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.
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.

Ricatti equation.

he Ricatti equation is an ODE of the form MATH where the $u$ is the unknown function of $t$ and the $p,q,r\,$ are known functions of $t$ .

We introduce a new unknown function MATH then MATH for some new known functions $Q,R$ .

We further perform the change MATH We have MATH We arrived to a linear ODE.

Notation. Index. Contents.

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