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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.
IV. Data Analysis.
V. Implementation tools.
1. Finite differences.
2. Gauss-Hermite Integration.
3. Asymptotic expansions.
4. Monte-Carlo.
A. Generation of random samples.
B. Acceleration of convergence.
a. Antithetic variables.
b. Control variate.
c. Importance sampling.
d. Stratified sampling.
C. Longstaff-Schwartz technique.
D. Calculation of sensitivities.
5. Convex Analysis.
VI. Basic Math II.
VII. Implementation tools II.
VIII. Bibliography
Notation. Index. Contents.

Antithetic variables.

e approximate $E\left( X\right) $ with MATH MATH where $\xi$ is the standard normal variable. Suppose the $X_{k}$ is drawn as a function of some uniformly distributed on $\left[ 0,1\right] $ variable : MATH . We consider MATH as an alternative procedure for simulation of $E\left( X\right) $ . The $\tilde{X}$ is an unbiased estimator: MATH and the convergence in distribution is MATH We want to compare MATH with MATH . This is a valid comparison if it costs nothing to generate $F\left( -U\right) $ in addition to $F\left( U\right) $ . We have MATH MATH MATH Hence, it suffices to have MATH to improve efficiency of simulation.

Notation. Index. Contents.

Copyright 2007