@article {Brown83, author = {Gregory Brown and Klaus Bjerre Toft}, title = {Constructing Binomial Trees From Multiple Implied Probability Distributions}, volume = {7}, number = {2}, pages = {83--100}, year = {1999}, doi = {10.3905/jod.1999.319142}, publisher = {Institutional Investor Journals Umbrella}, abstract = {Rubinstein{\textquoteright}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.}, issn = {1074-1240}, URL = {https://jod.pm-research.com/content/7/2/83}, eprint = {https://jod.pm-research.com/content/7/2/83.full.pdf}, journal = {The Journal of Derivatives} }