Related papers: Equivalence between forward rate interpolations an…
The method of constructing Hermite trigonometric polynomials, which interpolate the values of a certain periodic function and its derivatives up to (including ) the -th ( ) order in nodes of a uniform grid, is considered. The proposed…
This note discusses an interpolation technique for univariate distributions. In other words, the question is how to obtain a good approximation for f(x|a) if a0 < a < a1 is a control variable and f(x|a0) and f(x|a1) are known. The technique…
In the setting of polynomial jump-diffusion dynamics, we provide an explicit formula for computing correlators, namely, cross-moments of the process at different time points along its path. The formula appears as a linear combination of…
We develop foundations for computing Craig-Lyndon interpolants of two given formulas with first-order theorem provers that construct clausal tableaux. Provers that can be understood in this way include efficient machine-oriented systems…
This paper introduces an interpolation-based method, called the reconstruction approach, for nonparametric regression. Based on the fact that interpolation usually has negligible errors compared to statistical estimation, the reconstruction…
We develop a model for the dynamic evolution of default-free and defaultable interest rates in a LIBOR framework. Utilizing the class of affine processes, this model produces positive LIBOR rates and spreads, while the dynamics are…
This article presents a generic framework for modeling the dynamics of forward curves in commodity market as commodity derivatives are typically traded by futures or forwards. We have theoretically demonstrated that commodity prices are…
We present a new formula for divided difference and few new schemes of divided difference tables in this paper. Through this, we derive new interpolation, numerical differentiation and numerical integration formulas with arbitrary order of…
The manuscript describes efficient algorithms for the computation of the CUR and ID decompositions. The methods used are based on simple modifications to the classical truncated pivoted QR decomposition, which means that highly optimized…
In this paper we discuss the problem of interpolation on straight lines by linear combinations of ridge functions with fixed directions. By using some geometry and/or systems of linear equations, we constructively prove that it is…
The last two decades have seen major developments in interpolatory methods for model reduction of large-scale linear dynamical systems. Advances of note include the ability to produce (locally) optimal reduced models at modest cost; refined…
We introduce a new method to price American options based on Chebyshev interpolation. In each step of a dynamic programming time-stepping we approximate the value function with Chebyshev polynomials. The key advantage of this approach is…
We introduce a new class of forward performance processes that are endogenous and predictable with regards to an underlying market information set and, furthermore, are updated at discrete times. We analyze in detail a binomial model whose…
This note proposes a method for pricing high-dimensional American options based on modern methods of multidimensional interpolation. The method allows using sparse grids and thus mitigates the curse of dimensionality. A framework of the…
One of the possible variants of the classification of trigonometric interpolation splines is considered, depending on the chosen convergence factors, the distribution of signs of the basis functions and the interpolation factors. The…
In this paper a multi-factor generalization of Ho-Lee model is proposed. In sharp contrast to the classical Ho-Lee, this generalization allows for those movements other than parallel shifts, while it still is described by a recombining…
Interpolation is an important property of classical and many non-classical logics that has been shown to have interesting applications in computer science and AI. Here we study the Interpolation Property for the the non-monotonic system of…
The method of constructing trigonometric Hermite splines, which interpolate the values of some periodic function and its derivatives in the nodes of a uniform grid, is considered. The proposed method is based on the periodicity properties…
Fractal interpolation functions (FIFs) generated using iterated function systems (IFS) provide a powerful framework for modeling self-similar and irregular data, yet traditional constructions often neglect geometric fidelity such as…
We extend the now classic structural credit modeling approach of Black and Cox to a class of "two-factor" models that unify equity securities such as options written on the stock price, and credit products like bonds and credit default…