Option-implied probability density functions

The Bank of England publishes weekly estimates of probability density functions for future values of the FTSE 100 index and short sterling interest rates.

Please note that the Bank has discontinued the publication of option-implied probability density functions.

The discontinuation of this data will mean that the two datasets – for short sterling futures and the FTSE 100 – will no longer be updated, but the data to end-March 2021 will continue to be accessible on the website.


Options are contracts used to insure against or speculate/take a view on uncertainty about the future prices of a wide range of financial assets and physical commodities. The prices at which options are traded contain information about the markets’ uncertainty about the future prices of these ‘underlying’ assets. On certain assumptions the information in options prices can be expressed in terms of the probability that the price of the underlying asset will lie within particular ranges.

We publish weekly estimates of such implied ‘probability density functions’ for future values of the FTSE 100 index and short sterling interest rates. These probability density functions do not necessarily provide us with the actual probabilities of an asset price realising particular values in the future. Instead they can provide us with an idea of the probabilities that option market participants in aggregate attach to different outcomes. 

The files below (updated weekly) show a range of summary statistics for option-implied probability density functions for FTSE 100 equity index and for short sterling (three-month sterling LIBOR) futures-implied interest rates. These statistics are used to describe the location, dispersion and shape of the probability density functions. Information on the probabilities attached to various equity index levels and interest rates is also provided. 

This page was last updated 31 January 2023