Quantitative Analysis
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Python for Excel
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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.

Transformation of SDE based on term matching.

e consider two assets $X_{t}$ and $Y_{t}$ that are acceptable as numeraires (see ( Suitable_numeraire )) MATH for some $\sigma$ . The drift term MATH is absent because $Z=X/Y$ is a martingale in the $Y$ -measure. Also, MATH for some $\omega$ . We regard these last SDEs as MATH and MATH for $Z=X/Y$ . We derive the connection between $dW^{X}$ and $dW^{Y}$ as follows: MATH Hence, MATH and MATH It remains to find the expression for $\sigma$ . We use the formula ( Useful formula ): MATH Hence, MATH and we conclude that MATH

Notation. Index. Contents.

Copyright 2007