Browsing by Author "Badescu, Alexandru M."
Now showing 1 - 6 of 6
Results Per Page
Sort Options
Item Open Access Applications of Mean-reverting Processes in Alberta Energy Markets(2020-09-21) Lu, Weiliang; Swishchuk, Anatoliy V.; Goutte, Stéphane; Swishchuk, Anatoliy V.; Goutte, Stéphane; Qiu, Jinniao; Badescu, Alexandru M.This thesis introduce fuel-switching price, which designed for encouraging power plant companies to switch from coal to natural gas when they produce electricity and successfully applied on European market, to Albertan Market. Moreover, we consider a energy-switching price which consider power switch from natural gas to wind. We modeled these two prices using five mean reverting processes including Regime-switching processes, Lévy-driven Ornstein-Uhlenbeck process and Inhomogeneous Geometric Brownian Motion, and estimate them based on multiple procedures such as Maximum likelihood estimation and Expectation-Maximization algorithm. At last, this thesis prove previous result applied on Albertan Market that the jump modeling techniques is needed when modeling fuel-switching data. In addition, it not only give promising conclusion on the necessity of introducing Regime-switching models to the fuel-switching data, but also show that Regime-switching model is better fitted to the data.Item Open Access Difference population equation with the variable Allee effect and periodic carrying capacity(2018-08-09) Chugunova, Marina Alexandrovna; Bates, Larry M.; Badescu, Alexandru M.; Liao, Wenyuan; Chruchill, Richard C.The subject of this research is the location, stability, and the basin of attraction for the equilibrium points and periodic solutions for the Ricker equation enhanced with the mechanism for both weak and strong types of the Allee effect and periodic carrying capacity. The research has shown that just an addition of one biological phenomenon to Ricker equation, namely, the Allee effect, significantly changes the necessary conditions for the equilibrium point of the equation to obtain stability. This also increases the range of the parameters which allow for the equilibrium solution or a cycle to remain globally asymptotically stable. It was shown that the p-periodic carrying capacity always generates the p-periodic solutions which can be global attractors. Embedding the mechanism for the strong Allee effect generates several basins of attraction with either an equilibrium point or a stable cycle as an attractor. Concavity was proven not necessary for the attenuant property of the cycle.Item Open Access Market Power in Electricity Markets(2019-12) Chan, Erik; Ware, Antony Frank; Qiu, Jinniao; Badescu, Alexandru M.Electricity markets exhibit unique price dynamics not found elsewhere in other commodity markets. Characteristics such as limited storability, highly inelastic demand, and physical laws requiring continuous production to match consumption cause erratic price dynamics and short periods of extremely high prices known as spikes. We create a diffusion model under the assumption that a participating firm controls sufficient production capacity can significantly increase the spot price by bidding according to a strategy defined by a decision curve. We then extend Barlow's diffusion model to incorporate the decision curve and show results.Item Open Access Option Pricing Using Neural Networks(2019-08-30) Que, Danfeng; Badescu, Alexandru M.; Ware, Antony Frank; Swishchuk, Anatoliy V.Due to the properties of large transaction volumes, high innovation and positive promotion to the financial market development, options play an essential role. However, the flexible design of options leads to complicated pricing, which makes accurate option pricing a challenging task for a long time. In this paper, two types of neural networks - feed-forward networks such as the radial basis function (RBF), multilayer perceptron (MLP), Modular network and a recurrent deep learning network Long short-term memory (LSTM) - and three stochastic process pricing models (Black-Scholes-Merton model, Heston stochastic volatility model and Merton Jump-diffusion model) are proposed so as to predict European call option prices. Firstly, it generates simulated option prices data from three stochastic process models to test the effectiveness and approximation ability of the neural networks. Secondly, effective factors such as moneyness, time to maturity and greeks via the Black-Scholes-Merton formula are used as input variables for neural networks. Historical data of S&P 500 European option prices empirically analyzes validity and stability of the neural networks. The performance measures R2, statistical error of the root mean square error (RMSE), mean absolute error (MAE), and mean absolute percentage error (MAPE) are used to evaluate the performance of two types of pricing models. It shows that the MLP network with two hidden layers performs best. In addition, neural networks do outperform the pricing ability of stochastic process pricing models.Item Open Access Semi-Markov Switching Lévy Processes and their Applications in Finance(2020-07-23) Zhang, Yi (Ivy); Swishchuk, Anatoliy V.; Ambagaspitiya, Rohana S.; Badescu, Alexandru M.; Choi, Kyoungjin; Simard, ClarenceWe, as humans, learn from our mistakes. Ultimately, we progress and grow, both as an individual and as a society. After the catastrophic recession period due to the sub-prime mortgage crisis in 2007, researchers and mathematicians began to look for answers about the massive damages done by the crisis. These events suggested that there must be some other factors that had hidden and needed to be accounted for in the previous prevailing models of our financial markets. As many different explanations arose, the main focus was to find a way to account for these more significant crises with some economically interpretable assumptions. The existence of different states or regimes in our financial market is one of the most acceptable ideas so far, as we tend to notice that the market has been switching between cycles of booms and recessions. This idea has triggered many studies on regime-switching models, but mostly with Markov regimes, as they are mathematically simple and relatively easy to solve. However, some of the assumptions made behind the Markov switching models have been questionable and unrealistic. For instance, Markov regimes imply that each one of them can switch to any other state no matter how long we have stayed in the current state. This is deviating from what we would expect, as we usually observe that the likelihood of recovery has some correlation with the recession’s age; the longer we stay in a recession, the harder for the market to recover. Thus, the primary purpose of this thesis is to find a better model with a better explanation. The introduction of semi-Markov markets intuitively has a time-varying propensity of regime changes using the conditional intensity matrix. In general, the semi-Markov switching models should be more in line with our financial market and generate better results when simulating financial derivatives prices. In this thesis, we will start by introducing some related definitions and theorems first. We will develop a semi-martingale representation for both the discrete-time semi-Markov chains and continuous-time semi-Markov processes, with some examples and applications. Then, we will construct the theoretical framework of a stochastic model under a semi-Markov regime-switching process driven by Lévy processes. The first step is to derive its Itô’s formula, as we need it to find the semi-closed form formulas for the characteristic function of log prices. Then, we will be developing the risk-neutral measure specific to our semi-Markov switching models. As some of us may already know, the Lévy driven regime-switching markets are incomplete, which means that there is more than one risk-neutral measure when pricing financial derivatives. When pricing a European-style option, since we already have the semi-closed form of the characteristic function for log asset prices, it allows us to use a Fourier transform method, first derived by Carr and Madan, namely the Fractional Fast Fourier Transform (FRFT) algorithm to obtain the estimated option prices. When comparing with Markov switching models, estimations and simulations show that the semi-Markov model performs better. It also offers more insight into the dynamics of market regimes, providing us with a better explanation of where the financial market is headed to next.Item Open Access VIX-linked GMMB under affine GARCH models and its Diffusion Limits(2018-07-06) Chen, Yuyu; Badescu, Alexandru M.; Ware, Antony F.; Swishchuk, Anatoliy V.In variable annuity (VA) industry, to compensate for the liability coming from embedded riders in VA, insurer usually charge a fixed percentage of investment fund as the riders fee. However, the traditional fixed-fee structure would misalign insurer’s income and liability and in consequence cause risk management challenges for insurer. In 2013, the Chicago Board of Options Exchange (CBOE) suggests linking riders fee in variable annuity with VIX index in a white paper and shows that VIX-linked fee structure can help to re-align insurer’s income and liability using non-parametric models. Affine GARCH models are used in this work to analyze VIX-linked fee structure for VA with guarantee minimum maturity benefit (GMMB). A closed-form solution to GMMB has been derived and is used to determine a fair fee structure. Comparison between fixed-fee structure and VIX-linked fee structure has been been shown by numerical examples.