Why Barrier Options Are Difficult to Price on Binomial Trees

Summary

The document asks how to price single-barrier options with a binomial tree and whether the resulting prices converge to Black–Scholes values. The response cautions that tree methods can handle barriers poorly because tree nodes usually do not line up with the barrier. A pricing scheme must then estimate how probability is divided around the boundary, often through interpolation, which can make numerical results unstable.

The response adds that Greeks may be even less reliable and recommends partial differential equation methods, described as standard in industry practice for barrier options. It does not provide a derivation, convergence study, or comparison across specific tree implementations, so it is a warning about numerical challenges rather than a quantitative benchmark. The choice of method still depends on the model and implementation, and the document gives no details on calibration, rebates, monitoring frequency, or other contract features.

Key ideas

• Binomial tree nodes generally do not coincide with a barrier level.
• Tree-based barrier valuation therefore needs a method to handle probabilities near the boundary.
• Interpolation around the barrier can produce numerical instability.
• Greeks from tree methods may be less reliable than prices.
• The response recommends PDE methods but supplies no implementation comparison or convergence evidence.

Tags

# How to price barrier options (binomial tree)


# How to price barrier options (binomial tree)












What is the easiest way to price single barrier options using binomial tree? I found This method. Is this method good or maybe should I use another one? Does this price converge to price from BS model?

## Answer by Marco (score 4, accepted)

https://quant.stackexchange.com/a/59669

This may not be answering your question - but it is worth noting that valuing barrier options on a binomial / trinomial tree is at best problematic. It is difficult to enforce the boundary conditions because nodes will not typically sit on the barrier itself, necessitating some kind of probability-weighted interpolation - which is unlikely to be numerically stable. Greeks will be even worse. Strongly suggest you look at PDE approaches which are the industry-standard for Barrier options. Google "barrier options PDE" - there's a tonne of literature out there.

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