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.
A.One dimensional Black equation.
B.Two dimensional Black equation.
3.Mean reverting equation.
4.Affine SDE.
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

One dimensional Black equation.


uppose we would like to compute the quantity MATH given by the relationshipsMATHMATH where the math math are real numbers, MATH is an integrable function and $dW_{t}$ is the increment of the standard Brownian motion. According to the backward Kolmogorov's theorem, see the section ( Backward equation section), the quantityMATH is a solution of the problemMATHMATH Introduce the process MATH According to the Ito formula ( Ito formula)MATHMATH With such observation we can writeMATHMATHMATH





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