Robust binomial lattices for univariate and multivariate applications: choosing probabilities to match local densities

A wide variety of diffusions used in financial economics are mean-reverting and many have state- and time-dependent volatilities. For processes with the latter property, a transformation along the lines suggested by Nelson and Ramaswamey can be used to give a diffusion with constant volatility and t...

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Bibliographic Details
Published in:Quantitative finance 2014-01, Vol.14 (1), p.101-110
Main Author: Hilliard, Jimmy E.
Format: Article
Language:English
Subjects:
American options
Applied mathematical finance
Computational finance
Financial mathematics
Lattice theory
Mathematical functions
Multivariate analysis
Numerical analysis
Numerical methods for option pricing
Probability
Quantitative finance
Studies
Volatility
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Summary:A wide variety of diffusions used in financial economics are mean-reverting and many have state- and time-dependent volatilities. For processes with the latter property, a transformation along the lines suggested by Nelson and Ramaswamey can be used to give a diffusion with constant volatility and thus a computationally simple binomial lattice. Drift terms in mean-reverting and transformed processes frequently result in either ill-defined probabilities or complex grids. We develop closed-form, legitimate probabilities on a simple grid for univariate and multivariate lattices for well-posed smooth diffusions. The probabilities are based on conditional normal density functions with parameters determined by the diffusion. We demonstrate convergence in distribution under mild restrictions and provide numerical comparisons with other univariate and multivariate approaches.
ISSN:1469-7688
1469-7696
DOI:10.1080/14697688.2013.793815