B-spline techniques for volatility modeling

B-spline techniques for volatility modeling

This paper is devoted to the application of B-splines to volatility modeling, specifically the calibration of the leverage function in stochastic local volatility models and the parameterization of an arbitrage-free implied volatility surface calibrated to sparse option data. We use an extension of classical B-splines obtained by including basis functions with infinite support. We first come ba...

Bézier- and B-spline Techniques Errata

Fuzzy B-spline Modeling of Uncertainty Data

In this paper, we purposed a new method in modeling the uncertainty data based on the theory of fuzzy sets and the interpolation B-spline model curve. The uncertainty data firstly defined by using fuzzy number concept and fuzzy relation by defined them in real data form. The existed coefficient control of interpolation B-spline basis function is substituted with the fuzzy data points(FDPs) whic...

Curve modeling with constrained B-spline wavelets

In this paper we present a novel approach to construct B-spline wavelets under constraints, taking advantage of the lifting scheme. Constrained B-spline wavelets allow multiresolution analysis of B-splines which fixes positions, tangents and/or high order derivatives at some user specified parameter values, thus extend the ability of B-spline wavelets: smoothing a curve while preserving user sp...

A rational B-spline hypervolume for multidimensional multivariate modeling

This paper proposes a rational B-spline hypervolume that represents a volume object which has multiple attributes defined in a multidimensional space. This representation provides a mathematical framework for modeling and visualizing a multidimensional multivariate object as well as analyzing the object interiors to extract its intrinsic features that are directly inaccessible. We discuss the N...