Related papers: Additive energy forward curves in a Heath-Jarrow-M…
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…
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…
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…
In energy markets, joint historical and implied calibration is of paramount importance for practitioners, yet notoriously challenging due to the need to align historical correlations of futures contracts with implied volatility smiles from…
In this article we discuss the application of the Heath-Jarrow-Morton framework Heath et al. [26] to energy markets. The goal of the article is to give a detailed overview of the topic, focusing on practical aspects rather than on theory,…
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…
In this paper we introduce a flexible HJM-type framework that allows for consistent modelling of intraday, spot, futures, and option prices. This framework is based on stochastic processes with economic interpretations and consistent with…
We present a function-valued stochastic volatility model designed to capture the continuous-time evolution of forward curves in fixed-income or commodity markets. The dynamics of the (logarithmic) forward curves are defined by a…
This paper introduces a no-arbitrage, Monte Carlo-free approach to pricing path-dependent interest rate derivatives. The Heath-Jarrow-Morton model gives arbitrage-free contingent claims prices but is infinite-dimensional, making traditional…
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…
Based on forward curves modelled as Hilbert-space valued processes, we analyse the pricing of various options relevant in energy markets. In particular, we connect empirical evidence about energy forward prices known from the literature to…
We propose a general framework for the simultaneous modeling of equity, government bonds, corporate bonds and derivatives. Uncertainty is generated by a general affine Markov process. The setting allows for stochastic volatility, jumps, the…
We consider a stochastic factor financial model where the asset price process and the process for the stochastic factor depend on an observable Markov chain and exhibit an affine structure. We are faced with a finite time investment horizon…
We introduce a new and highly tractable structural model for spot and derivative prices in electricity markets. Using a stochastic model of the bid stack, we translate the demand for power and the prices of generating fuels into electricity…
Demographic projections of future mortality rates involve a high level of uncertainty and require stochastic mortality models. The current paper investigates forward mortality models driven by a (possibly infinite dimensional) Wiener…
We price European-style options written on forward contracts in a commodity market, which we model with an infinite-dimensional Heath-Jarrow-Morton (HJM) approach. For this purpose we introduce a new class of state-dependent volatility…
Given a Heath-Jarrow-Morton (HJM) interest rate model $\mathcal{M}$ and a parametrized family of finite dimensional forward rate curves $\mathcal{G}$, this paper provides a technique for projecting the infinite dimensional forward rate…
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…
We propose a multi-scale stochastic volatility model in which a fast mean-reverting factor of volatility is built on top of the Heston stochastic volatility model. A singular pertubative expansion is then used to obtain an approximation for…