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.
1. Black-Scholes formula.
A. No drift calculation.
B. Calculation with drift.
2. Change of variables for Kolmogorov equation.
3. Mean reverting equation.
4. Affine SDE.
5. Heston equations.
6. Displaced Heston equations.
7. Stochastic volatility.
8. Markovian projection.
9. Hamilton-Jacobi Equations.
IV. Data Analysis.
V. Implementation tools.
VI. Basic Math II.
VII. Implementation tools II.
VIII. Bibliography
Notation. Index. Contents.

No drift calculation.

e are calculating the expectation MATH where the $K,x,t,T$ are given numbers, MATH is a deterministic function and $W_{t}$ is the standard Brownian motion.

According to the Ito formula ( Ito_formula ) MATH We integrate the above equality over the time interval $[t,T]$ and obtain MATH We introduce the notations $\theta,\sigma$ according to the relationship MATH and write MATH for some standard normal variable $\xi$ .

We proceed with evaluation of the quantity $C_{0}$ : MATH where $d$ is the number defined by the relationship MATH or MATH We introduce the notation MATH and continue MATH


The expectation MATH evaluates to

MATH (No drift Black Scholes)

Notation. Index. Contents.

Copyright 2007