Constructing Binomial Trees From Multiple Implied Probability Distributions

Abstract

Rubinstein's seminal work on implied binomial trees showed how to fit a tree to a set of market prices for options maturing on a single date. A problem with the technique is that the tree it produces cannot match option prices for multiple maturities, so it cannot simultaneously cover a full set of options traded in a given market. The tree structure needed for that task is significantly more complex than a simple binomial. Brown and Toft show how such a general tree may be implied out of a set of option market prices. They then illustrate the technique using S&P 500 index options and currency options on the deutschemark. The resulting trees even embody patterns of path dependence commonly observed in volatilities.