Related papers: Forward rate models with linear volatilities
The problem of existence of solution for the Heath-Jarrow-Morton equation with linear volatility and purely jump random factor is studied. Sufficient conditions for existence and non-existence of the solution in the class of bounded fields…
We consider the Heath-Jarrow-Morton model of forward rates processes with linear volatility. The noise is either a Wiener or a pure jump Leevy process. We provide formulae for the forward rate processes, and discus the problem of their…
An extension of the Heath--Jarrow--Morton model for the development of instantaneous forward interest rates with deterministic coefficients and Gaussian as well as L\'evy field noise terms is given. In the special case where the L\'evy…
The paper is concerned with the problem of existence of solutions for the Heath-Jarrow-Morton equation with linear volatility. Necessary conditions and sufficient conditions for the existence of weak solutions and strong solutions are…
A market with defaultable bonds where the bond dynamics is in a Heath-Jarrow-Morton setting and the forward rates are driven by an infinite number of Levy factors is considered. The setting includes rating migrations driven by a Markov…
The paper studies the Heath-Jarrow-Morton-Musiela equation of the bond market. The equation is analyzed in weighted spaces of functions defined on $[0,+\infty)$. Sufficient conditions for local and global existence are obtained . For…
The problem of completeness of the forward rate based bond market model driven by a L\'evy process under the physical measure is examined. The incompleteness of market in the case when the L\'evy measure has a density function is shown. The…
L\'evy driven term structure models have become an important subject in the mathematical finance literature. This paper provides a comprehensive analysis of the L\'evy driven Heath-Jarrow-Morton type term structure equation. This includes a…
A new test of a wide class of interest rate models is proposed and applied to a recently developed quantum field theoretic model and the industry standard Heath-Jarrow-Morton model. This test is independent of the volatility function unlike…
We give sufficient conditions for existence, uniqueness and ergodicity of invariant measures for Musiela's stochastic partial differential equation with deterministic volatility and a Hilbert space valued driving L\'evy noise. Conditions…
The completeness problem of the bond market model with the random factors determined by a Wiener process and Poisson random measure is studied. Hedging portfolios use bonds with maturities in a countable, dense subset of a finite time…
The problem of existence of arbitrage free and monotone CDO term structure models is studied. Conditions for positivity and monotonicity of the corresponding Heath-Jarrow-Morton-Musiela equation for the $x$-forward rates with the use of the…
The completeness of a bond market model with infinite number of sources of randomness on a finite time interval in the Heath-Jarrow-Morton framework is studied. It is proved that the market is not complete. A construction of a bounded…
In a recent formulation of a quantum field theory of forward rates, the volatility of the forward rates was taken to be deterministic. The field theory of the forward rates is generalized to the case of stochastic volatility. Two cases are…
In this paper, we study term structure movements in the spirit of Heath, Jarrow, and Morton [Econometrica 60(1), 77-105] under volatility uncertainty. We model the instantaneous forward rate as a diffusion process driven by a G-Brownian…
In this paper we show how to approximate a Heath-Jarrow-Morton dynamics for the forward prices in commodity markets with arbitrage-free models which have a finite dimensional state space. Moreover, we recover a closed form representation of…
We study the pricing of European-style options written on forward contracts within function-valued infinite-dimensional affine stochastic volatility models. The dynamics of the underlying forward price curves are modeled within the…
One of the peculiarities of power and gas markets is the delivery mechanism of forward contracts. The seller of a futures contract commits to deliver, say, power, over a certain period, while the classical forward is a financial agreement…
One-dimensional stochastic differential equations with additive L\'evy noise are considered. Conditions for existence and uniqueness of a strong solution are obtained. In particular, if the noise is a L\'evy symmetric stable process with…
This paper aims at transferring the philosophy behind Heath-Jarrow-Morton to the modelling of call options with all strikes and maturities. Contrary to the approach by Carmona and Nadtochiy (2009) and related to the recent contribution…