This paper discusses a new pricing method of European options through the binomial tree model using discrete cosine transform. The transform has been used as fundamental tool for image compression, including creation JPEG files. A was also recently to derive price financial options. enables us option prices model. Using this approach, we on classical Black and Scholes, exponential jump–diffusio...

Abstract: During the past and this decade, a new generation of continuous-time financial models has been intensively investigated in a quest to incorporate the so-called stylized empirical features of asset prices like fat-tails, high kurtosis, volatility clustering, and leverage. Modeling driven by “memoryless homogeneous” jump processes (Lévy processes) constitutes one of the most plausible d...

In this paper we consider discontinuous Galerkin (DG) finite element approximations of a model scalar linear hyperbolic equation. We show that in order to ensure continuous stabilization of the method it suffices to add a jump-penalty-term to the discretized equation. In particular, the method does not require upwinding in the usual sense. For a specific value of the penalty parameter we recove...

Keywords: Fractional calculus Anomalous diffusion Continuous time random walk Central limit theory Operator stable law a b s t r a c t In a continuous time random walk (CTRW), a random waiting time precedes each random jump. The CTRW is coupled if the waiting time and the subsequent jump are dependent random variables. The CTRW is used in physics to model diffusing particles. Its scaling limit ...

This paper considers the pricing of options when there are jumps in the pricing kernel and correlated jumps in asset returns and volatilities. Our model nests Duan’s GARCH option models where conditional returns are constrained to being normal, as well as extends Merton’s jump-diffusion model by allowing return volatility to exhibit GARCH-like behavior. Empirical analysis on the S&P 500 index r...

We consider a Markov process X which is the solution of a stochastic differential equation driven by a Lévy process Z and an independent Wiener process W . Under some regularity conditions, including non-degeneracy of the diffusive and jump components of the process as well as smoothness of the Lévy density of Z outside any neighborhood of the origin, we obtain a small-time secondorder polynomi...

A system of jump-diffusion stochastic differential equations is considered for modelling the dynamics of the spread of an amphibian disease. In this investigation, it is assumed that the amphibians are located in M regions which are widely and uniformly spaced on the surface of the earth and that the disease is present initially in only one region. Within each region, the amphibians live in N s...