BASICALLY TWO DI ERENT BUT MATHEMATICALLY EQUIVALENT APPROACHES MAY BE DISTINGUISHED FOR OPTIONS PRICING IN A PURE DIF-FUSION SETUP: THE PROBABILISTIC APPROACH AND THE PARTIAL DI EREN-TIAL EQUATION (PDE) APPROACH. THE PRESENCE OF A JUMP TERM IN THE PRICE PROCESS OF THE ASSET LEADS TO THE PARTIAL INTEGRO DI EREN-TIAL EQUATION (PIDES), WHICH IS AN EXTENSION OF THE BLACK {SCHOLES PDE WITH AN ADDITIONAL INTEGRAL TERM. IN MANY CASES, HOWEVER, AN EXPLICIT CLOSED-FORM VALUATION OF OPTIONS IN JUMP DI USIONS IS NOT POSSIBLE AND ONE IS RESTRICTED TO NUMERICAL PROCEDURES. THE AIM IS TO SHOW HOW OPTION PRICES IN THE JUMP-DI USION MODELS, MAINLY ON THE MERTON AND KOU MODELS, CAN BE COMPUTED USING MESHLESS METHODS BASED ON RADIAL BASIS FUNCTION. WE WOULD LIKE TO INVESTIGATE THE RBF {PU FOR NUMERICAL SOLUTION OF PARTIAL INTEGRO DI ERENTIAL EQUATION ARISING FORM THE MULTI-ASSET EUROPEAN VANILLA CALL/PUT OPTIONS BASED ON JUMP-DI USION MODELS.