Recombining binomial tree approximations for diffusions
Date
2009
Authors
van der Hoek, J.
Editors
Bensoussan, A.
Zhang, Q.
Zhang, Q.
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Journal article
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Handbook of Numerical Analysis, 2009; 15:361-368
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Abstract
In this chapter, we present a novel way to approximate a diffusion by a recombining binomial tree model. The method is obtained by approximating a procedure to find a weak solution of a stochastic differential equation. We shall indicate some theory that provides analysis that the method does indeed provide an approximation. If the original diffusion is expressed in risk neutral terms, then the binomial tree can be used to approximate the value of a wide number of financial derivatives, and if the the original diffusion is expressed in real-world probabilities, then the tree could be used to provide approximate simulations that could be used in risk analysis. We present a list of examples of one-dimensional diffusions and an illustrative two-dimensional example.
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Copyright 2009 Elsevier