European option pricing under model involving slow growth volatility with jump

In this paper, we suggest a new model for establishing numerical study related to European options pricing problem where assets' prices can be described by stochastic equation with discontinuous sample path (Slow Growth Volatility Jump SGVJ model) which uses non-standard volatility. A special attention is given characteristics of the proposed represented its volatility defined parameters α and β. The mathematical modeling in presence jump shows that one has resort degenerate partial integro-differential (PIDE) resolution gives price option as function time, underlying asset instantaneous However, general, an exact or closed solution not available. For reason approximate it using finite difference method. At end present some comparison results classical models known literature.