Markets With Random Lifetimes and Private Values: Mean-Reversion and Option to Trade

We consider a market in which traders arrive at random times, with random private values for the single traded asset. A trader’s optimal trading decision is formulated in terms of exercising the option to trade one unit of the asset at the optimal stopping time. We solve the optimal stopping problem under the assumption that the market price follows a mean-reverting diffusion process. The model is calibrated to experimental data taken from Alton and Plott (2010), resulting in a very good fit.