Market symmetry in time-changed Brownian models

In this paper we examine which Brownian subordination with drift exhibits (lie symmetry property introduced by Fajardo and Mordecki [2006. Quantitative Finance 6, 219-227]. We find that when the subordination results in a Levy 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 tire NIG, CGMY and Meixner processes are symmetric or not. Finally, we perform some tests with real financial data. (C) 2009 Elsevier Inc. All rights reserved.