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 and that are acceptable as numeraires (see ( Suitable_numeraire )) for some . The drift term is absent because is a martingale in the -measure. Also, for some . We regard these last SDEs as and for . We derive the connection between and as follows: Hence, and It remains to find the expression for . We use the formula ( Useful formula ): Hence, and we conclude that

 Notation. Index. Contents.