Diffusion Equations: Convergence of the Functional Scheme Derived from the Binomial Tree with Local Volatility for Non Smooth Payoff Functions

The function solution to the functional scheme derived from the binomial tree financial model with local volatility converges to the solution of a diffusion equation of type as the number of discrete dates . Contrarily to classical numerical methods, in particular finite difference methods, the prin...

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Bibliographic Details
Published in:Applied mathematical finance. 2018-11, Vol.25 (5-6), p.511-532
Main Authors: Baptiste, Julien, Lépinette, Emmanuel
Format: Article
Language:English
Subjects:
Analysis of PDEs
And phrases: binomial tree model
Convergence
diffusion partial differential equations
Economic models
European option pricing
Finite difference method
finite difference scheme
Finite element method
finite element scheme
Formulas (mathematics)
Functionals
Mathematical analysis
Mathematical models
Mathematics
Numerical methods
Volatility
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Summary:The function solution to the functional scheme derived from the binomial tree financial model with local volatility converges to the solution of a diffusion equation of type as the number of discrete dates . Contrarily to classical numerical methods, in particular finite difference methods, the principle behind the functional scheme is only based on a discretization in time. We establish the uniform convergence in time of the scheme and provide the rate of convergence when the payoff function is not necessarily smooth as in finance. We illustrate the convergence result and compare its performance to the finite difference and finite element methods by numerical examples.
ISSN:1350-486X
1466-4313
DOI:10.1080/1350486X.2018.1513806