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Connecting Binomial Trees to Finite-Difference Stability

Article Quant Q&A · Author: Medan
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Summary

The document raises a numerical-methods question about the relationship between binomial option-pricing trees and explicit finite-difference schemes. It asks how a choice of time and space steps can make the finite-difference update correspond to a binomial model, and whether removing a coefficient in that update is enough to ensure stability.

It also asks whether stability has a meaningful role for binomial trees themselves and whether implicit finite-difference methods can be applied in this setting. The text provides no derivation, answer, numerical example, or stability criterion, so it serves as a focused statement of open questions rather than a tutorial. Readers should not infer that the proposed step relationship guarantees stability; the document leaves that issue unresolved.

Key ideas

  • A binomial pricing tree can be related to an explicit finite-difference scheme through a relationship between time and space steps.
  • The document questions whether eliminating a finite-difference coefficient ensures numerical stability.
  • It asks whether stability concepts apply directly to binomial trees.
  • The applicability of implicit methods to this connection is left open.

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Derivatives pricingStatistics
Full text
# binomial trees and finite differences


# binomial trees and finite differences












I was reading Tavella Randall book and their explanation why binomial trees are a particular example of finite differences. I started having additional questions. So, they way they do that is saying that if there is a certain relation between $\Delta t$ and $\Delta x$, then the explicit finite difference scheme can be viewed as a binomial model. But how about stability? Is it always when I eliminate the second coefficient in my finite differences I will have a stable scheme? What is the stability then for the binomial trees, is there such a concept applied here as well?

Also, is there anything can be said about implicit method application here? Can binomial trees be stable and unstable?

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.