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Quantitative Analysis
Parallel Processing
Numerical Analysis
C++ Multithreading
Python for Excel
Python Utilities
Services
Author
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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.
A. One dimensional Black equation.
B. Two dimensional Black equation.
3. Mean reverting equation.
4. Affine SDE.
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.

Change of variables for Kolmogorov equation.


he duality between SDE and PDE allows to find change-of-variable transformations that reduce complexity of the problem.

Consider two SDEs MATH and MATH We are interested in evaluation of the expectation MATH We already established in section ( Backward_equation_section ) that the function $u$ is a solution of the following PDE problem: MATH Assume existence of a one-to-one relationship MATH for some functions $f$ and $g$ . We calculate MATH where the function MATH is a solution of the PDE problem MATH

We provide two examples.




A. One dimensional Black equation.
B. Two dimensional Black equation.

Notation. Index. Contents.


















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