This paper will demonstrate how European and American option prices can be computed under the jump-diffusion model using the radial basis function (RBF) interpolation scheme. The RBF interpolation scheme is demonstrated by solving an option pricing formula, a one-dimensional partial integro-differential equation (PIDE). We select the cubic spline radial basis function and adopt a simple numeric...

Quadratic Spline Collocation Methods for Systems of Elliptic PDEs Kit Sun Ng Master of Science Graduate Department of Computer Science University of Toronto 2000 We consider Quadratic Spline Collocation (QSC) methods for solving systems of two linear second-order PDEs in two dimensions. Optimal order approximation to the solution is obtained, in the sense that the convergence order of the QSC a...

This note is concerned with the provision of an interpolant for o.d.e. initial value codes based upon backward differentiation formulae (b.d.f.) in which both the solution and its first time derivative are continuous over the range of integrationa C’ interpolant. The construction and implementation of the interpolant is described and the continuity achieved in practice is illustrated by two exa...

Interpolant-based model checking is an approximate method for computing invariants of transition systems. The performance of the model checker is contingent on the approximation computed, which in turn depends on the logical strength of the interpolants. A good approximation is coarse enough to enable rapid convergence but strong enough to be contained within the weakest inductive invariant. We...

We study the Lebesgue constant of the rational interpolant of Berrut (cf. [1]) when the interpolation points are equally distributed. In the more general case of the rational interpolant of Floater and Hormann (cf. [6]), we show by several numerical results, that the behavior of the Lebesgue constant on equally distributed points is consistent with that of Berrut’s interpolant.

Univariate spline discrete quasi-interpolants (abbr. dQIs) are approximation operators using B-spline expansions with coefficients which are linear combinations of discrete values of the function to be approximated. When working with nonuniform partitions, the main challenge is to find dQIs which have both good approximation orders and bounded uniform norms independent of the given partition. N...

This paper considers the interpolation for multi-dimensional data using Voronoi diagrams. Sibson's interpolant is well-known as an interpolation method using Voronoi diagrams for discretely distributed data, and it is extended to continuously distributed data by Gross. On the other hand, the authors studied another interpolation method using Voronoi diagrams recently. This paper outlines the au...

The problem of computing Craig interpolants in SMT has recently received a lot of interest, mainly for its applications in formal verification. Efficient algorithms for interpolant generation have been presented for some theories of interest –including that of equality and uninterpreted functions (EUF), linear arithmetic over the rationals (LA(Q)), and some fragments of linear arithmetic over t...