Related papers: Continuous time Ehrenfest process in term structur…
A new multi-factor short rate model is presented which is bounded from below by a real-valued function of time. The mean-reverting short rate process is modeled by a sum of pure-jump Ornstein--Uhlenbeck processes such that the related bond…
This paper introduces a short rate model in continuous time that adds one or more memory (delay) components to the Merton model (Merton 1970, 1973) or the Vasi\v{c}ek model (Vasi\v{c}ek 1977) for the short rate. The distribution of the…
We consider a continuous-time Ehrenfest model defined over the integers from -N to N, and subject to catastrophes occurring at constant rate. The effect of each catastrophe instantaneously resets the process to state 0. We investigate both…
No-arbitrage models of term structure have the feature that the return on zero-coupon bonds is the sum of the short rate and the product of volatility and market price of risk. Well known models restrict the behavior of the market price of…
We introduce a Vasicek-type short rate model which has two additional parameters representing memory effect. This model presents better results in yield curve fitting than the classical Vasicek model. We derive closed-form expressions for…
We analyze analytic approximation formulae for pricing zero-coupon bonds in the case when the short-term interest rate is driven by a one-factor mean-reverting process with a volatility nonlinearly depending on the interest rate itself. We…
We introduce a class of short-rate models that exhibit a ``higher for longer'' phenomenon. Specifically, the short-rate is modeled as a general time-homogeneous one-factor Markov diffusion on a finite interval. The lower endpoint is assumed…
We consider a general one-factor short rate model, in which the instantaneous interest rate is driven by a univariate diffusion with time independent drift and volatility. We construct recursive formula for the coefficients of the Taylor…
Generative modeling via stochastic processes has led to remarkable empirical results as well as to recent advances in their theoretical understanding. In principle, both space and time of the processes can be discrete or continuous. In this…
We consider a financial market in which the short rate is modeled by a continuous time Markov chain (CTMC) with a finite state space. In this setting, we show how to price any financial derivative whose payoff is a function of the state of…
In this paper, we consider a discrete time economy where we assume that the short term interest rate follows a quadratic term structure of a regime switching asset process. The possible non-linear structure and the fact that the interest…
An economic modeling approach for cavity quantum electrodynamics is provided by mean-field dynamics, wherein the optical field is described classically while a self-consistent interaction with quantum emitters is incorporated through the…
We study the optimal timing strategies for trading a mean-reverting price process with afinite deadline to enter and a separate finite deadline to exit the market. The price process is modeled by a diffusion with an affine drift that…
We propose a unifying framework for the pricing of debt securities under general time-inhomogeneous short-rate diffusion processes. The pricing of bonds, bond options, callable/putable bonds, and convertible bonds (CBs) is covered. Using…
We prove that a large class of discrete-time insurance surplus processes converge weakly to a generalized Ornstein-Uhlenbeck process, under a suitable re-normalization and when the time-step goes to 0. Motivated by ruin theory, we use this…
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…
We study a basic model for mutations. We derive exact formulae for the mean time needed to discover the master sequence, the mean returning time to the initial state, or to any Hamming class. These last two formulae are the same than the…
In this paper we compare two classical one-factor diffusion models which are used to model the term structure of interest rates. One of them is based on the Wiener-Bachelier process while the second one is based on the Ornstein-Uhlenbeck…
The paper is concerned with stochastic equations for the short rate process $R$ $$ dR(t)=F(R(t))dt+G(R(t-))dZ(t), $$ in the affine model of the bond prices. The equation is driven by a L\'evy martingale $Z$. It is shown that the discounted…
In this paper, we consider the N-urn Ehrenfest model. By utilizing an auxiliary continuous-time Markov chain, we obtain the explicit formula for the Laplace transform of the hitting time from a single state to a set A of states where A…