scholarly journals A Non‐Gaussian Ornstein–Uhlenbeck Process for Electricity Spot Price Modeling and Derivatives Pricing

2007 ◽  
Vol 14 (2) ◽  
pp. 153-169 ◽  
Author(s):  
Fred Espen Benth ◽  
Jan Kallsen ◽  
Thilo Meyer‐Brandis
Keyword(s):  
Spot Price ◽  
Uhlenbeck Process ◽  
Derivatives Pricing ◽  
Electricity Spot Price ◽  
Ornstein Uhlenbeck Process ◽  
Non Gaussian

scholarly journals Beyond Brownian motion and the Ornstein-Uhlenbeck process: Stochastic diffusion models for the evolution of quantitative characters

2016 ◽  
Author(s):  
Simon Phillip Blomberg
Keyword(s):  
Brownian Motion ◽  
Stochastic Processes ◽  
Comparative Methods ◽  
Diffusion Models ◽  
Mathematical Framework ◽  
Phylogenetic Comparative Methods ◽  
Uhlenbeck Process ◽  
Trait Evolution ◽  
Ornstein Uhlenbeck Process ◽  
Non Gaussian

AbstractGaussian processes such as Brownian motion and the Ornstein-Uhlenbeck process have been popular models for the evolution of quantitative traits and are widely used in phylogenetic comparative methods. However, they have drawbacks which limit their utility. Here I describe new, non-Gaussian stochastic differential equation (diffusion) models of quantitative trait evolution. I present general methods for deriving new diffusion models, and discuss possible schemes for fitting non-Gaussian evolutionary models to trait data. The theory of stochastic processes provides a mathematical framework for understanding the properties of current, new and future phylogenetic comparative methods. Attention to the mathematical details of models of trait evolution and diversification may help avoid some pitfalls when using stochastic processes to model macroevolution.

GENERALIZED BARNDORFF-NIELSEN AND SHEPHARD MODEL AND DISCRETELY MONITORED OPTION PRICING

2016 ◽  
Vol 19 (04) ◽  
pp. 1650024 ◽  
Author(s):  
AKIRA YAMAZAKI
Keyword(s):  
Stochastic Volatility ◽  
Joint Distribution ◽  
Closed Form Expression ◽  
European Options ◽  
Form Expression ◽  
Uhlenbeck Process ◽  
Lookback Options ◽  
Ornstein Uhlenbeck Process ◽  
Path Dependent ◽  
Non Gaussian

This paper proposes a generalization of the Barndorff-Nielsen and Shephard model, in which the log return on an asset is governed by a Lévy process with stochastic volatility modeled by a non-Gaussian Ornstein–Uhlenbeck process. Under the generalized model, we derive a closed-form expression of the multivariate characteristic function of the intertemporal joint distribution of the underlying log return. Then, we also investigate asymptotic behavior of the log return and its variance. Moreover, we evaluate discretely monitored path-dependent derivatives such as geometric Asian, forward start, barrier, fade-in, and lookback options as well as European options.

scholarly journals Valuation of Swing Options under a Regime-Switching Mean-Reverting Model

2019 ◽  
Vol 2019 ◽  
pp. 1-14
Author(s):  
Lingjie Shao ◽  
Kaili Xiang
Keyword(s):  
Electricity Market ◽  
Regime Switching ◽  
Seasonal Pattern ◽  
Market Price ◽  
Spot Price ◽  
Programming Approach ◽  
Volume Constraint ◽  
Uhlenbeck Process ◽  
Swing Options ◽  
Ornstein Uhlenbeck Process

In this paper, we study the valuation of swing options on electricity in a model where the underlying spot price is set to be the product of a deterministic seasonal pattern and Ornstein-Uhlenbeck process with Markov-modulated parameters. Under this setting, the difficulties of pricing swing options come from the various constraints embedded in contracts, e.g., the total number of rights constraint, the refraction time constraint, the local volume constraint, and the global volume constraint. Here we propose a framework for the valuation of the swing option on the condition that all the above constraints are nontrivial. To be specific, we formulate the pricing problem as an optimal stochastic control problem, which can be solved by the trinomial forest dynamic programming approach. Besides, empirical analysis is carried out on the model. We collect historical data in Nord Pool electricity market, extract the seasonal pattern, calibrate the Ornstein-Uhlenbeck process parameters in each regime, and also get market price of risk. Finally, on the basis of calibration results, a specific numerical example concerning all typical constraints is presented to demonstrate the valuation procedure.

scholarly journals Functional Limit Theorems for the Fractional Ornstein–Uhlenbeck Process

2020 ◽  
Author(s):  
Johann Gehringer ◽  
Xue-Mei Li
Keyword(s):  
Functional Limit ◽  
Uhlenbeck Process ◽  
Order Problem ◽  
Smooth Curves ◽  
Effective Dynamics ◽  
Sample Paths ◽  
Ornstein Uhlenbeck Process ◽  
Markovian Random Process ◽  
Brownian Motion Model ◽  
Non Gaussian

Abstract We prove a functional limit theorem for vector-valued functionals of the fractional Ornstein–Uhlenbeck process, providing the foundation for the fluctuation theory of slow/fast systems driven by both long- and short-range-dependent noise. The limit process has both Gaussian and non-Gaussian components. The theorem holds for any $$L^2$$ L 2 functions, whereas for functions with stronger integrability properties the convergence is shown to hold in the Hölder topology, the rough topology for processes in $$C^{\frac{1}{2}+}$$ C 1 2 + . This leads to a ‘rough creation’ / ‘rough homogenization’ theorem, by which we mean the weak convergence of a family of random smooth curves to a non-Markovian random process with non-differentiable sample paths. In particular, we obtain effective dynamics for the second-order problem and for the kinetic fractional Brownian motion model.

Ornstein--Uhlenbeck Process with Non-Gaussian Structure

2013 ◽  
Vol 44 (5) ◽  
pp. 1123 ◽  
Author(s):  
J. Obuchowski ◽  
A. Wyłomańska
Keyword(s):  
Uhlenbeck Process ◽  
Ornstein Uhlenbeck Process ◽  
Non Gaussian

A Critical Empirical Study of Three Electricity Spot Price Models

2011 ◽  
Author(s):  
Fred Espen Benth ◽  
Ruediger Kiesel ◽  
Anna Nazarova
Keyword(s):  
Empirical Study ◽  
Spot Price ◽  
Electricity Spot Price
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