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Quantitative Analysis
Parallel Processing
Numerical Analysis
C++ Multithreading
Python for Excel
Python Utilities
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I. Basic math.
II. Pricing and Hedging.
III. Explicit techniques.
1. Black-Scholes formula.
2. Change of variables for Kolmogorov equation.
3. Mean reverting equation.
4. Affine SDE.
A. Ricatti equation.
B. Evaluation of option price.
C. Laplace transform.
D. Example: CDFX model.
a. Definition of CDFX model.
b. The martingale normalization (CDFX).
c. Fourier transform (CDFX).
d. Calculation of Fourier transform (CDFX).
e. Calculation of Premium Leg of CDS.
f. Calculation of the protection leg of the CDS.
5. Heston equations.
6. Displaced Heston equations.
7. Stochastic volatility.
8. Markovian projection.
9. Hamilton-Jacobi Equations.
IV. Data Analysis.
V. Implementation tools.
VI. Basic Math II.
VII. Implementation tools II.
VIII. Bibliography
Notation. Index. Contents.

Calculation of the protection leg of the CDS.

e would like to calculate the expression MATH We proceed similarly to the previous section. We calculate the drift MATH Hence, MATH We conclude that MATH Following logic of the previous section we will be seeking for a function $V_{t}$ of the form MATH for some deterministic functions MATH having the property MATH We have MATH We introduce notation MATH with

MATH then MATH Hence we calculate the drift part as MATH MATH MATH MATH We want the above expression to be MATH Hence, it suffices to have MATH where we made an assertion that $\alpha$ and $\beta$ are the same as in the previous section and $a$ and $b$ are given by the same expressions MATH Consequently, MATH We separate the coordinates MATH We substitute the expressions for the $g,h,q$ . The equations for $\alpha,~\beta$ have been calculated before. The equations for $\gamma,\delta$ resolve to MATH

Notation. Index. Contents.

Copyright 2007