Choosing Binomial or Trinomial Trees for Option Pricing

Summary

This exchange distinguishes theoretical trinomial trees from trinomial trees constructed to approximate a specified risk-neutral model, such as Black–Scholes. In the theoretical setting, a trinomial framework may permit a range of prices rather than determine one unique value. When the tree is calibrated as a numerical approximation to a risk-neutral measure, both binomial and trinomial trees can be used to price options.

The practical guidance is that trinomial trees can be advantageous when the model needs nodes at a particular level, such as a barrier, because aligning the grid with that level can improve convergence. The response gives no numerical comparison, implementation details, or conditions that quantify the advantage. Its advice is therefore a useful general distinction, not a complete method for choosing a tree in every pricing problem.

Key ideas

• A theoretical trinomial tree may not determine a unique price.
• A trinomial tree approximating a specified risk-neutral model can serve as a numerical pricing method.
• Binomial trees can also approximate risk-neutral option prices.
• Trinomial trees may converge better when the grid can place nodes on a barrier level.

Tags

# Binomial tree vs trinomial tree in pricing options


# Binomial tree vs trinomial tree in pricing options












Very new to pricing models. Is there a general guideline when to use binomial tree and when trinomial tree is preferred? As far as I know, unlike binomial tree, trinomial tree only gives a range instead of a unique value. Thank you.

## Answer by Mark Joshi (score 6, accepted)

https://quant.stackexchange.com/a/17523

you have to be careful to distinguish between trinomial trees in a theoretical sense which do not give unique prices, and trinomial trees chosen as an approximation to the risk-neutral measure of the BS model. In the second case, they are an effective numerical method as are binomial trees.

Trinomial trees are more useful when you want to ensure nodes lie on a given level such as a barrier since this gives better convergence.

I discuss the theoretical point you are making at length in More Mathematical Finance. I have done paper on numerical comparisons as well, see my ssrn author page.

http://papers.ssrn.com/sol3/cf_dev/AbsByAuth.cfm?per_id=550354

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