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.
F. Credit correlation.
a. Generic Copula.
b. Gaussian copula.
c. Example: two dimensional Gaussian copula.
d. Simplistic Gaussian copula.
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.

Generic Copula.

e consider several random variables MATH given by the joint distribution MATH For every variable $X_{i}$ we introduce MATH Suppose $U_{i}$ is some uniform random variable supported on $\left[ 0,1\right] $ . Observe that MATH Hence, the variable $X_{i}$ is distributed as MATH for some $U_{i}$ , uniformly distributed on [0,1]. Therefore, MATH


(Sklar theorem 1) Let MATH be uniform on $\left[ 0,1\right] $ random variables given by joint distribution MATH . Pick a set of non decreasing functions MATH MATH and introduce the random variables MATH then

MATH (Sklar theorem 1)


(Sklar theorem 2) Conversely, for any set of random variables MATH given by the joint distribution MATH the expression

MATH (Sklar theorem 2)
is a joint distribution for some uniform on $[0,1]$ random variables MATH .

Notation. Index. Contents.

Copyright 2007