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.

Example: quanto caplet.

quanto caplet is a contract that pays at $T_{2}$ an amount proportional to MATH units of dollar. The MATH is the $\U{a3}$ -Libor. Hence, from the $ point of view, the value of the contract is MATH The MATH is a martingale with respect to the MATH -measure: MATH We wish to transform to the MATH -measure. Hence, we use the ( Change of numeraire recipe ) MATH The combination under the log-sign is the forward exchange rate ( Forward exchange rate ) for the time $T$ as observed at $t$ MATH Therefore, MATH 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.

Copyright 2007