## Search

Now showing items 1-85 of 85

(Journal article / Tidsskriftartikkel / PublishedVersion; Peer reviewed, 2020)

Spot option prices, forwards and options on forwards relevant for the commodity markets are computed when the underlying process S is modelled as an exponential of a process ξ with memory as, e.g., a Volterra equation ...

(Journal article / Tidsskriftartikkel / AcceptedVersion; Peer reviewed, 2020)

Successful trading in electricity markets relies on the market actor's ability to accurately forecast the electricity price. The fundamental electricity price models use market information, provided by various price drivers, ...

(Journal article / Tidsskriftartikkel / AcceptedVersion; Peer reviewed, 2020)

The liberalization of energy markets worldwide during recent decades has introduced severe implications for the price formation in these markets. Especially within the European day-ahead electricity markets, increased ...

(Journal article / Tidsskriftartikkel / AcceptedVersion; Peer reviewed, 2019)

(Journal article / Tidsskriftartikkel / AcceptedVersion; Peer reviewed, 2019)

We develop cointegration for multivariate continuous-time stochastic processes, both in finite and infinite dimension. Our definition and analysis are based on factor processes and operators mapping to the space of prices ...

(Journal article / Tidsskriftartikkel / AcceptedVersion; Peer reviewed, 2019)

Two stationary and non-negative processes that are based on continuous-time autoregressive moving average (CARMA) processes are discussed. First, we consider a generalization of Cox–Ingersoll–Ross (CIR) processes. Next, ...

(Journal article / Tidsskriftartikkel / AcceptedVersion; Peer reviewed, 2018)

We extend the Heston stochastic volatility model to a Hilbert space framework. The tensor Heston stochastic variance process is defined as a tensor product of a Hilbert-valued Ornstein–Uhlenbeck process with itself. The ...

(Journal article / Tidsskriftartikkel / AcceptedVersion; Peer reviewed, 2018)

In this paper, we show how to approximate 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 ...

(Journal article / Tidsskriftartikkel / PublishedVersion; Peer reviewed, 2018)

We model the logarithm of the spot price of electricity with a normal inverse Gaussian (NIG) process and the wind speed and wind power production with two Ornstein–Uhlenbeck processes. In order to reproduce the correlation ...

(Journal article / Tidsskriftartikkel / AcceptedVersion, 2018)

We propose a non-Gaussian operator-valued extension of the Barndorff-Nielsen and Shephard stochastic volatility dynamics, defined as the square-root of an operator-valued Ornstein–Uhlenbeck process with Lévy noise and ...

(Journal article / Tidsskriftartikkel / AcceptedVersion; Peer reviewed, 2018)

The recent introduction of wind power futures written on the German wind power production index has brought with it new interesting challenges in terms of modelling and pricing. Some particularities of this product are the ...

(Journal article / Tidsskriftartikkel / SubmittedVersion, 2017)

In recent years, renewable energy has gained importance in producing power in many markets. The aim of this article is to model photovoltaic (PV) production for three transmission operators in Germany. PV power can only ...

(Journal article / Tidsskriftartikkel / SubmittedVersion, 2017)

We propose and investigate a valuation model for the income of selling tradeable green certificates (TGCs) in the Swedish–Norwegian market, formulated as a singular stochastic control problem. Our model takes into account ...

(Journal article / Tidsskriftartikkel / SubmittedVersion, 2017)

We lift ambit fields to a class of Hilbert space-valued volatility modulated Volterra processes. We name this class Hambit fields, and show that they can be expressed as a countable sum of weighted real-valued volatility ...

(Journal article / Tidsskriftartikkel / AcceptedVersion; Peer reviewed, 2017)

Stochastic models for forward electricity prices are of great relevance nowadays, given the major structural changes in the market due to the increase of renewable energy in the production mix. In this study, we derive a ...

(Journal article / Tidsskriftartikkel / AcceptedVersion; Peer reviewed, 2017)

The recent price coupling of many European electricity markets has triggered a fundamental change in the interaction of day-ahead prices, challenging additionally the modeling of the joint behavior of prices in interconnected ...

(Journal article / Tidsskriftartikkel / AcceptedVersion; Peer reviewed, 2017)

In this paper, we propose a new multivariate model for the dynamics of regional ocean freight rates. We show that a cointegrated system of regional spot freight rates can be decomposed into a common non-stationary market ...

(Journal article / Tidsskriftartikkel / PublishedVersion; Peer reviewed, 2016)

We treat a stochastic integration theory for a class of Hilbert-valued, volatility-modulated, conditionally Gaussian Volterra processes. We apply techniques from Malliavin calculus to define this stochastic integration as ...

(Journal article / Tidsskriftartikkel / SubmittedVersion, 2015)

We analyze cointegration in commodity markets, and propose a parametric class of pricing measures which preserves cointegration for forward prices with fixed time to maturity. We present explicit expressions for the term ...

(Journal article / Tidsskriftartikkel / AcceptedVersion; Peer reviewed, 2015)

We solve the problem of pricing and hedging Asian-style options on energy with a quadratic risk criterion when trading in the underlying future is restricted. Liquid trading in the future is only possible up to the start ...

(Journal article / Tidsskriftartikkel / PublishedVersion; Peer reviewed, 2015)

Based on forward curves modelled as Hilbert-space valued processes, we analyze the pricing of various options relevant in energy markets. In particular, we connect empirical evidence about energy forward prices known from ...

(Journal article / Tidsskriftartikkel / SubmittedVersion, 2015)

We investigate multivariate subordination of Lévy processes which was first introduced by Barndorff-Nielsen et al. [O.E. Barndorff-Nielsen, F.E. Benth, and A. Veraart, Modelling electricity forward markets by ambit fields, ...

(Journal article / Tidsskriftartikkel / SubmittedVersion, 2015)

For a commodity spot price dynamics given by an Ornstein–Uhlenbeck (OU) process with Barndorff-Nielsen and Shephard stochastic volatility, we price forwards using a class of pricing measures that simultaneously allow for ...

(Chapter / Bokkapittel / AcceptedVersion; Peer reviewed, 2014)

In this paper we derive power futures prices from a two-factor spot model being a generalization of the classical Schwartz–Smith commodity dynamics. We include non-Gaussian effects by introducing Lévy processes as the ...

(Journal article / Tidsskriftartikkel / PublishedVersion; Peer reviewed, 2014)

In electricity markets, it is sensible to use a two-factor model with mean reversion for spot prices. One of the factors is an Ornstein–Uhlenbeck (OU) process driven by a Brownian motion and accounts for the small variations. ...

(Chapter / Bokkapittel / AcceptedVersion; Peer reviewed, 2014)

Published by Palgrave Macmillan. Reproduced with permission of Palgrave Macmillan. This extract is taken from the author's original manuscript and has not been edited. The definitive, published, version of record is available ...

(Journal article / Tidsskriftartikkel / AcceptedVersion; Peer reviewed, 2014)

In this paper an infinite-dimensional approach to model energy forward markets is introduced. Similar to the Heath–Jarrow–Morton framework in interest-rate modelling, a first-order hyperbolic stochastic partial differential ...

(Journal article / Tidsskriftartikkel / SubmittedVersion, 2014)

In this paper we propose a new modelling framework for electricity futures markets based on so-called ambit fields. The new model can capture many of the stylised facts observed in electricity futures and is highly ...

(Journal article / Tidsskriftartikkel / SubmittedVersion, 2014)

We develop a general approach to portfolio optimization in futures markets. Following the Heath–Jarrow–Morton (HJM) approach, we model the entire futures price curve at once as a solution of a stochastic partial differential ...

(Journal article / Tidsskriftartikkel / PublishedVersion; Peer reviewed, 2014)

The present paper discusses simulation of Lévy semistationary (LSS) processes in the context of power markets. A disadvantage of applying numerical integration to obtain trajectories of LSS processes is that such a scheme ...

(Journal article / Tidsskriftartikkel / SubmittedVersion, 2014)

This paper generalizes the integration theory for volatility modulated Brownian-driven Volterra processes onto the space of Potthoff–Timpel distributions. Sufficient conditions for integrability of generalized processes ...

(Journal article / Tidsskriftartikkel / SubmittedVersion, 2014)

(Journal article / Tidsskriftartikkel / PublishedVersion; Peer reviewed, 2013)

(Research report / Forskningsrapport, 2013)

The present paper discusses Levy semistationary processes in the context of power markets. A Fourier simulation scheme for obtaining trajectories of these processes is discussed and its rate of convergence is analysed. ...

(Journal article / Tidsskriftartikkel / SubmittedVersion, 2013)

Due to the non-storability of electricity and the resulting lack of arbitrage-based arguments to price electricity forward contracts, a significant time-varying risk premium is exhibited. Using EEX data during the introduction ...

(Research report / Forskningsrapport, 2013)

We propose a finite difference scheme to simulate solutions to a certain type of hyperbolic stochastic partial differential equation (SPDE). These solutions can in turn estimate so called volatility modulated Volterra (VMV) ...

(Journal article / Tidsskriftartikkel / AcceptedVersion; Peer reviewed, 2013)

We give a short introduction to energy markets, describing how they function and what products are traded. Next we survey some of the popular models that have been proposed in the literature. We extend the analysis of one ...

(Research report / Forskningsrapport, 2012)

We study the pricing of spread options. We consider a bivariate jump-diffusion model for the price process and we obtain a Margrabe type formula for the evaluation of the spread option. Moreover, we consider models in which ...

(Journal article / Tidsskriftartikkel / PublishedVersion; Peer reviewed, 2012)

The aim of this paper is to study pricing of weather insurance contracts based on temperature indices. Three different pricing methods are analysed: the classical burn approach, index modelling and temperature modelling. ...

(Journal article / Tidsskriftartikkel / SubmittedVersion, 2012)

In this paper we present a stochastic model for daily average temperature. The model contains seasonality, a low-order autoregressive component and a variance describing the heteroskedastic residuals. The model is estimated ...

(Journal article / Tidsskriftartikkel / SubmittedVersion, 2012)

In power markets one frequently encounters a risk premium being positive in the short end of the forward curve and negative in the long end. Economically it has been argued that the positive premium is reflecting retailers ...

(Journal article / Tidsskriftartikkel / SubmittedVersion, 2012)

This is the pre-peer reviewed version of the following article: Benth, Fred Espen; Lempa, Jukka; Nilssen, Trygve Kastberg, On the optimal exercise of swing options in electricity markets, Journal of Energy Markets. 2012, ...

(Research report / Forskningsrapport, 2011)

The aim of this paper is to study pricing of weather insurance contracts based on temperature indices. Three different pricing methods are analysed: the classical burn approach, index modelling and temperature modelling. ...

(Research report / Forskningsrapport, 2011)

Merton's classical portfolio optimisation problem for an investor, who can trade in a risk-free bond and a stock, can be extended to the case where the driving noise of the log-returns is a pure jump process instead of a ...

(Research report / Forskningsrapport, 2010)

We study the robustness of option prices to model variation after a change of measure where the measure depends on the model choice. We consider geometric Lévy models in which the infinite activity of the small jumps is ...

(Research report / Forskningsrapport, 2010)

We study the robustness of option prices to model variation within a jump-diffusion framework. In particular we consider models in which the small variations in price dynamics are modeled with a Poisson random measure with ...

(Research report / Forskningsrapport, 2010)

We study the computation of the Greeks of options written on assets modelled by a multi-factor dynamics. For this purpose, we apply the conditional density method in which the knowledge of the density of one factor is ...

(Research report / Forskningsrapport, 2009)

A great challenge using the traditional regression based Bermuda option valuation based on Longstaff and Schwartz (LS) (see Longstaff and Schwartz [10]) is the stability of solutions for different basis functions. In this ...

(Research report / Forskningsrapport, 2009)

Spot prices in energy markets exhibit special features like price spikes, mean-reversion inverse, stochastic volatility, inverse leverage effect and co-integration between the different commodities. In this paper a ...

(Research report / Forskningsrapport, 2009)

We study the robustness of the sensitivity with respect to parameters in expectation functionals with respect to various approximations of a Lévy process. As sensitivity parameter, we focus on the delta of an European ...

(Research report / Forskningsrapport, 2008)

In this paper we study the approximation of a sum of assets having marginal logreturns being multivariate normal inverse Gaussian distributed. We analyse the choice of a univariate exponential NIG distribution, where the ...

(Research report / Forskningsrapport, 2008)

The main objective of this work is to construct optimal temperature futures from available market-traded contracts to hedge spatial risk. Temperature dynamics are modelled by a stochastic differential equation with spatial ...

(Research report / Forskningsrapport, 2008)

Electricity is a commodity which is non-storable, and therefore difficult to move forward in time. Hence, forward looking information about market conditions is not necessarily incorporated in today's prices, and the typical ...

(Research report / Forskningsrapport, 2007)

In this paper we develop a model for electricity spot price dynamics. The spot price is assumed to follow an exponential Ornstein-Uhlenbeck (OU) process with an added compound Poisson process, therefore the model allows ...

(Research report / Forskningsrapport, 2007)

We derive derivative-free formulas for the delta and other Greeks of options written on an asset modeled by a geometric Brownian motion with stochastic volatility of Barndorff-Nielsen and Shephard type. The method applies ...

(Research report / Forskningsrapport, 2007)

In recent decades, there has been a growing interest for utility indifference based approaches to solve the question of pricing of derivatives in incomplete markets. In this paper we consider a stochastic volatility model ...

(Research report / Forskningsrapport, 2006)

We propose a non-symmetric copula to model the evolution of electricity and gas prices by a bivariate non-Gaussian Ornstein- Uhlenbeck pure jump process. We identify the marginal processes as driven by normal inverse ...

(Research report / Forskningsrapport, 2006)

Following the increasing awareness of the risk from volatility fluctuations the markets for hedging contracts written on realised volatility has surged. Companies looking for means to secure against unexpected accumulation ...

ARBITRAGE-FREE PRICING DYNAMICS OF INTEREST-RATE GUARANTEES BASED ON THE UTILITY INDIFFERENCE METHOD

(Research report / Forskningsrapport, 2005)

We consider the problem of utility indifference pricing of a put option written on a non-tradeable asset, where we can hedge in a correlated asset. The dynamics are assumed to be a two-dimensional geometric Brownian motion, ...

(Research report / Forskningsrapport, 2005)

We propose a spatial-temporal stochastic model for daily average temperature data. First we build a model for a single spatial location, independently on the spatial information. The model includes trend, seasonality and ...

(Research report / Forskningsrapport, 2005)

We propose a quasi-Monte Carlo (qMC) algorithm to simulate variates from the normal inverse Gaussian (NIG) distribution. The algorithm is based on a Monte Carlo technique found in the Rydberg reference, and is based on ...

(Research report / Forskningsrapport, 2005)

We propose an mean-reverting model for the spot price dynamics of electricity which includes seasonality of the prices and spikes. The dynamics is a sum of non-Gaussian Ornstein-Uhlenbeck processes with jump processes ...

(Research report / Forskningsrapport, 2005)

We propose an Ornstein-Uhlenbeck process with seasonal volatility to model the time dynamics of daily average temperatures. The model is fitted to almost 43 years of daily observations recorded in Stockholm, one of the ...

(Research report / Forskningsrapport, 2005)

This paper presents an analytic approximation for the pricing dynamics of spark spread options in terms of Fourier transforms. We propose to model the spark spread, that is, the price difference of electricity and gas, ...

(Research report / Forskningsrapport, 2005)

We discuss the modeling of electricity contracts traded in many deregulated power markets. These forward/futures type contracts deliver (either physically or financially) electricity over a specified time period, and is ...

(Research report / Forskningsrapport, 2005)

We develop and apply a numerical scheme for pricing options for the stochastic volatility model proposed by Barndorff-Nielsen and Shephard. This non-Gaussian Ornstein-Uhlenbeck type of volatility model gives rise to an ...

(Research report / Forskningsrapport, 2004)

We use the dynamic programming approach to derive an equation for the utility indifference price of Markovian claims in a stochastic volatility model proposed by Barndorff-Nielsen and Shephard (2001). The pricing equation ...

(Research report / Forskningsrapport, 2004)

We analyze the classical Merton's portfolio optimization problem when the risky asset follows an exponential Ornstein-Uhlenbeck process, also known as the Schwartz mean-reversion dynamics. The corresponding Hamilton-Jacobi-Bellman ...

(Research report / Forskningsrapport, 2004)

We model the daily average temperature variations with a mean-reverting Ornstein-Uhlenbeck process driven by generalized hyperbolic Lévy process and having seasonal mean and volatility. It is emirically demonstrated that ...

(Research report / Forskningsrapport, 2003)

We derive arbitrage-free pricing dynamics for claims on temperature, where the temperature follows a fractional Ornstein-Uhlenbeck process. Using a fractional white noise calculus, we can express the dynamics as a special ...

(Research report / Forskningsrapport, 2003)

Under general conditions stated in Rheinländer 30], we prove that in a stochastic volatility market the Radon-Nikodym density of the minimal entropy martingale measure can be expressed in terms of the solution of a semilinear ...

(Research report / Forskningsrapport, 2003)

We model spot prices in energy markets with exponential non-Gaussian Ornstein-Uhlenbeck processes. We generalize the classical geometric Brownian motion and Schwartz' mean-reversion model by introducing Lévy processes as ...

(Research report / Forskningsrapport, 2002)

We develop an anticipative calculus for Lévy processes with finite second moment. The calculus is based on the chaos expansion of square-integrable random variables in terms of iterated integrals of the compensated Poisson ...

(Research report / Forskningsrapport, 2002)

In this paper we investigate the recently introduced Malliavin approach compared to more classical approaches to find sensitivities of options in commodity and energy markets. The Malliavin approach has been developed in ...

(Research report / Forskningsrapport, 2001)

In a market driven by a Lévy martingale, we consider a claim x. We study the problem of minimal variance hedging and we give an explicit formula for the minimal variance portfolio in terms of Malliavin derivatives. We ...

(Research report / Forskningsrapport, 2000)

(Research report / Forskningsrapport, 2000)

(Research report / Forskningsrapport, 2000)

(Research report / Forskningsrapport, 1996)

(Research report / Forskningsrapport, 1996)

(Research report / Forskningsrapport, 1995)

(Research report / Forskningsrapport, 1995)

(Research report / Forskningsrapport, 1995)

(Research report / Forskningsrapport, 1993)

(Research report / Forskningsrapport, 1993)