A non-Markov model for volatility jumps

Volatility has a significant role to play in the determination of risk and in the valuation of options and other financial derivatives. The well-known Black-Scholes model for the financial derivatives deals with constant volatility. This paper presents a new model based on shot noise behaviour, in which the volatility jump occurs in random instant of times. The closed form solution is derived for the proposed model. Further, numerical results are illustrated to validate the above observations.