Related papers: Forward rate models with linear volatilities
This paper deals with an extension of the so-called Black-Scholes model in which the volatility is modeled by a linear combination of the components of the solution of a differential equation driven by a fractional Brownian motion of Hurst…
The paper is devoted to the study of the short rate equation of the form $$ d R(t)=F(R(t)) dt+\sum_{i=1}^{d}G_i(R(t-)) dZ_i(t), \quad R(0)=x\geq 0,\quad t>0, $$ with deterministic functions $F,G_1,...,G_d$ and a multivariate L\'evy process…
We provide a unified framework for modeling LIBOR rates using general semimartingales as driving processes and generic functional forms to describe the evolution of the dynamics. We derive sufficient conditions for the model to be…
We prove a large deviation principle result for solutions of abstract stochastic evolution equations perturbed by small Levy noise. We use general large deviations theorems of Varadhan and Bryc, viscosity solutions of integro-partial…
We propose and investigate two model classes for forward power price dynamics, based on continuous branching processes with immigration, and on Hawkes processes with exponential kernel, respectively. The models proposed exhibit jumps…
We establish the local existence of pathwise solutions for the stochastic Euler equations in a three-dimensional bounded domain with slip boundary conditions and a very general nonlinear multiplicative noise. In the two-dimensional case we…
This paper gives examples of explicit arbitrage-free term structure models with L\'evy jumps via state price density approach. By generalizing quadratic Gaussian models, it is found that the probability density function of a L\'evy process…
We introduce a Hawkes-like process and study its scaling limit as the system becomes increasingly endogenous. We derive functional limit theorems for intensity and fluctuations. Then, we introduce a high-frequency model for a price of a…
In this article, we introduce a time-independent version of the L\'evy colored noise considered in Balan (2015) and Balan and Jim\'enez (2026). We study the existence of the solution of a linear stochastic partial differential equation with…
We study the short maturity asymptotics for prices of forward start Asian options under the assumption that the underlying asset follows a local volatility model. We obtain asymptotics for the cases of out-of-the-money, in-the-money, and…
We model the dynamics of asset prices and associated derivatives by consideration of the dynamics of the conditional probability density process for the value of an asset at some specified time in the future. In the case where the price…
We derive explicit valuation formulae for an exotic path-dependent interest rate derivative, namely an option on the composition of LIBOR rates. The formulae are based on Fourier transform methods for option pricing. We consider two models…
We present an overview of the broad class of financial models in which the prices of assets are L\'evy-Ito processes driven by an $n$-dimensional Brownian motion and an independent Poisson random measure. The Poisson random measure is…
We describe a general strategy for the verification of variational source condition by formulating two sufficient criteria describing the smoothness of the solution and the degree of ill-posedness of the forward operator in terms of a…
Martingale solutions of stochastic Navier-Stokes equations in 2D and 3D possibly unbounded domains, driven by the L\'evy noise consisting of the compensated time homogeneous Poisson random measure and the Wiener process are considered.…
L\'evy ratchets are minimal models of fluctuation-driven transport in the presence of L\'evy noise and periodic external potentials with broken spatial symmetry. In these systems, a net ratchet current can appear even in the absence of time…
We model the term structure of the forward default intensity and the default density by using L\'evy random fields, which allow us to consider the credit derivatives with an after-default recovery payment. As applications, we study the…
We prove here a general closed-form expansion formula for forward-start options and the forward implied volatility smile in a large class of models, including the Heston stochastic volatility and time-changed exponential L\'evy models. This…
The critical variational setting was recently introduced and shown to be applicable to many important SPDEs not covered by the classical variational setting. In this paper, we extend the critical variational setting in several ways. We…
In this paper, we investigate the Leray problem for steady Navier-Stokes system under full slip boundary conditions in a two dimensional channel with straight outlets. The existence of solutions with arbitrary flux in a general channel with…