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.

## Credit Default Swap. he credit default swap contract is designed to provide protection from a credit event associated with a risky bond. The coupon leg of the CDS pays coupon while there is no credit event. The protection leg of the credit default swap pays only if there is a credit event before maturity of the CDS. At the time of the credit event the protection buyer (=coupon payer) receives par from the protection seller (=coupon receiver) and delivers the bond to the protection seller. On default the coupon leg pays the accrued interest.

Let be the coupon payment dates, be the effective date of the swap, be the coupon, the default time (first and the only one), be recovery rate at default and is the MMA interest rate. The value of the coupon leg at time is The value of the protection leg is We proceed to evaluate each of the components. We apply the formula ( Common_application_of_change_of_measure ) and results of the section ( T-forward probability measure ): where we introduced the notation We introduce a fine mesh on the interval and use the previously developed techniques (see section ( Distribution of Poisson process section )):  The other leg of the contract is valued in the similar manner:  where we introduced the new function modelling the expectation of the recovery rate. We collect all the pieces together: Conventionally, it is assumed that the is flat: .

 Notation. Index. Contents.