When underlying financial variables follow a Markov jump-diffusion process, the value function of a derivative security satisfies a partial integro-differential equation (PIDE) for European-style exercise or a partial integro-differential variational inequality (PIDVI) for American-style exercise. Unless the Markov process has a special structure, analytical solutions are generally not availabl...

In this paper, we generalize the pure diffusion approach for structural credit risk modeling by including jumps in the firm-value process. In pure diffusion models, the probability for a solvent company to default within a small interval of time is negligible, whereas a real company may face sudden financial distress. Our generalization allows those unpredicted extremal events, raising the prob...

The present work is devoted to approximation of the statistical moments of the unknown solution of a class of elliptic transmission problems in R with uncertainly located transmission interfaces. Within this model, the diffusion coefficient has a jump discontinuity across the random transmission interface which models linear diffusion in two different media separated by an uncertain surface. We...

Signatures of chemical exchange and spectral diffusion in 2D photon-echo line shapes of molecular aggregates are studied using model calculations for a dimer whose Hamiltonian parameters are stochastically modulated. Cross peaks induced by chemical exchange and by exciton transport have different dynamics and distinguish two models which have the same absorption spectrum (a two-state jump bath ...

In this paper, we study the pricing of credit risky securities under a threefirms contagion model. The interacting default intensities not only depend on the defaults of other firms in the system, but also depend on the default-free interest rate which follows jump diffusion stochastic differential equation, which extends the previous three-firms models (see R.A. Jarrow and F.Yu (2001), S.Y.Leu...

We consider European options pricing with double jumps and stochastic volatility. We derived closed-form solutions for European call options in a double exponential jump-diffusion model with stochastic volatility SVDEJD . We developed fast and accurate numerical solutions by using fast Fourier transform FFT technique. We compared the density of our model with those of other models, including th...

We present a new spectral element method for solving partial integro-differential equations for pricing European options under the Black–Scholes and Merton jump diffusion models. Our main contributions are: (i) using an optimal set of orthogonal polynomial bases to yield banded linear systems and to achieve spectral accuracy; (ii) using Laguerre functions for the approximations on the semi-infi...

The diffusion of a walk in the presence of traps is investigated. Different diffusion regimes are obtained considering the magnitude of the fluctuations in waiting times and jump distances. A constant velocity during the jump motion is assumed to avoid the divergence of the mean squared displacement. Using the limit theorems of the theory of Lévy stable distributions we have provided a characte...

Since its inception in 2009, Bitcoin has increasingly gained main stream attention from the general population to institutional investors. Several models, GARCH type jump-diffusion type, have been developed dynamically capture price movement of this highly volatile asset. While fitting Gaussian and Generalized Hyperbolic Normal Inverse (NIG) distributions log-returns Bitcoin, NIG distribution a...