We use an exact holon and spinon Landau-liquid functional, which describes the holon-spinon interactions at all scattering orders, to study correlation functions of integrable multicomponent many-particle problems showing both linear and nonlinear energy bands. Motivated by recent photoemission experiments, we consider specific cases when the dominant nonlinear band terms are quadratic and apply our results to the evaluation of the half-filling 1D Hubbard model one-particle spectral functions beyond conformal field theory.

This paper presents a multinomial method for option pricing when the underlying asset follows an exponential Variance Gamma (VG) process. The continuous time VG process is approximated by a continuous time process with the same first four cumulants and then discretized in time and space. This approach is particularly convenient for pricing American and Bermudan options, which can be exercised before the expiration date. Numerical computations of European and American options are presented and compared with results obtained with finite differences method and with the Black–Scholes prices.

We present and prove a triple sum series formula for the European call option price in a market model where the underlying asset price is driven by a Variance Gamma process. In order to obtain this formula, we present some concepts and properties of multidimensional complex analysis, with particular emphasis on the multidimensional Jordan Lemma and the application of residue calculus to a Mellin–Barnes integral representation in ${\mathbb{C}}^3$, for the call option price. Moreover, we derive triple sum series formulas for some of the Greeks associated to the call option and we discuss the numerical accuracy and convergence of the main pricing formula.

The authors offer a VIX pricing algorithm for stochastic Volterra rough volatility models where the volatility is dependent of the vol-of-vol which reproduces

We present a finite difference method to solve a system of two Partial-Integro Differential Equations which arise from pricing an option under a Jump-Telegraph Diffusion Model for the underlying asset, considering the risk-neutral valuation formula under an equivalent martingale measure. This system is fully discretized using an Implicit-Explicit two-time level scheme and quadrature formulas. The resulting two tridiagonal algebraic linear system is solved recursively using Thomas Algorithm. Some numerical results are presented and the numerical order of convergence for the method is estimated. Finally, the robustness of the method is validated against an exact solution obtained for a perturbed problem.