It is well established that stock market volatility has a memory of the past, moreover it is found that volatility correlations are long ranged. As a consequence, volatility cannot be characterized by a single correlation time in general. Recent empirical work suggests that the volatility correlation functions of various assets actually decay as a power law. Moreover it is well established that the distribution functions for the returns do not obey a Gaussian distribution, but follow more the type of distributions that incorporate what are commonly known as fat–tailed distributions. As a result, if one is to model the evolution of the stock price, stock market or any financial derivative, then standard Brownian motion models are inaccurate. One must take into account the results obtained from empirical studies and work with models that include realistic features observed on the market. In this thesis we show that it is possible to derive the path integral for a non-Gaussian option pricing model that can capture fat–tails. However we find that the path integral technique can only be used on a very small set of problems, as a number of situations of interest are shown to be intractable. / http://proxy.library.adelaide.edu.au/login?url= http://library.adelaide.edu.au/cgi-bin/Pwebrecon.cgi?BBID=1378473 / Thesis (Ph.D.) -- University of Adelaide, School of Electrical and Electronic Engineering, 2010

There is a growing number of applications of machine learning and deep learning in quantitative and computational finance. In this thesis, we focus on two of them. In the first application, we employ machine learning and deep learning in derivative pricing. The models considering jumps or stochastic volatility are more complicated than the Black-Merton-Scholes model and the derivatives under these models are harder to be priced. The traditional pricing methods are computationally intensive, so machine learning and deep learning are employed for fast pricing. I n Chapter 2, we propose a method for pricing American options under the variance gamma model. We develop a new fast and accurate approximation method inspired by the quadratic approximation to get rid of the time steps required in finite difference and simulation methods, while reducing the error by making use of a machine learning technique on pre-calculated quantities. We compare the performance of our method with those of the existing methods and show that this method is efficient and accurate for practical use. In Chapters 3 and 4, we propose unsupervised deep learning methods for option pricing under Lévy process and stochastic volatility respectively, with a special focus on barrier options in Chapter 4. The unsupervised deep learning approach employs a neural network as the candidate option surface and trains the neural network to satisfy certain equations. By matching the equation and the boundary conditions, the neural network would yield an accurate solution. Special structures called singular terms are added to the neural networks to deal with the non-smooth and discontinuous payoff at the strike and barrier levels so that the neural networks can replicate the asymptotic behaviors of options at short maturities. Unlike supervised learning, this approach does not require any labels. Once trained, the neural network solution yields fast and accurate option values. The second application focuses on financial time series simulation utilizing deep learning techniques. Simulation extends the limited real data for training and evaluation of trading strategies. It is challenging because of the complex statistical properties of the real financial data. In Chapter 5, we introduce two generative adversarial networks, which utilize the convolutional networks with attention and the transformers, for financial time series simulation. The networks learn the statistical properties in a data-driven manner and the attention mechanism helps to replicate the long-range dependencies. The proposed models are tested on the S&P 500 index and its option data, examined by scores based on the stylized facts and are compared with the pure convolutional network, i.e. QuantGAN. The attention-based networks not only reproduce the stylized facts, including heavy tails, autocorrelation and cross-correlation, but also smooth the autocorrelation of returns.

In the multifaceted landscape of financial markets, the understanding and application of data science methods are crucial for achieving robustness, fairness, and strategic advancement. This dissertation addresses these critical areas through three interconnected studies. The first study investigates the problem of data imbalance, with particular emphasis on financial applications such as credit risk assessment, where the prevalence of non-defaulting entities overshadows defaulting ones. Traditional classification models often falter under such imbalances, leading to biased predictions. By analyzing linear discriminant functions under conditions where one class's sample size grows indefinitely while the other remains fixed, this study reveals that certain parameters stabilize, providing robust predictions. This robustness ensures model reliability even in skewed data environments. The second study explores anomalies in option pricing, specifically the total positivity of order 2 (TP₂) in call options and the reverse sign rule of order 2 (RR₂) in put options within the S&P 500 index. By examining the empirical significance and occurrence patterns of these violations, the research identifies potential trading opportunities. The findings demonstrate that while these conditions are mostly satisfied, violations can be strategically exploited for consistent positive returns, providing practical insights into profitable trading strategies. The third study addresses the fairness of regulatory stress tests, which are crucial for assessing the capital adequacy of banks. The uniform application of stress test models across diverse banks raises concerns about fairness and accuracy. This study proposes a method to aggregate individual models into a common framework, balancing forecast accuracy and equitable treatment. The research demonstrates that estimating and discarding centered bank fixed effects leads to more reliable and fair stress test outcomes. The conclusions of these studies highlight the importance of understanding the behavior of commonly used models in handling imbalanced data, the strategic exploitation of option pricing anomalies for profitable trading, and the need for fair regulatory practices to ensure financial stability. Together, these findings contribute to a deeper understanding of data science in finance, offering practical insights for regulators, financial institutions, and traders.

Thesis (MSc)--Stellenbosch University, 2013. / ENGLISH ABSTRACT: We study Monte Carlo methods for pricing American options where the stock price dynamics follow exponential pure jump L évy models. Only stock price dynamics for a single underlying are considered. The thesis begins with a general introduction to American Monte Carlo methods. We then consider two classes of these methods. The fi rst class involves regression - we briefly consider the regression method of Tsitsiklis and Van Roy [2001] and analyse in detail the least squares Monte Carlo method of Longsta and Schwartz [2001]. The variance reduction techniques of Rasmussen [2005] applicable to the least squares Monte Carlo method, are also considered. The stochastic mesh method of Broadie and Glasserman [2004] falls into the second class we study. Furthermore, we consider the dual method, independently studied by Andersen and Broadie [2004], Rogers [2002] and Haugh and Kogan [March 2004] which generates a high bias estimate from a stopping rule. The rules we consider are estimates of the boundary between the continuation and exercise regions of the option. We analyse in detail how to obtain such an estimate in the least squares Monte Carlo and stochastic mesh methods. These models are implemented using both a pseudo-random number generator, and the preferred choice of a quasi-random number generator with bridge sampling. As a base case, these methods are implemented where the stock price process follows geometric Brownian motion. However the focus of the thesis is to implement the Monte Carlo methods for two pure jump L évy models, namely the variance gamma and the normal inverse Gaussian models. We first provide a broad discussion on some of the properties of L évy processes, followed by a study of the variance gamma model of Madan et al. [1998] and the normal inverse Gaussian model of Barndor -Nielsen [1995]. We also provide an implementation of a variation of the calibration procedure of Cont and Tankov [2004b] for these models. We conclude with an analysis of results obtained from pricing American options using these models. / AFRIKAANSE OPSOMMING: Ons bestudeer Monte Carlo metodes wat Amerikaanse opsies, waar die aandeleprys dinamika die patroon van die eksponensiële suiwer sprong L évy modelle volg, prys. Ons neem slegs aandeleprys dinamika vir 'n enkele aandeel in ag. Die tesis begin met 'n algemene inleiding tot Amerikaanse Monte Carlo metodes. Daarna bestudeer ons twee klasse metodes. Die eerste behels regressie - ons bestudeer die regressiemetode van Tsitsiklis and Van Roy [2001] vlugtig en analiseer die least squares Monte Carlo metode van Longsta and Schwartz [2001] in detail. Ons gee ook aandag aan die variansie reduksie tegnieke van Rasmussen [2005] wat van toepassing is op die least squares Monte Carlo metodes. Die stochastic mesh metode van Broadie and Glasserman [2004] val in die tweede klas wat ons onder oë neem. Ons sal ook aandag gee aan die dual metode, wat 'n hoë bias skatting van 'n stop reël skep, en afsonderlik deur Andersen and Broadie [2004], Rogers [2002] and Haugh and Kogan [March 2004] bestudeer is. Die reëls wat ons bestudeer is skattings van die grense tussen die voortsettings- en oefenareas van die opsie. Ons analiseer in detail hoe om so 'n benadering in die least squares Monte Carlo en stochastic mesh metodes te verkry. Hierdie modelle word geï mplementeer deur beide die pseudo kansgetalgenerator en die verkose beste quasi kansgetalgenerator met brug steekproefneming te gebruik. As 'n basisgeval word hierdie metodes geï mplimenteer wanneer die aandeleprysproses 'n geometriese Browniese beweging volg. Die fokus van die tesis is om die Monte Carlo metodes vir twee suiwer sprong L évy modelle, naamlik die variance gamma en die normal inverse Gaussian modelle, te implimenteer. Eers bespreek ons in breë trekke sommige van die eienskappe van L évy prossesse en vervolgens bestudeer ons die variance gamma model soos in Madan et al. [1998] en die normal inverse Gaussian model soos in Barndor -Nielsen [1995]. Ons gee ook 'n implimentering van 'n variasie van die kalibreringsprosedure deur Cont and Tankov [2004b] vir hierdie modelle. Ons sluit af met die resultate wat verkry is, deur Amerikaanse opsies met behulp van hierdie modelle te prys.

Thesis (MBA)--Stellenbosch University, 2000. / ENGLISH ABSTRACT: The price earnings multiple is a ratio of valuation and is published widely in the media as a comparative instrument of investment decisions. It is used to compare company valuation levels and their future growth/franchise opportunities. There have been numerous research studies done on the price earnings multiple, but no study has been able to design or derive a model to successfully predict the future price earnings multiple where the current stock price and following year-end earnings per share is used. The most widely accepted method of share valuation is to discount the future cash flows by an appropriate discount rate. Popular and widely used stock valuation models are the Dividend Discount Model and the Gordon Model. Both these models assume that future dividends are cash flows to the shareholder. Thomas K. Philips, the chief investment officer at Paradigm Asset Management in New York, constructed a valuation model at the end of 1999, which he published in The Journal of Portfolio Management. The model (Philips price earnings multiple model) was derived from the Dividend Discount Model and calculates an implied future price earnings multiple. The Philips price earnings multiple model includes the following independent variables: the cost of equity, the return on equity and the dividend payout ratio. Each variable in the Philips price earnings multiple model is a calculated present year-end point value, which was used to calculate the implied future price earnings multiple (present year stock price divided by following year-end earnings per share). This study used a historical five year (1995-2000) year-end data to calculate the implied and actual future price earnings multiple. Out of 225, Johannesburg Stock Exchange listed companies studied, only 36 were able to meet the criteria of the Philips price earnings multiple model. Correlation and population mean tests were conducted on the implied and constructed data sets. It proved that the Philips price earnings multiple model was unsuccesful in predicting the future price earnings multiple, at a statistical 0,20 level of significance. The Philips price earnings multiple model is substantially more complex than the Discount Dividend Model and includes greater restrictions and more assumptions. The Philips price earnings multiple model is a theoretical instrument which can be used to analyse hypothetical (with all model assumptions and restrictions having been met) companies. The Philips price earnings multiple model thus has little to no applicability in the practical valuation of stock price on Johannesburg Stock Exchange listed companies. / AFRIKAANSE OPSOMMING: Die prysverdienste verhouding is 'n waarde bepalingsverhouding en word geredelik gepubliseer in die media. Hierdie verhouding is 'n maatstaf om maatskappye se waarde vlakke te vergelyk en om toekomstige groei geleenthede te evalueer. Daar was al verskeie navorsingstudies gewy aan die prysverdiensteverhouding, maar nog geen model is ontwikkel wat die toekomstige prysverdiensteverhouding (die teenswoordige aandeelprys en toekomstige jaareind verdienste per aandeel) suksesvol kon modelleer nie. Die mees aanvaarbare metode vir waardebepaling van aandele is om toekomstige kontantvloeie te verdiskonteer teen 'n toepaslike verdiskonteringskoers. Van die vernaamste en mees gebruikte waardeberamings modelle is die Dividend Groei Model en die Gordon Model. Beide modelle gebruik die toekomstige dividendstroom as die toekomstige kontantvloeie wat uitbetaal word aan die aandeelhouers. Thomas K. Philips, die hoof beleggingsbeampte by Paradigm Asset Management in New York, het 'n waardeberamingsmodel ontwerp in 1999. Die model (Philips prysverdienste verhoudingsmodei) was afgelei vanaf die Dividend Groei Model en word gebruik om 'n geïmpliseerde toekomstige prysverdiensteverhouding te bereken. Die Philips prysverdienste verhoudingsmodel sluit die volgende onafhanklike veranderlikes in: die koste van kapitaal, die opbrengs op aandeelhouding en die uitbetalingsverhouding. Elke veranderlike in hierdie model is 'n berekende teenswoordige jaareinde puntwaarde, wat gebruik was om die toekomstige geïmpliseerde prysverdiensteverhouding (teenswoordige jaar aandeelprys gedeel deur die toekomstige verdienste per aandeel) te bereken. In hierdie studie word vyf jaar historiese jaareind besonderhede gebruik om die geïmpliseerde en werklike toekomstige prysverdiensteverhouding te bereken. Van die 225 Johannesburg Effektebeurs genoteerde maatskappye, is slegs 36 gebruik wat aan die vereistes voldoen om die Philips prysverdienste verhoudingsmodel te toets. Korrelasie en populasie gemiddelde statistiese toetse is op die berekende en geïmpliseerde data stelle uitgevoer en gevind dat die Philips prysverdienste verhoudingsmodel, teen 'n statistiese 0,20 vlak van beduidenheid, onsuksesvol was om die toekomstige prysverdiensteverhouding vooruit te skat. Die Philips prysverdienste verhoudingsmodel is meer kompleks as die Dividend Groei Model met meer aannames en beperkings. Die Philips prysverdienste verhoudingsmodel is 'n teoretiese instrument wat gebruik kan word om hipotetiese (alle model aannames en voorwaardes is nagekom) maatskappye te ontleed. Dus het die Philips prysverdienste verhoudingsmodel min tot geen praktiese toepassingsvermoë in die werkilke waardasie van aandele nie.

Thesis (MBA (Business Management))--Stellenbosch University, 2008. / ENGLISH ABSTRACT: This research report investigated whether evidence of volatility clustering exists on the FTSE/JSE Top 40 Index. The presence of volatility clustering has practical implications relating to market decisions as well as the accurate measurement and reliable forecasting of volatility. This research report was conducted as an in-depth analysis of volatility, measured over five different return interval sizes covering the sample in non-overlapping periods. Each of the return interval sizes' volatility were analysed to reveal the distributional characteristics and if it violated the normality assumption. The volatility was also analysed to identify in which way, if any, subsequent periods are correlated. For each of the interval sizes one-step-ahead volatility forecasting was conducted using Linear Regression, Exponential Smoothing, GARCH(1,1) and EGARCH(1,1) models. The results were analysed using appropriate criteria to determine which of the forecasting models were more powerful. The forecasting models range from very simple to very complex, the rationale for this was to determine if more complex models outperform simpler models. The analysis showed that there was sufficient evidence to conclude that there was volatility clustering on the FTSE/JSE Top 40 Index. It further showed that more complex models such as the GARCH(1,1) and EGARCH(1,1) only marginally outperformed less complex models, and does not offer any real benefit over simpler models such as Linear Regression. This can be ascribed to the mean reversion effect of volatility and gives further insight into the volatility structure over the sample period. / AFRIKAANSE OPSOMMING: Die navorsingsverslag ondersoek die FTSE/JSE Top 40 Indeks om te bepaal of daar genoegsame bewyse is dat volatiliteitsbondeling teenwoordig is. Die teenwoordigheid van volatiliteitsbondeling het praktiese implikasies vir besluite in finansiele markte en akkurate en betroubare volatiliteitsvooruitskattings. Die verslag doen 'n diepgaande ontleding van volatiliteit, gemeet oor vyf verskillende opbrengs interval groottes wat die die steekproef dek in nie-oorvleuelende periodes. Elk van die opbrengs interval groottes se volatiliteitsverdelings word ontleed om te bepaal of dit verskil van die normaalverdeling. Die volatiliteit van die intervalle word ook ondersoek om te bepaal tot watter mate, indien enige, opeenvolgende waarnemings gekorreleer is. Vir elk van die interval groottes word 'n een-stap-vooruit vooruitskatting gedoen van volatiliteit. Dit word gedoen deur middel van Lineêre Regressie, Eksponensiële Gladstryking, GARCH(1,1) en die EGARCH(1,1) modelle. Die resultate word ontleed deur middel van erkende kriteria om te bepaal watter model die beste vooruitskattings lewer. Die modelle strek van baie eenvoudig tot baie kompleks, die rasionaal is om te bepaal of meer komplekse modelle beter resultate lewer as eenvoudiger modelle. Die ontleding toon dat daar genoegsame bewyse is om tot die gevolgtrekking te kom dat daar volatiliteitsbondeling is op die FTSE/JSE Top 40 Indeks. Dit toon verder dat meer komplekse vooruitskattingsmodelle soos die GARCH(1,1) en die EGARCH(1,1) slegs marginaal beter presteer het as die eenvoudiger vooruitskattingsmodelle en nie enige werklike voordeel soos Lineêre Regressie bied nie. Dit kan toegeskryf word aan die neiging van volatiliteit am terug te keer tot die gemiddelde, wat verdere insig lewer oor volatiliteit gedurende die steekproef.

Tam Chun Yu. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2002. / Includes bibliographical references (leaves 141-147). / Abstracts in English and Chinese. / Abstract --- p.I / Acknowledgements --- p.III / Table of Contents --- p.IV / List of Tables --- p.V / List of Figures --- p.VI / Chapter Chapter 1. --- Introduction --- p.1 / Chapter Chapter 2. --- Literature Review --- p.5 / Chapter 2.1 --- Real Estate Literature --- p.5 / Chapter 2.2 --- Financial Literature --- p.6 / Chapter 2.3 --- Impulse Response --- p.10 / Chapter Chapter 3. --- Methodology --- p.12 / Chapter 3.1 --- Augmented Dickey Fuller Test --- p.12 / Chapter 3.2 --- GARCH Model --- p.14 / Chapter 3.3 --- VAR Model --- p.16 / Chapter Chapter 4. --- Data Description --- p.18 / Chapter Chapter 5. --- Empirical Results --- p.20 / Chapter 5.1 --- Overview for the Data Set --- p.21 / Chapter 5.2 --- ADF Test --- p.22 / Chapter 5.3 --- GARCH Model --- p.22 / Chapter 5.4 --- VAR Model --- p.24 / Chapter 5.5 --- Impulse Response (IR) --- p.34 / Chapter Chapter 6. --- Conclusion --- p.38 / Appendix 1. Variable Definition --- p.41 / Appendix 2. Tables --- p.44 / Appendix 3. Figures --- p.61 / Appendix 4. Comparison of IR for different model in full sample case --- p.93 / Appendix 5. Comparison of IR for different model in first sub period --- p.109 / Appendix 6. Comparison of IR for different model in second sub period --- p.125 / Bibliography --- p.141

Although idiosyncratic return volatility has been used in a number of studies to capture the informativeness of stock prices, the relation between the two is still under controversy. Researchers raise more questions about the existence of such a relation in emerging markets since the efficient market hypothesis (EMH) may not sustain in these markets. Therefore, use idiosyncratic return volatility estimated from the common asset pricing models as a measure of stock price informativeness becomes questionable. The first part of this thesis serves to validate the use of idiosyncratic return volatility as a stock price informativeness measure in the China settings. In particular, using a battery of information flow proxies, I empirically test the relation between stock price informativeness and idiosyncratic return volatility; the empirical evidence supports the existence of such a relation. However, there exists an inverse U-shape relation between firm-specific information and idiosyncratic return volatility. Therefore, in the second essay, when using idiosyncratic return volatility as a measure of informativeness of stock prices, I truncate the sample as Morek et al. (2000) do in their study. / From an institutional perspective, my dissertation attempts to explain why firms operating in emerging markets such as China have inferior information environments. The main theme of this thesis is to provide firm-level evidence that the institutional settings in China change firms' incentives to provide firm-specific information to the stock market and thus impair the information environments and lower the idiosyncratic return volatilities of these firms. / Keywords: Institutions; information environments; performance hiding / The second part of this thesis addresses the research question on how firms' information environments are shaped by a country's institutions. Morek et al. (2000) document that more developed countries usually have better information environments, and vice versa. The authors offer an "institutional explanation" that attributes the poor information environments in emerging markets to the lack of property rights protections in these markets. However, previous literature provides only limited evidences on how institutions affect the supply of firm-specific information to the market. Hence, this paper uses China as case to investigate how extensive government interventions in China generate incentives for firms to hide their information. I find that, first, excessive local government in a region increases firms' incentives to hide their true performance, after controlling for firm characteristics. A further analysis shows that the directions of firms' hiding activities vary across firms and are contingent on the nature of the firms' ultimate owners, because of different political pressures exerted. In particular, I find that family firms are more likely to suppress good news to avoid governments' "grabbing hands", while State-owned Enterprises (SOEs) are more likely to hide their bad performances to protect local governments' image from being damaged. Second, firms' hiding activities do impair firms' information environment, resulting in lower idiosyncratic stock return volatilities. To strengthen this argument, I test the "information link" between firms' hiding activities and their information environments. I find that firms' incentives to hide their performances reduce market participants' motives to acquire private information, evident by fewer analyst following. Moreover, my results show that involvement of information intermediaries alleviates the negative effects of firms' hiding activities on the information environments. / pt. 1. Information environments in China: availability of firm-specific information to the capital market -- pt. 2. Government intervention, firms' hiding activities and information environments: evidence from China. / Lin, Jingrong. / Adviser: T. J. Wong. / Source: Dissertation Abstracts International, Volume: 73-04, Section: A, page: . / Thesis (Ph.D.)--Chinese University of Hong Kong, 2011. / Includes bibliographical references. / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [201-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstract also in Chinese.

This study investigates whether earnings components are correctly priced by the Chinese investors. Under the Chinese GAAP, total earnings can be easily decomposed into core earnings and non-core earnings. Core earnings are more persistent than non-core earnings and cash flows from operations are more persistent than accruals, as expected. However, the market underestimates (overestimates) the value implications of current core (non-core) earnings for future earnings. Furthermore, the market overprices (underprices) accruals (cash flows from operations). Therefore, future returns adjusted for risk factors identified in this study are predictable by the information contained in the components of current earnings. Both the portfolio tests and regression analysis generate economically significant abnormal returns that are robust to sensitivity checks. Further analysis suggests that there is no significant difference in the extent of mispricing across firms with different characteristics such as transaction costs, arbitrage risks, investor sophistication, or firm size. This could be due to the measurement errors in the proxy variables for these characteristics. / Wu Donghui. / "July 2003." / Advisers: In-Mu Haw; James Xie. / Source: Dissertation Abstracts International, Volume: 64-07, Section: A, page: 2551. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2003. / Includes bibliographical references (p. 121-130). / Available also through the Internet via Current research @ Chinese University of Hong Kong under title: Mispricings of earnings components empirical evidence from China. / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. Ann Arbor, MI : ProQuest dissertations and theses, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. Ann Arbor, MI : ProQuest Information and Learning Company, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstracts in English and Chinese. / School code: 1307.

University of Macau / Faculty of Science and Technology / Department of Mathematics