Modelling the term structure of interest rates á la Heath-Jarrow-Morton but with non Gaussian fluctuations

Przemyslaw Repetowicz; Brian Lucey; Peter Richmond

Home/Archive/arXiv

arXiv · cond-mat/0408292

Modelling the term structure of interest rates á la Heath-Jarrow-Morton but with non Gaussian fluctuations

Przemyslaw Repetowicz·Brian Lucey·Peter Richmond

View original source ↗Read source document ↗Export metadata ↓

Abstract

We consider a generalization of the Heath Jarrow Morton model for the term structure of interest rates where the forward rate is driven by Paretian fluctuations. We derive a generalization of Itô's lemma for the calculation of a differential of a Paretian stochastic variable and use it to derive a Stochastic Differential Equation for the discounted bond price. We show that it is not possible to choose the parameters of the model to ensure absence of drift of the discounted bond price. Then we consider a Continuous Time Random Walk with jumps driven by Paretian random variables and we derive the large time scaling limit of the jump probability distribution function (pdf). We show that under certain conditions defined in text the large time scaling limit of the jump pdf in the Fourier domain is \tilde{omega}_t(k,t) \sim \exp{-K/(\ln(k t))^2} and is different from the case of a random walk with Gaussian fluctuations. We also derive the master equation for the jump pdf and discuss the relation of the master equation to Distributed Order Fractional Diffusion Equations.

Explore related subjects

cond-mat.other q-fin.PR

Keep this discovery

Explore connections, maps & timelines

BibTeX RIS

Przemyslaw Repetowicz, Brian Lucey, Peter Richmond. 2004-09-07. Modelling the term structure of interest rates á la Heath-Jarrow-Morton but with non Gaussian fluctuations. https://arxiv.org/abs/cond-mat/0408292

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Microscopic Understanding of Thermal-magnon Transport in a Low-damping Ferrimagnetic Thin Films

Thermally generated magnons enable heat-driven spin transport in magnetic insulators, yet the microscopic mechanisms governing their propagation remain poorly understood. Here, we investigate thermal magnon transport in low-damping Li$_{0.5}$Al$_{1.0}$Fe$_{1.5}$O$_4$/Pt nanodevices using a nonlocal spin Seebeck geometry that separates magnon transport from local thermoelectric effects. Thermal imaging establishes a detector region outside the thermal healing length, enabling intrinsic nonlocal measurements. We find that thermal magnon transport is strongly suppressed by magnetic fields far above saturation. Brillouin light scattering reveals that increasing field reduces the group velocity of backward volume magnons, providing a microscopic origin for the observed reduction in magnon spin diffusion length. We further find that thermal magnon transport decreases with increasing temperature despite an increasing magnon population. Micromagnetic simulations reproduce this behavior only when a temperature-dependent exchange stiffness is included. These results identify magnon group velocity and exchange stiffness as key parameters governing thermal magnon transport in ferrimagnetic thin films.

cond-mat.other↗

arXiv2026

Transport properties and topological phase transitions for a Creutz-Su-Schrieffer-Heeger ladder

In this work, we investigate the electronic, topological, and transport properties of a Creutz-Su-Schrieffer-Heeger (CSSH) ladder. Using a tight-binding model within the Green's function formalism, we calculate the energy spectrum, local density of states (LDOS), and electronic transmission. We first determine the energy spectrum of the CSSH ladder and analyze the different topological phases present in the system, identifying one trivial phase and three distinct nontrivial regions. We then study electronic transport and show that the transmission reproduces the different topological phases through characteristic transport signatures. Finally, we derive the conditions for the emergence of non-topological flat bands and demonstrate that these bands also provide the necessary conditions for the formation of bound states in the continuum (BICs). Our results establish a direct connection between the topological properties, flat-band formation, and electronic transport in the CSSH ladder.

cond-mat.other↗

arXiv2026

Exact Phase-Space Rotation in the Trapped Quantum Calogero Model

We develop a microscopic phase-space description of the quantum Calogero model in the presence of an external harmonic confining potential. Building on the quantum Lax-pair structure, we construct a Hermitian Wigner operator whose expectation value obeys the exact phase-space evolution equation d_t rho + lambda d_x rho - Omega^2 x d_lambda rho = 0 for arbitrary initial states and to all orders in the interaction strength. The resulting dynamics is a rigid rotation in phase space with period 2 pi/Omega, providing a microscopic realization of the isochronous dynamics of the trapped Calogero model. We further show that the moments of the phase-space density form rotating multiplets rather than independent conserved quantities. In particular, within the quadratic sector, the unique conserved combination is proportional to the trapped Hamiltonian, providing a nontrivial consistency check of the construction. In the limit Omega -> 0, the equation reduces to the exact free-streaming equation of the untrapped model.

cond-mat.other↗