Quantitative Analysis.
Trading Platform.
Python for Excel.
Author.

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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.
A.Analytical tractability of the displaced Heston equations.
B.Displaced Heston equations with term structure.
a.Parameter averaging.
b.Parameter averaging applied to the displaced diffusion.
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

Parameter averaging applied to the displaced diffusion.

e apply the result of the previous section ( Parameter averaging) to the equations ( displaced diffusion with term structure):MATH We approximate $X_{t}$ with the $Y_{t}$ given byMATH and we are seeking for the best parameter $b$. Using the notation of the previous sectionMATH The MATH is introduced because of the normalizationMATH According to the result ( parameter averaging) the best parameter $b$ comes from the relationshipsMATH According to the relationships MATH and MATH the $X_{0,t}$ is given by the SDE MATH





Forum Notation Index Contents


















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