  In this paper a simple model for the evolution of the forward density of the
future value of an asset is proposed. The model allows for a straightforward
initial calibration to option prices and has dynamics that are consistent with
empirical findings from option price data. The model is constructed with the
aim of being both simple and realistic, and avoid the need for frequent
re-calibration. The model prices of $n$ options and a forward contract are
expressed as time-varying functions of an $(n+1)$-dimensional Brownian motion
and it is investigated how the Brownian trajectory can be determined from the
trajectories of the price processes. An approach based on particle filtering is
presented for determining the location of the driving Brownian motion from
option prices observed in discrete time. A simulation study and an empirical
study of call options on the S&P 500 index illustrates that the model provides
a good fit to option price data.
