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.

Two dimensional Black equation.

e compute the quantity MATH MATH MATH where the MATH are volatilities of the assets (positive real numbers), $\rho$ is correlation (real number, $-1\leq\rho\leq1$ ), MATH is an integrable function and $W_{1,t}$ , $W_{2,t}$ are independent standard Brownian motions.

According to the multidimensional version of the backward Kolmogorov's equation ( Backward equation section ) the function MATH is a solution of the problem MATH MATH Similarly to the previous section ( one-dim case ) we introduce the process MATH and observe MATH In addition MATH MATH and MATH Therefore, we define the process MATH MATH MATH Conversely, MATH MATH Hence, for the function MATH may be represented as MATH with $w$ being the solution of MATH MATH

Notation. Index. Contents.

Copyright 2007