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.
 a. Credit Default Swap.
 b. At-the-money CDS coupon.
 c. Option on CDS.
 d. Basket Credit derivative.
 F. Credit correlation.
 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.

## Basket Credit derivative. e have two instruments with prices and , default intensities and and default times . The default times are independent random variables (or conditionally independent, see ( Copula calculation for CDO )). The default times generate filtration . The generate filtration . The composition of the two filtrations and is . Let be the time of the first default of any asset. We aim to calculate According to the transformation (see the ( Total probability rule )) it suffices to compute as if the are deterministic functions of time. We proceed according to such recipe and use the techniques of the section ( Distribution of Poisson process section ),  We perform evaluation of the summation terms:    and continue the main calculation,  Suppose that we have three instruments and we are interested in calculation of the defined as the time of second default.    Notation. Index. Contents.