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.

## Acceleration of convergence.

et be a random variables and are random samples from . The letter usually denotes size of a sample. The notation stands for standard deviation, is mean. The letters denote real numbers. The letters usually denote functions of real variable.

 a. Antithetic variables.
 b. Control variate.
 c. Importance sampling.
 d. Stratified sampling.
 Notation. Index. Contents.