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: quanto caplet. quanto caplet is a contract that pays at an amount proportional to units of dollar. The is the -Libor. Hence, from the \$ point of view, the value of the contract is The is a martingale with respect to the -measure: We wish to transform to the -measure. Hence, we use the ( Change of numeraire recipe ) The combination under the log-sign is the forward exchange rate ( Forward exchange rate ) for the time as observed at  Therefore, Similarly to the previous section we now construct a martingale combination and observe that the price of the contract is given by the Black-Scholes type formula.

 Notation. Index. Contents.