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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.
 a. Credit Default Swap.
 b. At-the-money CDS coupon.
 c. Option on CDS.
 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.

## Option on CDS.

e are considering the right to enter into a given CDS contract at some time in the future (maturity of the option). If the reference name of CDS defaults before the expiration of the option then the option vanishes. Hence, if the spread widens then the option appreciates greatly but also is more likely to vanish. Let denote the market value of the CDS with coupon as observed at time . The option matures at . The payoff at the time is . The value of the option at the time is ( )

We perform the change of measure where we introduced the expectation with respect to the numeraire that makes such separation possible (see the ( Common_application_of_change_of_measure )). The existence of such numeraire was discussed before, see ( Risky annuity ).

At this point we recall from ( Risky annuity ) that the itself is a risk neutral expectation of cashflows discounted with . It easy to see that such cashflows combine with yielding

 Notation. Index. Contents.