We consider the problem of estimating the density of buyers and vendors in a nonlinear parabolic price formation model using measurements of the price and the transaction rate. Our approach is based on a work by Puel et al., see [20], and results in a optimal control problem. We analyse this problems and provide stability estimates for the controls as well as the unknown density in the presence of measurement errors. Our analytic findings are supported with numerical experiments.The positive part f + = max(f, 0) of the function f = f (x, t) corresponds to the distribution of buyers over the price x ∈ Ω, the negative part f . = min(f, 0) to the is the vendor distribution over the price. The free boundary p = p(t) corresponds to the price where f (·, t) = 0, the function Λ to the total number of transactions executed at that price. The immediate placement and execution of new bids and orders after the trading event are modeled by the Delta Diracs at the shifted prices p(t) + a and p(t) − a, where a ∈ R + denotes the transaction