New candidates for arbitrage-free stock price models via generalized conditional symmetry method

In this paper a new perspective upon generating arbitrage-free stock price models is proposed. The generalized conditional symmetry (GCS) method is applied to the governing second order (1+1) partial differential equation which does contain a rational parameter p drawn from the interval [12,1]. We investigate the conditions that yield the concerned equation admitting a special class of second-order GCSs. The determining system is solved in several special cases and, from invariance surface condition associated to each of the GCS operator, for all values of p, some invariant solutions are pointed out. New candidate models for arbitrage-free stock price are derived.