Quantitative Analysis
Parallel Processing
Numerical Analysis
C++ Multithreading
Python for Excel
Python Utilities
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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.
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.

Basket Credit derivative.

e have two instruments with prices MATH and MATH , default intensities MATH and MATH and default times $\tau_{1},\tau_{2}$ . The default times are independent random variables (or conditionally independent, see ( Copula calculation for CDO )). The default times generate filtration $\QTR{cal}{H}_{t}$ . The MATH generate filtration $\QTR{cal}{F}_{t}$ . The composition of the two filtrations $\QTR{cal}{H}_{t}$ and $\QTR{cal}{F}_{t}$ is $\QTR{cal}{G}_{t}$ . Let $\tau$ be the time of the first default of any asset. We aim to calculate MATH According to the transformation MATH (see the ( Total probability rule )) it suffices to compute MATH as if the MATH are deterministic functions of time. We proceed according to such recipe and use the techniques of the section ( Distribution of Poisson process section ), MATH MATH We perform evaluation of the summation terms: MATH MATH MATH MATH and continue the main calculation, MATH MATH

Suppose that we have three instruments and we are interested in calculation of the $\tau$ defined as the time of second default. MATH MATH MATH MATH

Notation. Index. Contents.

Copyright 2007