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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.
5. Heston equations.
6. Displaced Heston equations.
7. Stochastic volatility.
8. Markovian projection.
A. Markovian projection on displaced diffusion.
a. Example of Markovian projection of a separable process on a displaced diffusion.
B. Markovian projection on Heston model.
9. Hamilton-Jacobi Equations.
IV. Data Analysis.
V. Implementation tools.
VI. Basic Math II.
VII. Implementation tools II.
VIII. Bibliography
Notation. Index. Contents.

Example of Markovian projection of a separable process on a displaced diffusion.

e aim to approximate the process $X_{t}$ given by the SDEs MATH with the displaced diffusion process MATH Here the $a_{1}$ , $a_{2}$ , $b_{ij}$ , $X_{0}$ are numbers. MATH are single dimensional stochastic processes.

We apply the recipes ( MarkPr1 Sigma ) and ( MarkPr1 Beta ). Such recipes require expressions for several expectations that we calculate below. MATH MATH MATH MATH MATH MATH The first term is zero because MATH and MATH We continue MATH At this point we have expressions for the quantities of interest in terms of MATH and MATH . We apply the operation $E^{\ast}$ to the SDE for $X_{1,t}$ and obtain MATH MATH The quantities of interest MATH are calculated above to be MATH We substitute the expressions for MATH and calculate the integrals: MATH MATH MATH We substitute these expressions into ( MarkPr1 Sigma ) and ( MarkPr1 Beta ): MATH MATH

Notation. Index. Contents.

Copyright 2007