Browsing by Author "Ware, Antony"
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- ItemOpen AccessA Study in Hybrid Monte Carlo Methods in Computing Derivative Prices(2012-12-05) Wang, Binbin; Ware, AntonyHybrid Monte Carlo (HMC) method is defined in this thesis as Monte Carlo method that utilizes conditional expectation so that the regular Monte Carlo method and other computational methods can be combined to price financial derivatives. This thesis introduces several hybrid Monte Carlo methods and studies the algorithm and efficiency of these methods, which include three methods combining Monte Carlo with fast Fourier transform, cosine series, and Black-Scholes formula respectively. These methods can be considered as ways of variance reduction. The thesis also introduces a new variance reduction method using orthogonal transformation which further reduces the variance. It is shown in this thesis that the HMC methods can significantly improve the efficiency when compared to the regular Monte Carlo method. A basket option example is used throughout this thesis for implementation and efficiency comparison.
- ItemOpen AccessAdvection-based spatiotemporal reconstruction techniques for turbulent velocity fields(2023-05-01) Vocke, Maegan; Martinuzzi, Robert; Morton, Chris; Wood, David; Ware, AntonyTurbulent flows are characterized by interactions of widespread spatiotemporal scales. Experimental techniques such as Particle Image Velocimetry can provide correlated flow measurements, however, obtaining suitable resolution of temporal and spatial scales remains challenging. This work investigates the ability of an advection-based flow reconstruction technique to increase the temporal resolution of turbulent flow data. A semi-Lagrangian technique is used to obtain instantaneous fluid trajectories through a forward and backward integration of the known data. The estimates are then fused using a temporal weighting scheme to yield velocity fields at intermediate times. The performance of the method is verified against a benchmark direct numerical simulation (DNS) data set. Spectral information up to two orders of magnitude beyond the Nyquist criteria is successfully - surpassing the performance of previously introduced methods. Correlation maps are used to quantify the spatial loss of memory and define a criterion for the maximum recoverable frequency.
- ItemOpen AccessAnalytical Unsteady Aerodynamic Models for Horizontal Axis Wind Turbines(2016) Hammam, Mohamed; Wood, David; Crawford, Curran; Morton, Chris; Johansen, Craig; Ware, Antony; Visser, KenThis thesis describes the development of unsteady aerodynamic models of wind turbines within the framework of blade element momentum theory. The main purpose is to build analytical models, and test them against available wind tunnel and field test data. The unsteady wake is modeled using vortex methods. The analysis covers unsteady loading due to fast pitch change at constant wind speed, and varying wind speed at constant pitch. The analysis can be extended to more complex conditions. The work starts by modeling dynamic inflow effects as an inertia force, with a new developed expression of the apparent mass and rotational inertia of the rotor vortices. Further assumptions lead to a Ricatti differential equation for the axial induction, which has an analytical solution. First, linear pitch changes are investigated, and the unsteady thrust and torque are calculated. The model is shown to be accurate in comparison to the available experiments. The model is then extended to low tip speed ratios in the form of an Abel differential equation, which appeared to be more accurate. However, comparison with measurements has shown that the assumptions leading to the Abel equation model are inconsistent. The unsteady load is characterized by a large overshoot for high pitch rate. To alleviate this an analytical solution of exponential pitch angle is developed. %An analytical model is obtained for the exponential pitch case and validated against experiment. Next, the unsteady load due to varying wind speed at constant pitch is modeled. The dynamic inflow model is extended to include the circulatory effect of the wake. A new unsteady model is developed from first principles. The wake is modeled as an initial vortex cylinder and vortex rings released onto the wake with each revolution of the blades. The circulatory effect is described by a new function. The model is simplified further by approximating the wake effect to get an analytical solution for the case of linearly varying wind speed. The unsteady lift is modeled and combined with the dynamic inflow model to obtain a fully unsteady model in state space form. The different models are validated with experiments, and the unsteady lift effect is found to have importance for short time period transients.
- ItemOpen AccessAssessing the Accuracy of Convective Heat Transfer from Overhead Conductor at Low Wind Speed Using Large Eddy Simulations (LES)(2017-12-22) Abdelhady, Mohamed; Wood, David; Morton, Christopher; Ware, AntonyThis project uses Computational Fluid Dynamics (CFD) to assess the accuracy of the forced cooling term for Real Time Thermal Rating (RTTR) of power lines in overhead conductor codes, IEEE 738 and CIGRÉ 207. The analysis is done for low wind speed, corresponding to Reynolds Number of 1,000, and 3,000. The project uses Large Eddy Simulation (LES) in the ANSYS Fluent software. The primary goal is to calculate the convective heat transfer for cylindrical and stranded conductors in non-turbulent flow and for cylindrical conductors with free-stream turbulence. The results showed that the heat transfer correlations used in the codes are accurate for low turbulent flows and that the stranded conductor causes an increase in heat transfer of ~9 % over a cylindrical conductor at low wind speed. The constant heat flux boundary condition experiences ~15 % higher Nusselt Number than uniform temperature boundary condition. The calculated increase in heat transfer due to turbulence was significant; increased heat transfer due to turbulence ~24 % at Reynolds Number of 3,000 at a turbulence intensity of 8% and length scale to diameter ratio of 0.4.
- ItemOpen AccessContinuous Time Portfolio Selection under Conditional Capital at Risk(2010-06-17) Dmitrasinovic-Vidovic, Gordana; Lari-Lavassani, Ali; Li, Xun; Ware, AntonyPortfolio optimization with respect to different risk measures is of interest to both practitioners and academics. For there to be a well-defined optimal portfolio, it is important that the risk measure be coherent and quasiconvex with respect to the proportion invested in risky assets. In this paper we investigate one such measure—conditional capital at risk—and find the optimal strategies under this measure, in the Black-Scholes continuous time setting, with time dependent coefficients.
- ItemOpen AccessContinuous Time Portfolio Selection under Conditional Capital at Risk(Hindawi Publishing Corporation, 2010) Dmitrasinovic-Vidovic, Gordana; Lari-Lavassani, Ali; Li, Xun; Ware, Antony
- ItemOpen AccessCredit Risk Pricing via Epstein-Zin Pricing Kernel(2017) Ogunsolu, Mobolaji; Sezer, Deniz; Frei, Christoph; Badescu, Alexandru; Ware, Antony; David, Alexander; Liao, WenyuanWe present an equilibrium framework for pricing corporate bonds with information delay in an Epstein-Zin setting. As in structural models of credit risk, the default time is modeled as the first hitting time of a default boundary by the unobservable process; the firm's asset value. The observable state variables; log consumption and volatility are affine processes which drive the unobservable firm's value process. The stochastic pricing kernel is expressed in terms of the state variables. The price of a zero-coupon bond is expressed as the solution of a multidimensional partial differential equation which is solved numerically. Our equilibrium price model is also calibrated to fit available corporate bond and consumption data. Finally, we analyze the implications of investor’s preferences and information delay on the credit yield spreads.
- ItemOpen AccessDeep Learning-based Numerical Methods for Stochastic Partial Differential Equations and Applications(2021-03-14) Yao, Yao; Qiu, Jinniao; Ware, Antony; Badescu, AlexandruIn this thesis, we are concerned with approximating solutions of stochastic partial differential equations (SPDEs) and their applications. Inspired by Huré, Pham, and Warin [15], we propose and study the deep learning-based methods for both the forward and backward SPDEs. In particular, the forward SPDEs may allow for Neumann boundary conditions. We also prove the convergence analysis of the proposed algorithms. The numerical results indicate that the performance of the algorithm is quite effective for solving the SPDEs, even in high-dimensional cases. The applications include various pricing problems under exchange rate target zone models as well as under rough volatility models.
- ItemOpen AccessDelta Hedging Variable Annuities under Wiener Chaos Expansion(2017) Wiredu, David; Ambagaspitiya, Rohana Shantha; Ware, Antony; Swishchuk, Anatoliy; Scollnik, DavidWe present a method for Delta-Hedging of variable annuity products under the Guaranteed Minimum withdrawal Benefit (GMWB) Rider based on Wiener Chaos expansion. We also discuss well-known Monte-Carlo methods for computing Delta for derivatives, particularly for variable annuities. A detailed discussion of Wiener Chaos expansion is then provided. A discussion on the Heath-Jarrow-Morton (HJM) framework in the context of constant and exponential volatility is given. Choosing a Geometric Brownian motion for the underlying in the variable annuity account and the Heath-Jarrow-Morton model for interest rates we present results of delta computed by the Wiener Chaos technique in MATLAB using the UQLab framework. Comparisons between this method and the Monte-Carlo benchmark are then presented.
- ItemOpen AccessDerivatives Pricing with Fractional Discrete-time Models(2022-07-07) Jayaraman, Sarath Kumar; Badescu, Alexandru; Godin, Frederic; Qiu, Jinniao; Swishchuk, Anatoliy; Ware, AntonyThis thesis studies the pricing of European style derivatives with various affine models. Most of this thesis focuses on the impact of long memory on asset return modelling and option pricing. We propose a general discrete-time pricing framework based on affine multi-component volatility models that admit ARCH(∞) representations. It not only nests a large variety of option pricing models from the literature, but also allows for the introduction of novel fractionally integrated processes for option valuation purposes. Using an infinite sum characterization of the log-asset price’s cumulant generating function, we derive semi-explicit expressions for European option prices under a variance-dependent stochastic discount factor. We carry out an extensive empirical analysis which includes estimations based on different combinations of returns and options of the S&P 500 index for a variety of short- and long-memory models. Our results indicate that the inclusion of long memory into return modelling substantially improves the option pricing performance. Using a set of out-of-sample option pricing errors, we show that long-memory models outperform richer parametrized one- and two-component models with short-memory dynamics. The last part of the thesis studies the pricing of volatility derivatives with affine models. We propose semi-closed form solutions, subject to an inversion of the Fourier transform, for the price of VIX options and target volatility options under affine GARCH models based on Gaussian and Inverse Gaussian distributions. The empirical performance of the two affine GARCH models is tested using different calibration exercises based on historical returns and market quotes on VIX and SPX options.
- ItemOpen AccessEstimating Spot Price and Smooth Forward Curve in Electricity Markets with Bayesian Penalized Spline(2014-05-05) Gezahagne, Azamed; Ware, AntonyThe first part of this thesis presents a Bayesian penalized spline approach to constructing smooth forward curves in electricity markets. Since electricity should be delivered as a continuous flow, power contracts have settlement periods rather than a fixed delivery time. In addition, electricity forward curves have strong seasonal shape. Our approach provides a method for estimating a continuous forward price curve from market forward prices quoted over a period. The approach is illustrated using observed market data from the Mid-Columbia (Mid-C) and California Oregon Border (COB) pricing hubs. Since Mid-C is a liquid market where forward contracts are quoted every day and COB is an illiquid hub, a two step estimation procedure is developed from Bayesian perspective.First, the Mid-C smooth curve is constructed using Bayesian penalized spline. Next, the COB smooth curve is estimated by adding a spread to the constructed Mid-C smooth curve and incorporating the positive spread between the two hubs as an informative prior. In the second part, we present a mean reverting model for the electricity spot price and we employ a Bayesian penalized spline approach to model the deterministic seasonal function exhibited in the monthly averages. Based on the historical spot price from Alberta power market, we calibrated the model parameters, also by implementing Bayesian estimation techniques.
- ItemOpen AccessHydrological Time Series Modelling and Applications(2016) Asadzadeh, Ilnaz; Ware, Antony; Badescu, Alexandru; Swishchuk, Anatoliy; Zinchenko, YuriyWe consider the problem of measuring reliability of a hydro reservoir over a finite horizon with a stochastic optimal control technique. To apply this technique, we need to model the underlying stochastic process which is the inflow of water to the reservoir. Typical time series models for such problems only capture linear dependency (simple correlation) in the data. Alternative approaches include artificial neural network methods but these lack a theoretical foundation and a systematic procedure for the construction of the model. To overcome both of these limitations, we propose a new framework based on the application of copulas to univariate time series modelling. Our model shows that some important statistical characteristics of hydrological time series, such as upper and lower tail dependencies, persistence, etc., can be described with the aid of copulas. In turn, this provides insight regarding the qualitative properties of the underlying time series. Our main contribution is a new method of estimation based on a semi-parametric technique. By semi-parametric we mean using empirical autocopula (copula of a time series with itself with different lags), and parametric marginal distributions. Goodness of fit analysis is carried out and numerical results are illustrated with variety of concrete examples and sample data sets. We then benchmark and compare our scheme to alternative methods such as parametric models and various other time series modelling techniques. The final part of the dissertation proposes an application of stochastic optimal control to measure the reliability function (the probability that a system will perform the required function for a specified period of time under stated conditions) of the reservoir. For this section, we work with both uncorrelated and correlated inflow time series. For the first case, we generate independent inflow series using some probability distribution and for the second assumption, correlated inflow series, we employ the values of inflow generated using the autocopula method.
- ItemOpen AccessLarge-scale coherent structures and three-dimensional velocity estimation in the turbulent wake of a low aspect ratio surface-mounted cone(2017) Chen, Zixiang; Martinuzzi, Robert; Piomelli, Ugo; Ware, Antony; Wood, David; Sudak, Leszek; Morton, ChristopherThe turbulent wake of a low-aspect-ratio right angle cone mounted on a flat surface, partially submerged in a steady turbulent boundary layer, is investigated using planar Stereoscopic Particle Image Velocimetry (SPIV) in a wind tunnel and Large Eddy Simulation (LES). The description of the dynamics of the large-scale quasi-periodic flow structures and their estimations using remote pressure sensors are considered in this study. The dominant vortex structures are first extracted from SPIV data using the traditional phase average method, which yields an average coherent velocity field that represents a typical shedding cycle. The formation and evolution of these large structures are visualized using volume rendering techniques and analyzed in the framework of vorticity dynamics. To go beyond the typical shedding cycle description, a technique to estimate the three-dimensional flow field from uncorrelated velocity measurements is presented. The method utilizes simultaneous pressure sensors mounted on the solid wall boundary in conjunction with the planar SPIV measurements. Compared to the typical shedding cycle representation, the technique can also characterize the low frequency modulation of the vortex shedding process. The capability of this technique to estimate the three-dimensional flow field is then assessed us- ing LES by applying the estimation techniques to planar LES velocity fields and comparing the results to the actual three-dimensional velocity field available from the simulation. The velocity estimation is found to be consistent with the actual three-dimensional velocity field. Additional coherent motions that are not captured in the experiment are also identified with the LES results, and strategies to capture these motions in SPIV measurements are developed based on the numerical data.
- ItemOpen AccessLocational Spread Options with Stochastic Correlation(2023-05-05) Ali, Syeda Fareeha; Ware, Antony; Swishchuk, Anatoliy; Zinchenko, YuriyContrary to the common assumption, the correlation between financial derivatives may not be constant across time. This thesis analyses the role of stochastic correlation in modeling for locational spread options for natural gas. We first derive a model with Ornstein–Uhlenbeck process between two spread assets with constant correlation and then a combination of the Ornstein–Uhlenbeck and Jacobi process is used to model a stochastic correlation. The Margrabe formula is employed to evaluate options prices with constant correlation, the solution for which is used to compare with Monte Carlo simulations for stochasticity. Comparing the results, we find out why stochastic correlation is more important in real markets.
- ItemOpen AccessLow Order Representations in the Turbulent Wake of a Normal Flat Plate(2015-12-22) Jochaud du Plessix, Phillip Alexandre; Martinuzzi, Robert; Morton, Chris; Ware, Antony; Wood, DavidThe turbulent wake of a normal flat plate, characterized by quasi-periodic vortex-shedding dynamics, is investigated in the context of low-order modeling, non-linear dynamics and kinetic energy transfer. The flow is characterized, coherent-structures are educed through the implementation of three models, and the transfer of kinetic energy between the most energetic structures and to the unresolved scales of motion is investigated. A low-order kinematic model (LOM) is constructed via the truncation of a Galerkin expansion using the energetically-optimal proper orthogonal decomposition (POD). The harmonic and shift modes of the LOM are coupled via the mean-field paraboloid in phase space, enabling the construction of a generalized phase-average (GPA). The GPA is shown to capture key flow behaviour and physics that traditional phase-averaging (TPA) cannot, including variation in the base flow and modulation of the vortex-shedding amplitude. A clearer understanding of energy transfer is made possible through the simplified representations of the models.
- ItemOpen AccessMultivariate General Compound Hawkes and Point Processes with Financial Applications(2022-10-20) Guo, Qi; Swishchuk, Anatoliy; Qiu, Jinniao; Badescu, Alexandru; Ware, Antony; Hyndman, Cody; Swishchuk, AnatoliyThe Hawkes process (HP) significantly affected the financial modeling area in the past 15 years, especially high-frequency trading. This thesis focuses on various new Hawkes processes and considers their applications in the limit order book (LOB). Preexisting studies of the HP in the LOB showed that the arrivals of orders could be modeled by univariate or multivariate HP because of its long memory property and clustering effect. Therefore, we propose the multivariate general compound Hawkes process (MGCHP), a stochastic model for the mid-price in the LOB. For the MGCHP, we prove the Law of Large Numbers (LLN) and two Functional Central Limit Theorems (FCLT); the latter provides insights into the link between price volatilities and order flows in limit order books with several assets. The parameter estimation for the high-dimensional Hawkes process is always time-consuming. This motivates us to consider a generalization of the MGCHP. We replace the multivariate HP with a more general point process, and we call it the multivariate general compound point process (MGCPP). We also prove limit theorems for the MGCPP and compared numerical simulations for the MGCPP with the MGCHP. The MGCHP model provides us with a perfect framework for the stock price dynamics in the LOB. It’s natural to apply it to other financial applications. We extend the MGCHP to the exponential MGCHP (EMGCHP) and consider the corresponding asset-liability management problem. Risky assets are molded by the EMGCHP while the liability follows a Brownian motion with drift. We derive the Hamilton–Jacobi–Bellman equation and transformed it into a system of PDEs. With the FCLT, we can approximate the EMGCHP to a geometric Brownian motion in the LOB and apply Xie et al.’s results. Numerical simulations for the Hawkes-based model and comparisons with the Poisson-based model are also provided. In the last part of the thesis, we give an option pricing formula under the EMGCHP framework. We believe our study can provide a strong tool for not only researchers but also traders in the high-frequency market.
- ItemOpen AccessOptimal Control of a Semi-Markov Limit Order Book(2017) Novak, Joshua; Swishchuk, Anatoliy; Ware, Antony; Choi, Kyoung JinA Limit Order Book (LOB) is a financial exchange that automatically matches the orders of buyers and sellers according to a predefined priority rule. As the popularity of Limit Order markets has increased, more attention has been paid to the optimal strategies for an agent who wishes to buy or sell an equity on the order book. In this thesis, we first introduce challenges of market microstructure and concepts of stochastic optimal control such as the Dynamic Programming Principle, the Hamilton-Jacobi-Bellman Equation, and tools such as the Feynman-Kac Formula. Then, we present Fodra and Pham's model for the optimal risk-neutral market making strategy in a limit order book that follows a Semi-Markov stochastic process, and use numerical techniques in MATLAB to apply the theory to real-word Limit Order data. Statistical techniques such as Maximum Likelihood Estimation, the Kolmogorov-Smirnov Test and Akaike Information Criterion are employed to distributions such as the Generalized Inverse Gaussian. Finally, we find the optimal risk-neutral strategy in an extension of the model when the price process contains a stochastic bid-ask spread following a Markov Chain.
- ItemOpen AccessProbabilistic Nonlinear Dimensionality Reduction(2022-11-04) Adams, Matthew; Rios, Cristian; Ware, Antony; Greenberg, MatthewHigh-dimensional datasets are present across scientific disciplines. In the analysis of such datasets, dimensionality reduction methods which provide clear interpretations of their model parameters are required. Principal components analysis (PCA) has long been a preferred method for linear dimensionality reduction, but is not recommended for data lying on or near low-dimensional nonlinear manifolds. On the other hand, neural networks have been used for dimension reduction but the associated model parameters have no clear interpretation. The main contribution of the current work is the introduction of probabilistic piecewise PCA, an interpretable model for approximating nonlinear manifolds embedded in high-dimensional space. Probabilistic piecewise PCA serves as a bridge between linear PCA and highly nonlinear neural network approaches to dimensionality reduction. Our model is an extension of probabilistic PCA and may be used when assuming any member of the natural exponential family of distributions on the observations. The model is explicitly defined for Gaussian and Poisson distributions, and posterior distributions for prediction and sampling are computed. A full comparative study of probabilistic piecewise PCA and existing dimensionality reduction methods is presented with a real-world bibliometric dataset.
- ItemOpen AccessSwaps in Energy Commodities Markets(2022-08) McGillivray, Joshua; Swishchuk, Anatoliy; Swishchuk, Anatoliy; Badescu, Alexandru; Ware, AntonyIn this paper, we discuss and value variance, volatility, covariance, and correlation swaps in the Vasicek, Schwartz one-factor, and Heston models using a continuous-time regime. The data used is primarily 2019 natural gas and crude oil futures closing prices due to the liquidity and size of the options market in the commodity energy sector. We derive approximations for covariance and correlation swap fair strikes in the Heston model following the continuous time regime, using the discrete regime for reference. We check the accuracy of our approximation using simulated error distributions of the calibrated parameters from the CIR component of the Heston model. We present the effect of varied parameters on the value of the fair strikes for covariance and correlation swaps. Finally, we evaluate the fair strikes of covariance and correlation swaps using three different approximations, yielding values and error bounds of dramatically varying sizes, demonstrating the limitations of the GARCH(1,1) calibration of the Heston model.
- ItemOpen AccessTheoretical and Computational Analysis and Comparison of Stochastic Models of Energy and Interest Rate Markets(2013-05-01) Bukharina, Tatiana; Ware, AntonyThe present work summarizes information about Interest Rate Market and Energy Market. A mathematical framework is the main aspect considered here. Different kinds of stochastic models are described for both markets. In addition, an introduction is given to a very interesting approach developed by Hinz et al. in 2005. The idea is in an application of interest rate market techniques to the energy market. Comparing this approach to the standard stochastic model we obtain the connection between two different sets of parameters. This significantly extends the possibilities of estimating the crucial parameters of the model. In the final chapter we explore two different ways of using Heath-Jarrow-Morton framework. Firstly, we estimate parameters of the model using a specific form of volatility function and sweet crude oil forward prices. Finally, we examine the general form of volatility function of natural gas forward prices. Then using Principal Component Analysis we obtain the main principal components which allow us to reproduce prices of forward contracts.