Related papers: Statistically consistent term structures have affi…
In this paper we provide the characterization of all finite-dimensional Heath--Jarrow--Morton models that admit arbitrary initial yield curves. It is well known that affine term structure models with time-dependent coefficients (such as the…
The purpose of this paper relies on the study of long term affine yield curves modeling. It is inspired by the Ramsey rule of the economic literature, that links discount rate and marginal utility of aggregate optimal consumption. For such…
We present a family of models for the term structure of interest rates which describe the interest rate curve as a stochastic process in a Hilbert space. We start by decomposing the deformations of the term structure into the variations of…
We introduce novel finite element schemes for curve diffusion and elastic flow in arbitrary codimension. The schemes are based on a variational form of a system that includes a specifically chosen tangential motion. We derive optimal $L^2$-…
We investigate the existence of affine realizations for term structure models driven by L\'evy processes. It turns out that we obtain more severe restrictions on the volatility than in the classical diffusion case without jumps. As special…
We consider the evolution of curve networks in two dimensions (2d) and surface clusters in three dimensions (3d). The motion of the interfaces is described by surface diffusion, with boundary conditions at the triple junction points/lines,…
We examine the shapes attainable by the forward- and yield-curve in the widely-used Svensson family, including the Nelson-Siegel and Bliss subfamilies. We provide a complete classification of all attainable shapes and partition the…
Filtered budgets for anelastic turbulence and a general expression of the turbulent sensible heat flux are derived for a multicomponent fluid with an arbitrary equation of state. A family of subgrid-scale closures is then found under the…
The Convolution and Master equations governing the time behavior of the term structure of Interest Rates are set up both for continuous variables and for their discretised forms. The notion of Seed is introduced. The discretised theoretical…
We consider a model for interest rates, where the short rate is given by a time-homogenous, one-dimensional affine process in the sense of Duffie, Filipovic and Schachermayer. We show that in such a model yield curves can only be normal,…
I prove that a centre manifold approach to creating finite difference models will consistently model linear dynamics as the grid spacing becomes small. Using such tools of dynamical systems theory gives new assurances about the quality of…
Subsurface flows are commonly modeled by advection-diffusion equations. Insufficient measurements or uncertain material procurement may be accounted for by random coefficients. To represent, for example, transitions in heterogeneous media,…
This paper introduces a novel stochastic model for credit spreads. The stochastic approach leverages the diffusion of default intensities via a CIR++ model and is formulated within a risk-neutral probability space. Our research primarily…
We develop a method for calculating the persistence landscapes of affine fractals using the parameters of the corresponding transformations. Given an iterated function system of affine transformations that satisfies a certain compatibility…
Accurate forecasting of zero coupon bond yields for a continuum of maturities is paramount to bond portfolio management and derivative security pricing. Yet a universal model for yield curve forecasting has been elusive, and prior attempts…
This paper introduces a new numerical scheme for a system that includes evolution equations describing a perfect plasticity model with a time-dependent yield surface. We demonstrate that the solution to the proposed scheme is stable under…
In fixed income sector, the yield curve is probably the most observed indicator by the market for trading and fifinancing purposes. A yield curve plots interest rates across different contract maturities from short end to as long as 30…
In the paper two important theorems about complete affine spheres are generalized to the case of statistical structures on abstract manifolds. The assumption about constant sectional curvature is replaced by the assumption that the…
We develop theory and applications of forward characteristic processes in discrete time following a seminal paper of Jan Kallsen and Paul Kr\"uhner. Particular emphasis is placed on the dynamics of volatility surfaces which can be easily…
In this paper, we analyze the diversity of term structure functions (e.g., yield curves, swap curves, credit curves) constructed in a process which complies with some admissible properties: arbitrage-freeness, ability to fit market quotes…