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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.
A. Recovering implied distribution.
B. Local volatility.
C. Gyongy's lemma.
a. Multidimensional Gyongy's lemma.
D. Static hedging of European claim.
E. Variance swap pricing.
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.

Multidimensional Gyongy's lemma.


Suppose the process $X_{t}$ taking values in $R^{N}$ is given by the SDE MATH where the $\beta_{t}$ is a matrix valued adapted stochastic process, $\alpha_{t}$ is a column-valued adapted process and the $dW_{t}$ is the column of the standard Brownian motions. The process $Y_{t}$ taking values in $R^{N}$ and given by the SDE MATH has the same component-wise distributions as $X_{t}$ if the deterministic functions MATH and MATH are given by the relationships MATH The $b_{k}$ is a $k$ -th row of the matrix $b$ and the multiplication $b_{k}b_{p}$ above is the scalar product.

Notation. Index. Contents.

Copyright 2007