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The paper treats the financial market as a communication system, using four information-theoretic assumptions to derive an idealized model with only one parameter. State variables are scalar stationary diffusions. The model minimizes the…
The use of an Ornstein-Uhlenbeck (OU) process is ubiquitous in business, economics and finance to capture various price processes and evolution of economic indicators exhibiting mean-reverting properties. When structural changes happen,…
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. The other…
Most energy and commodity markets exhibit mean-reversion and occasional distinctive price spikes, which results in demand for derivative products which protect the holder against high prices. To this end, in this paper we present exact and…
It is considered Ornstein-Uhlenbeck process $ x_t = x_0 e^{-\theta t} + \mu (1-e^{-\theta t}) + \sigma \int_0^t e^{-\theta (t-s)} dW_s$, where $x_0 \in R$, $\theta>0$, $ \mu \in R$ and $\sigma > 0$ are parameters. By use values $(z_k)_{k…
We consider a discrete-time approximation of paths of an Ornstein--Uhlenbeck process as a mean for estimation of a price of European call option in the model of financial market with stochastic volatility. The Euler--Maruyama approximation…
This paper develops a new stochastic volatility model for the temperature that is a natural extension of the Ornstein-Uhlenbeck model proposed by Benth and Benth (2007). This model allows to be more conservative regarding extreme events…
In this project, we propose to explore the Kalman filter's performance for estimating asset prices. We begin by introducing a stochastic mean-reverting processes, the Ornstein-Uhlenbeck (OU) model. After this we discuss the Kalman filter in…
The Ornstein-Uhlenbeck (OU) process, a mean-reverting stochastic process, has been widely applied as a time series model in various domains. This paper describes the design and implementation of a model-based synthetic time series model…
We conduct a preliminary analysis of a pairs trading strategy using the Ornstein-Uhlenbeck (OU) process to model stock price spreads. We compare this approach to a naive pairs trading strategy that uses a rolling window to calculate mean…
We propose a parsimonious stochastic model for characterising the distributional and temporal properties of rainfall. The model is based on an integrated Ornstein-Uhlenbeck process driven by the Hougaard L\'evy process. We derive properties…
The price of a financial derivative can be expressed as an iterated conditional expectation, where the inner term conditions on the future of an auxiliary process. We show that this inner conditional expectation solves an SPDE (a…
We consider a problem of parameter estimation for the state space model described by linear stochastic differential equations. We assume that an unobservable Ornstein-Uhlenbeck process drives another observable process by the linear…
A Levy-driven Ornstein-Uhlenbeck process is proposed to model the evolution of the risk-free rate and default intensities for the purpose of evaluating option contracts on a credit index. Time evolution in credit markets is assumed to…
This paper is devoted to parameter estimation of the mixed fractional Ornstein-Uhlenbeck process with a drift. Large sample asymptotical properties of the Maximum Likelihood Estimator is deduced using the Laplace transform computations or…
We consider the pricing problem related to payoffs that can have discontinuities of polynomial growth. The asset price dynamic is modeled within the Black and Scholes framework characterized by a stochastic volatility term driven by a…
In this paper hyperbolic partial differential equations with random coefficients are discussed. Such random partial differential equations appear for instance in traffic flow problems as well as in many physical processes in random media.…
This paper examines a heterogeneous beliefs model in which there is a process that is only partially observed by the agents. The economy contains a risky asset producing dividends continuously in time. The dividends are observed by the…
We consider estimation of the drift parameter $\vartheta>0$ in a \emph{partially observed} Ornstein--Uhlenbeck type model driven by a mixed fractional Brownian noise. Our framework extends the partially observed model of…
We consider the Black--Scholes model of financial market modified to capture the stochastic nature of volatility observed at real financial markets. For volatility driven by the Ornstein--Uhlenbeck process, we establish the existence of…