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.
2. Change of variables for Kolmogorov equation.
3. Mean reverting equation.
4. Affine SDE.
5. Heston equations.
6. Displaced Heston equations.
7. Stochastic volatility.
A. Recovering implied distribution.
B. Local volatility.
C. Gyongy's lemma.
D. Static hedging of European claim.
E. Variance swap pricing.
a. Variance swap pricing for drifting price process.
b. Volatility smile formula for fair variance.
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.

Variance swap pricing for drifting price process.

e expand considerations of the section ( Variance swap pricing ) to the process $Y_{t}$ given by MATH and the $\Omega_{T}^{Y}$ is defined as before: MATH

We introduce $X_{t}$ by the relationship MATH then MATH hence MATH Observe that MATH hence, according to the section ( Variance swap pricing ) MATH MATH

For the purposes of the next section we need a formula that expresses the MATH in terms of $Y_{T}$ . Hence, we calculate further

MATH (Fair Variance vs Log contract)

Notation. Index. Contents.

Copyright 2007