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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.
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.

One dimensional Black equation.

uppose we would like to compute the quantity MATH given by the relationships MATH MATH where the $\sigma>0,$ $T>0$ are real numbers, MATH is an integrable function and $dW_{t}$ is increment of standard Brownian motion. According to the backward Kolmogorov's theorem, see the section ( Backward equation section ), the quantity MATH is a solution of the problem MATH MATH We introduce the process MATH According to the Ito formula ( Ito formula ) MATH MATH With such observation we can write MATH MATH MATH

Notation. Index. Contents.

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