Option-implied probability density functions

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. If you have any queries or comments, please email impliedpdfs@bankofengland.co.uk.

Overview

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. 

• FTSE 100 probability density functions (ZIP)
• Short sterling probability density functions (ZIP)¹
• Terminology and concepts: implied probability density functions (pdf)
• Methodology: implied probability density functions (pdf)
• ¹ On 03 August 2020, the methodology behind the implied volatility calculation for our short sterling data was changed from the Black-Scholes model to the Bachelier model, which permits negative values of the underlying. Further, in light of this change, the implied volatilities are reported in basis points, as opposed to per cent.

If you have any enquiries, email ImpliedPDFs@bankofengland.co.uk.