Quantitative Analysis
Parallel Processing
Numerical Analysis
C++ Multithreading
Python for Excel
Python Utilities
Services
Author
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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.
C. Longstaff-Schwartz technique.
D. Calculation of sensitivities.
a. Pathwise differentiation.
b. Calculation of sensitivities for Monte-Carlo with optimal control.
5. Convex Analysis.
VI. Basic Math II.
VII. Implementation tools II.
VIII. Bibliography
Notation. Index. Contents.

Calculation of sensitivities.


e are interested in calculation of the derivative MATH of the function MATH evaluated by Monte-Carlo simulation of the SDE MATH The naive attempt to apply finite difference: MATH does not work because each of the components is evaluated by the Monte-Carlo procedure with a random error. These errors do not offset. Dividing it by the small quantity $\delta x$ amplifies the error in the final result.




a. Pathwise differentiation.
b. Calculation of sensitivities for Monte-Carlo with optimal control.

Notation. Index. Contents.


















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