Quantitative Finance Stack Exchange is a question and answer site for finance professionals and academics. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

How do I measure how quickly a binomial lattice converges to an option value as the number of steps is increased?

I'm charting option value versus number of steps for various binomial lattice models and while the values generally converge as the number of steps increases, the rate at which they converge differs. For example, Model A converges fastest for at-the-money puts but Model B converges fastest for an otherwise identical option that is deep in-the-money.

Eyeballing the charts it seems obvious (sometimes) which model pick for a particular scenario, but how do you quantify this?

share|improve this question
up vote 5 down vote accepted

You don't mention if the puts in question are exotic or vanilla, but assuming they are vanilla, you should read this paper by Chen and Joshi. In it, they find optimal performance by using smoothed, truncated Tian-parameter binomial lattices with Richardson extrapolation -- where the idea is to run one extra low-cost (long $\Delta T$) tree in order to extrapolate the lattice values to $\Delta T=0$.

Aside from a carefully-derived recommendation, the paper is an excellent review of most of the known tricks for extracting performance from binomial lattices.

share|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.