Quantitative Analysis.
Trading Platform.
Python for Excel.
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.
Bibliography.
Forum Notation Index Contents

Recovering implied distribution.


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

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

Note that all calculation are dependent on the point of observation MATH.





Forum Notation Index Contents


















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