Asset Return & Camel Process: Beauty and the Beast

In this paper, we propose a new diffusion process referred to as the “camel process” in order to model the cumulative return of a financial asset. This new process includes three parameters, the market condition parameter α, the overreaction correction parameter β, and the volatility parameter γ. Its steady state probability density function could be unimodal or bimodal, depending on the sign of the market condition parameter. The overreaction correction is realised through the non-linear drift term which incorporates the cube term of the instantaneous cumulative return. The time-dependent solution of its Fokker-Planck equation cannot be obtained analytically, but can be numerically solved using the finite difference method. The properties of the camel process are confirmed by our empirical estimation results of ten market indexes in two different periods.