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.
A.Ricatti equation.
B.Evaluation of option price.
C.Laplace transform.
D.Example: CDFX model.
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.
Bibliography.
Forum Notation Index Contents

Ricatti equation.


he Ricatti equation is an ODE of the formMATH where the $u$ is the unknown function of $t$ and the $p,q,r\,$ are known functions of $t$.

We introduce a new unknown functionMATH thenMATH for some new known functions $Q,R$.

We further perform the changeMATH We haveMATH Hence, we arrived to a linear ODE.





Forum Notation Index Contents


















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