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.

Importance sampling.

e are considering evaluation of MATH where the variable $X$ is sampled from density $f$ . We switch the density: MATH MATH We aim to decrease the variance by switching from MATH to MATH Clearly, the optimal density is MATH The last relationship means that we want to shift the density of our sampling to the values of $x$ that deliver greater values of $h\left( x\right) $ .

Notation. Index. Contents.

Copyright 2007