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.

## At-the-money CDS coupon. et be a fixed CDS coupon schedule. It makes sense to introduce a coupon that sets market value of a CDS to zero given market conditions at time moment . The is a stochastic process.

Based on the relationship we obtain The expression in the numerator is a price of combination of risky annuities. We can use it as a numeraire as long as there is no default. Hence, there exists a probability measure such that the is a martingale.

We represent the price of the CDS using the quantity : Hence, we replace a non-observable quantity with the directly quoted quantity .

We introduce the notation (Risky annuity)
and write the last result as Notation. Index. Contents.