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 I. Basic math.
 II. Pricing and Hedging.
 1 Basics of derivative pricing I.
 2 Change of numeraire.
 3 Basics of derivative pricing II.
 4 Market model.
 5 Currency Exchange.
 A. Change of numeraire in currency markets.
 B. Invariant form of SDE transformation formula.
 C. Delta hedging in currency markets.
 D. Example: forward contract to purchase foreign stock for domestic currency.
 E. Example: forward currency exchange contract.
 F. Example: quanto forward contract.
 G. Example: quanto caplet.
 H. Example: quanto fixed-for-floating swap.
 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: forward currency exchange contract.

e price at time a contract to exchange for at a future time and for fixed exchange rate . We determine a fair forward exchange rate by the following argument. We purchase units of riskless -bond, short one riskless -bond with maturity at and enter into the exchange contract in question. The forward exchange rate that makes such position of zero value is the correct exchange rate. These are the -values of the replicating position: where we used by definition of the bond and offset the contract in question at time . We obtained two equations for two unknown variables and . The solution is

 (Forward exchange rate)

 Notation. Index. Contents.