Content of present website is being moved to www.lukoe.com/finance . Registration of www.opentradingsystem.com will be discontinued on 2020-08-14.
 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 given by and the is defined as before:

We introduce by the relationship then hence Observe that hence, according to the section ( Variance swap pricing )

For the purposes of the next section we need a formula that expresses the in terms of . Hence, we calculate further

 (Fair Variance vs Log contract)

 Notation. Index. Contents.