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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.
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.
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.

Recovering implied distribution.


uppose we are given the functions MATH for all values $k$ . We recover the distribution density MATH given by the relationship MATH for values $x,t,T$ by repeated differentiation of $C$ or $P$ : MATH

MATH (Distribution density via Call)
Similarly, MATH Note, MATH

All calculations are dependent on the point of observation MATH .





Notation. Index. Contents.


















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