Related papers: Modeling interest rate dynamics: an infinite-dimen…
This note studies a certain stochastic evolution equation in the space of probability measures, including existence and uniqueness results. A solution of this equation gives rise, in a natural way, to an interest rate term structure model,…
The space of probability distributions on a given sample space possesses natural geometric properties. For example, in the case of a smooth parametric family of probability distributions on the real line, the parameter space has a…
We propose a formulation of the term structure of interest rates in which the forward curve is seen as the deformation of a string. We derive the general condition that the partial differential equations governing the motion of such string…
This paper offers a new class of models of the term structure of interest rates. We allow each instantaneous forward rate to be driven by a different stochastic shock, constrained in such a way as to keep the forward rate curve continuous.…
In this survey paper we discuss recent advances on short interest rate models which can be formulated in terms of a stochastic differential equation for the instantaneous interest rate (also called short rate) or a system of such equations…
This paper is concerned with finite dimensional models for the entire term structure for energy futures. As soon as a finite dimensional set of possible yield curves is chosen, one likes to estimate the dynamic behaviour of the yield curve…
We develop a general term structure framework taking stochastic discontinuities explicitly into account. Stochastic discontinuities are a key feature in interest rate markets, as for example the jumps of the term structures in…
US Yield curve has recently collapsed to its most flattened level since subprime crisis and is close to the inversion. This fact has gathered attention of investors around the world and revived the discussion of proper modeling and…
We study the problems of consistency and of the existence of finite-dimensional realizations for multi-curve interest rate models of Heath-Jarrow-Morton type, generalizing the geometric approach developed by T. Bj\"ork and co-authors in the…
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…
This paper considers the single factor Heath-Jarrow-Morton model for the interest rate curve with stochastic volatility. Its natural formulation, described in terms of stochastic differential equations, is solved through Monte Carlo…
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…
Explicitly taking into account the risk incurred when borrowing at a shorter tenor versus lending at a longer tenor ("roll-over risk"), we construct a stochastic model framework for the term structure of interest rates in which a frequency…
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…
The classical approach in finance attempts to model the term structure of interest rates using specified stochastic processes and the no arbitrage argument. Up to now, no universally accepted theory has been obtained for the description of…
With the reform of interest rate benchmarks, interbank offered rates (IBORs) like LIBOR have been replaced by risk-free rates (RFRs), such as the Secured Overnight Financing Rate (SOFR) in the U.S. and the Euro Short-Term Rate (\euro STR)…
It is well known that the Cox-Ingersoll-Ross (CIR) stochastic model to study the term structure of interest rates, as introduced in 1985, is inadequate for modelling the current market environment with negative short interest rates.…
The paper uses functional auto-regression to predict the dynamics of interest rate curve. It estimates the auto-regressive operator by extending methods of the reduced-rank auto-regression to the functional data. Such an estimation…
We introduce a flexible and tractable infinite-dimensional stochastic volatility model. More specifically, we consider a Hilbert space valued Ornstein-Uhlenbeck-type process, whose instantaneous covariance is given by a pure-jump stochastic…
Level, slope, and curvature are three commonly-believed principal components in interest rate term structure and are thus widely used in modeling. This paper characterizes the heterogeneity of how misspecified such models are through time.…