2007