Binomial lattice convergence

Question

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?

Answer 1

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.