Related papers: Stochastic Approaches to Asset Price Analysis
In this study we consider the pricing of energy derivatives when the evolution of spot prices is modeled with a normal tempered stable driven Ornstein-Uhlenbeck process. Such processes are the generalization of normal inverse Gaussian…
We consider high-dimensional asset price models that are reduced in their dimension in order to reduce the complexity of the problem or the effect of the curse of dimensionality in the context of option pricing. We apply model order…
We develop a mixed least squares Monte Carlo-partial differential equation (LSMC-PDE) method for pricing Bermudan style options on assets whose volatility is stochastic. The algorithm is formulated for an arbitrary number of assets and…
The rigorous linking of exact stochastic models to mean-field approximations is studied. Starting from the differential equation point of view the stochastic model is identified by its Kolmogorov equations, which is a system of linear ODEs…
The problem of analyzing the Ito stochastic differential system and its filtering has received attention. The classical approach to accomplish filtering for the Ito SDE is the Kushner equation. In contrast to the classical filtering…
Semi-analytical pricing of American options in a time-dependent Ornstein-Uhlenbeck model was presented in [Carr, Itkin, 2020]. It was shown that to obtain these prices one needs to solve (numerically) a nonlinear Volterra integral equation…
In this paper we study optimal trading strategies in a financial market in which stock returns depend on a hidden Gaussian mean reverting drift process. Investors obtain information on that drift by observing stock returns. Moreover, expert…
Stochastic approximation (SA) is a method for finding the root of an operator perturbed by noise. There is a rich literature establishing the asymptotic normality of rescaled SA iterates under fairly mild conditions. However, these…
We propose a novel group of Gaussian Process based algorithms for fast approximate optimal stopping of time series with specific applications to financial markets. We show that structural properties commonly exhibited by financial time…
Physics, chemistry, biology or finance are just some examples out of the many fields where complex Ornstein-Uhlenbeck (OU) processes have various applications in statistical modelling. They play role e.g. in the description of the motion of…
Consider a process, stochastic or deterministic, obtained by using a numerical integration scheme, or from Monte-Carlo methods involving an approximation to an integral, or a Newton-Raphson iteration to approximate the root of an equation.…
We study the problem of dynamically trading multiple futures whose underlying asset price follows a multiscale central tendency Ornstein-Uhlenbeck (MCTOU) model. Under this model, we derive the closed-form no-arbitrage prices for the…
Recent empirical studies suggest that the volatility of an underlying price process may have correlations that decay slowly under certain market conditions. In this paper, the volatility is modeled as a stationary process with long-range…
Kalman filtering has been traditionally applied in three application areas of estimation, state estimation, parameter estimation (a.k.a. model updating), and dual estimation. However, Kalman filter is often not sufficient when experimenting…
The stock market presents a challenging environment for accurately predicting future stock prices due to its intricate and ever-changing nature. However, the utilization of advanced methodologies can significantly enhance the precision of…
The state-space model and the Kalman filter provide us with unified and computationaly efficient procedure for computing the log-likelihood of the diverse type of time series models. This paper presents an algorithm for computing the…
In the first part of this thesis, we focus on American options in the Heston model. We first give an analytical characterization of the value function of an American option as the unique solution of the associated (degenerate) parabolic…
We show the application of an optimal transportation approach to estimate stochastic volatility process by using the flow that optimally transports the set of particles from the prior to a posterior distribution. We also show how to direct…
This paper proposes a method to detect bank frauds using a mixed approach combining a stochastic intensity model with the probability of fraud observed on transactions. It is a dynamic unsupervised approach which is able to predict…
In this paper we develop Maximum likelihood (ML) based algorithms to calibrate the model parameters in credit rating transition models. Since the credit rating transition models are not Gaussian linear models, the celebrated Kalman filter…