Content of present website is being moved to www.lukoe.com/finance . Registration of www.opentradingsystem.com will be discontinued on 2020-08-14.
Quantitative Analysis
Parallel Processing
Numerical Analysis
C++ Multithreading
Python for Excel
Python Utilities
Services
Author
Printable PDF file
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.


















Copyright 2007