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Finite-Difference PDE Methods for American Option Valuation

Article Quant Q&A · Author: Andrew Beaven
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Summary

The document asks which method to use for pricing American options after encountering a dismissive comment about binomial valuation. Its answer suggests that Paul Wilmott may favor a finite-difference partial differential equation approach. It presents PDE methods, including discretizations by finite differences, finite elements, or finite volumes, as more flexible than a binomial tree and supported by a broad literature.

The response is an informal opinion, not a worked comparison or demonstrated pricing result. It gives no implementation details, convergence analysis, or guidance on when a tree may still be suitable. Its claim that PDE approaches are generally superior is therefore not established by evidence in the document; choosing a numerical method would require considering the option features, accuracy needs, and computational constraints.

Key ideas

  • The answer proposes finite-difference PDE methods for American option pricing.
  • PDE approaches can be discretized using finite differences, finite elements, or finite volumes.
  • The response characterizes binomial trees as less flexible than PDE methods.
  • No benchmark, implementation guidance, or conditions favoring one method are provided.

Tags

OptionsDerivatives pricingStatistics
Full text
# Binomial Option Valuation Paul Wilmott


# Binomial Option Valuation Paul Wilmott












I recently purchased Paul Wilmott's Quant Finance FAQ book. In the book he states that the binomial option valuation method is 'rubbish'. Can anyone enlighten me as to what method he recommends for pricing an American option?

## Answer by Yian Pap (score 1, accepted)

https://quant.stackexchange.com/a/37139

Lol, Mr Wilmott likes to provoke. If I had to guess I'd say that he would recommend a finite difference PDE method. Compared to that a binomial tree looks crude and inferior indeed, in almost every respect. PDE-based methods (discretized with finite differences/elements/volumes) offer far more flexibility and the literature on them is huge (borrowed from other disciplines, such as Computational Fluid Dynamics). I honestly don't know why anyone would use a binomial tree instead of a PDE method.

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