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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.
F. Credit correlation.
G. Valuation of CDO tranches.
a. Definitions of CDO contract.
b. Present values of CDO tranches.
c. Distribution of defaulted notional 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.

Present values of CDO tranches.

ccording to the general recipe ( Risk neutral pricing ), the time $t$ value of the coupon payments of the tranche MATH is given by MATH where the MATH are the coupon payment dates and $T_{0}=t$ . The $c$ is the coupon rate. It is tranche-dependent: MATH As always in these notes, the MATH denotes the time $t$ value of riskless zero coupon bond with maturity $T$ . The time $t$ value of the protection/loss leg of the tranche contract is MATH Note that we do not change to the T-forward measure as we did in ( Credit_default_swap_section ). Instead, we assume that the defaults and interest rates are independent.

Notation. Index. Contents.

Copyright 2007