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We introduce a variant of the Barndorff-Nielsen and Shephard stochastic volatility model where the non Gaussian Ornstein-Uhlenbeck process describes some measure of trading intensity like trading volume or number of trades instead of…
We construct a generalization of the Ornstein-Uhlenbeck processes on the cone of covariance matrices endowed with the Log-Euclidean and the Affine-Invariant metrics. Our development exploits the Riemannian geometric structure of symmetric…
Our goal is to analyze the system of Hamilton-Jacobi-Bellman equations arising in derivative securities pricing models. The European style of an option price is constructed as a difference of the certainty equivalents to the value functions…
We model the time evolution of single win odds in Japanese horse racing as a stochastic process, deriving an Ornstein--Uhlenbeck process by analyzing the probability dynamics of vote shares and the empirical time series of odds movements.…
Given the observation of a high-dimensional Ornstein-Uhlenbeck (OU) process in continuous time, we proceed to the inference of the drift parameter under a row-sparsity assumption. Towards that aim, we consider the negative log-likelihood of…
A derivative is a financial security whose value is a function of underlying traded assets and market outcomes. Pricing a financial derivative involves setting up a market model, finding a martingale (``fair game") probability measure for…
We propose a parsimonious class of arbitrage-free, yields-only dynamic term structure models (DTSMs) with unspanned latent risks. To enable sequential estimation and forecasting, we develop a Sequential Monte Carlo framework that combines…
We refer by threshold Ornstein-Uhlenbeck to a continuous-time threshold autoregressive process. It follows the Ornstein-Uhlenbeck dynamics when above or below a fixed level, yet at this level (threshold) its coefficients can be…
In this work we study a continuous time exponential utility maximization problem in the presence of a linear temporary price impact. More precisely, for the case where the risky asset is given by the Ornstein-Uhlenbeck diffusion process we…
We introduce and treat rigorously a new multi-agent model of the continuous double auction or in other words the order book (OB). It is designed to explain collective behaviour of the market when new information affecting the market…
This paper builds a multivariate L\'evy-driven Ornstein-Uhlenbeck process for the management of non-maturing deposits, that are a major source of funding for banks. The contribution of the paper is both theoretical and operational. On the…
This paper proposes a novel model of financial prices where: (i) prices are discrete; (ii) prices change in continuous time; (iii) a high proportion of price changes are reversed in a fraction of a second. Our model is analytically…
We study a market model in which the volatility of the stock may jump at a random time from a fixed value to another fixed value. This model was already described in the literature. We present a new approach to the problem, based on partial…
We consider the infinite dimensional Heston stochastic volatility model proposed in \arXiv:1706:03500. The price of a forward contract on a non-storable commodity is modelled by a generalized Ornstein-Uhlenbeck process in the Filipovi\'{c}…
We formulate and analyze an inverse problem using derivatives prices to obtain an implied filtering density on volatility's hidden state. Stochastic volatility is the unobserved state in a hidden Markov model (HMM) and can be tracked using…
This paper develops a continuous-time filtering framework for estimating a hazard rate subject to an unobservable change-point. This framework naturally arises in both financial and insurance applications, where the default intensity of a…
This work considers a stochastic model in which the uncertainty is driven by a multidimensional Brownian motion. The market price of risk process makes the transition between real world probability measure and risk neutral probability…
In this article we study the asymptotic behaviour of the realized quadratic variation of a process $\int_{0}^{t}u_{s}dY_{s}^{(1)}$% , where $u$ is a $\beta$-H\"older continuous process with $\beta > 1-H$ and…
Employing probabilistic techniques we compute best possible upper and lower bounds on the price of an option on one or two assets with continuous piecewise linear payoff function based on prices of simple call options of possibly distinct…
L\'evy-driven Ornstein-Uhlenbeck (OU) processes represent an intriguing class of stochastic processes that have garnered interest in the energy sector for their ability to capture typical features of market dynamics. However, in the current…