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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.

## Delta hedging in currency markets.

e take the view of a dollar-based observer. We are valuing a contract dependent on pound price of a traded asset . The state variable is given by . We assume that the rates are constants to limit the size of the calculation. We compose the dollar valued portfolio where refers to the pound denominated MMA. The following calculation is similar to the section ( Transformation of SDE based on delta hedging section ). We proceed to calculate the differential where the bracket refers to the sum of the second derivatives in and , see ( XY_bracket ). If we set then we obtain Finally, Assuming that the only cashflow that the contract pays is the final cashflow we may represent as an expectation This result agrees with the result of the previous section because the price is given by the SDE in the risk neutral -measure. We change the numeraire to the risk-neutral \$-measure and obtain

 Notation. Index. Contents.