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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.
6. Credit risk.
A. Delta hedging in situation of predictable jump I.
B. Delta hedging in situation of predictable jump II.
C. Backward Kolmogorov's equation for jump diffusion.
D. Risk neutral valuation in predictable jump size situation.
E. Examples of credit derivative pricing.
F. Credit correlation.
a. Generic Copula.
b. Gaussian copula.
c. Example: two dimensional Gaussian copula.
d. Simplistic Gaussian copula.
G. Valuation of CDO tranches.
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.

Credit correlation.


e need a way to represent correlated default of several underlyings. Similarly to the previous chapter (see section ( Basket credit derivative section )) we will be separating the entire filtration $\QTR{cal}{G}_{t}$ into two filtrations $\QTR{cal}{H}_{t}$ and $\QTR{cal}{F}_{t}$ . The $\QTR{cal}{H}_{t}$ holds jump information. The $\QTR{cal}{F}_{t}$ is chosen so that the jumps described by $\QTR{cal}{H}_{t}$ would be independent conditionally on MATH . Such construction is what we will call "conditionally independent" credit events. Research literature holds a variety of recipes for such separations. The market accepted technique is Gaussian copula. According to Gaussian copula we will be representing the $j$ th underlying's default time $\tau_{j}$ using the Prob MATH calculated as Prob MATH for some properly chosen values MATH and correlated normal variables $X_{j}$ .




a. Generic Copula.
b. Gaussian copula.
c. Example: two dimensional Gaussian copula.
d. Simplistic Gaussian copula.

Notation. Index. Contents.


















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