Quantitative Analysis
Parallel Processing
Numerical Analysis
C++ Multithreading
Python for Excel
Python Utilities
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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 $V_{t}$ dependent on pound price of a traded asset $S_{t}^{\U{a3}}$ . The state variable is given by MATH . We assume that the rates are constants to limit the size of the calculation. We compose the dollar valued portfolio $\Pi$ MATH where $\beta_{t}^{\U{a3}}$ 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 MATH MATH MATH where the bracket MATH refers to the sum of the second derivatives in $S$ and $X$ , see ( XY_bracket ). If we set MATH then we obtain MATH MATH MATH Finally, MATH Assuming that the only cashflow that the contract pays is the final cashflow MATH we may represent $V$ as an expectation MATH This result agrees with the result of the previous section because the price $S_{t}$ is given by the SDE MATH in the risk neutral $\U{a3}$ -measure. We change the numeraire to the risk-neutral $-measure MATH and obtain MATH

Notation. Index. Contents.

Copyright 2007