Related papers: Forward rate models with linear volatilities
In this paper we investigate general linear stochastic volatility models with correlated Brownian noises. In such models the asset price satisfies a linear SDE with coefficient of linearity being the volatility process. This class contains…
As a consequence of the financial crises, risk management became more important and real-world dynamics of interest-rate models moved into the focus of interest. Since risk-neutral dynamics are classically important to compute prices of…
Pricing interest-rate financial derivatives is a major problem in finance, in which it is crucial to accurately reproduce the time-evolution of interest rates. Several stochastic dynamics have been proposed in the literature to model either…
We introduce a framework that allows to employ (non-negative) measure-valued processes for energy market modeling, in particular for electricity and gas futures. Interpreting the process' spatial structure as time to maturity, we show how…
This paper proves existence of the long bond, long forward measure and long-term factorization of the stochastic discount factor (SDF) of Alvarez and Jermann (2005) and Hansen and Scheinkman (2009) in Heath-Jarrow-Morton (HJM) models in the…
In the spirit of Bj\"ork-DiMasi-Kabanov-Runggaldier, we investigate term structure models driven by Wiener process and Poisson measures with forward curve dependent volatilities. This includes a full existence and uniqueness proof for the…
We consider a large market model of defaultable assets in which the asset price processes are modelled as Heston-type stochastic volatility models with default upon hitting a lower boundary. We assume that both the asset prices and their…
We consider a market with a term structure of credit risky bonds in the single-name case. We aim at minimal assumptions extending existing results in this direction: first, the random field of forward rates is driven by a general…
We consider a defaultable asset whose risk-neutral pricing dynamics are described by an exponential Levy-type martingale subject to default. This class of models allows for local volatility, local default intensity, and a locally dependent…
We study the asymptotics for large time of solutions to a one dimensional parabolic evolution equation with non-standard measure-valued right hand side, that involves derivatives of the solution computed at a free boundary point. The…
The non-gaussianity of processes observed in financial markets and relatively good performance of gaussian models can be reconciled by replacing the Brownian motion with Levy processes whose Levy densities decay as exp(-lambda|x|) or…
We discuss a simple extension of the Ho and Lee model with generic time-dependent drift in which: 1) we compute bond prices analytically; 2) the yield curve is sensible and the asymptotic yield is positive; and 3) our analytical solution…
We consider the problem of modelling the term structure of defaultable bonds, under minimal assumptions on the default time. In particular, we do not assume the existence of a default intensity and we therefore allow for the possibility of…
Recent developments on financial markets have revealed the limits of Brownian motion pricing models when they are applied to actual markets. L\'evy processes, that admit jumps over time, have been found more useful for applications. Thus,…
We consider a stochastic model of incompressible non-Newtonian fluids of second grade on a bounded domain of $\mathbb{R}^2$ driven by L\'evy noise. Applying the variational approach, global existence and uniqueness of strong probabilistic…
This article is concerned with a mutualism ecological model with Levy noise. The local existence and uniqueness of a positive solution are obtained with positive initial value, and the asymptotic behavior to the problem is studied.…
The derivation of a Moving Boundary Approximation or of the response of a coherent structure like a front, vortex or pulse to external forces and noise, is generally valid under two conditions: the existence of a separation of time scales…
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 It\^{o}'s lemma for the calculation of a…
This paper explores stochastic modeling approaches to elucidate the intricate dynamics of stock prices and volatility in financial markets. Beginning with an overview of Brownian motion and its historical significance in finance, we delve…
In an incomplete market driven by time-changed L\'evy noises we consider the problem of hedging a financial position coupled with the underlying risk of model uncertainty. Then we study hedging under worst-case-scenario. The proposed…