Market symmetry in time-changed Brownian models

In this paper we examine which Brownian subordination with drift exhibits the symmetry property introduced by Fajardo and Mordecki [2006. Quantitative Finance 6, 219-227]. We find that when the subordination results in a Lévy process, a necessary and sufficient condition for the symmetry to hold is that the drift must be equal to-1/2. Also, we derive explicit conditions to test whether the NIG, CGMY and Meixner processes are symmetric or not. Finally, we perform some tests with real financial data.