# Options distribution function. Option Price Probability Density Function

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

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 equity index and for short sterling three-month sterling Options distribution function futures-implied interest rates.

Published16 Jun Abstract A new class of distortion operators based on quantile function is proposed for pricing options. In particular, Black-Scholes formula can be recuperated by our distortion operator. Simulation analysis shows that our distortion operator is superior to normal distortion operator and NIG distortion operator.

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.