Ump Diffusion Process News Today

With more looming uncertainties in our present financial climate and environment, models with jump–diffusion more than ever are necessary. They are suited to reproduce the large and sudden fluctuations in the level of the underlying variable, and mimic various statistical properties in observed time series. The jump–diffusion modelling setup, however, brings complexity to the valuation and hedging of derivative securities. This paper delves into the subject of hedging along with the illustra...

Abstract An alternative approach is proposed for constructing a strongly continuous semigroup based on the classical method of successive approximations, or Picard iterations, together with generating functions. An application to a Black–Scholes integro-differential operator which arises in the pricing of European options under jump-diffusion dynamics is provided. The semigroup is expressed as the Mellin convolution of time-inhomogeneous jump and Black–Scholes kernel functions. Other applic...