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.

## Generic Copula.

e consider several random variables given by the joint distribution For every variable we introduce Suppose is some uniform random variable supported on . Observe that Hence, the variable is distributed as for some , uniformly distributed on [0,1]. Therefore,

Summary

(Sklar theorem 1) Suppose the uniform on random variables are given by the distribution . Pick a set of non decreasing functions and introduce the random variables then

 (Sklar theorem 1)

Summary

(Sklar theorem 2) Conversely, for any set of random variables given by the joint distribution the expression

 (Sklar theorem 2)
is a joint distribution for the random uniform on [0,1] variables . Here the functions are marginal distributions of .

 Notation. Index. Contents.