The main objective of this thesis is to examine the dependency structure among different agricultural and energy commodity markets in the United States. For achieving this goal, the paper makes use of the Copula-GARCH(1,1) model to study the financial return volatility and the co-movement between pair of commodities including corn, soybean and gasoline over the pre-COVID 19 pandemic period (from 01-01-2018 to 01-01-2020) and the ongoing COVID 19 pandemic period (from 01-01-2020 to 01-04-2021). First, the study has shown that the time-dependent volatilities of commodity returns display volatility clustering effect in the two periods and the volatility of volatility of commodity markets is higher during the pandemic period. Second, it is observed that the correlations among different commodities have increased significantly in the ongoing pandemic period and we also find that the strongest co-movement is between returns of corn and soybean over the two periods. Finally, the results suggest that the (extreme) co-movements between agricultural commodities (corn and soybean) are governed by symmetry; that is they tend to boom and crash together during extreme shocks or events. On the other hand, the (extreme) co-movements between an agricultural commodity (corn or soybean) and the energy commodity (gas) appear to co-move asymmetrically and they tend to experience the market crash together but not the market boom.

Volatility managing strategies have gained attention over the last few years due to theiralleged ability to increase portfolio return and mitigate risk. This thesis examines the performance and risk of a portfolio using such a strategy on the Swedish equity market. The strategy is dependent on the forecasting of volatility. Different volatility forecasting models are evaluated using different refitting intervals. The GARCH(1,1) model using a monthly refitting interval is found to be the most precise. When comparing it to the buy-and-hold portfolio, the results of the risk and return of the portfolio are ambiguous and the volatility managing strategy is only found to be beneficial when using a fixed volatility target when transaction costs are accounted for. Regarding distributional characteristics, the volatility managing strategy displays features of a lighter-tailed distribution in comparison to the buy-and-hold portfolio when using a dynamic volatility target. However, for the fixed target, the distributional characteristics are incoherent. Lastly, the volatility managing strategy is not found beneficial to the investor during a shorter period of high volatility. This thesis provides support for using a volatility managing strategy with a fixed volatility target for generating a higher return compared to the benchmark. However, it does not support conclusive evidence for obtaining a higher return without increasing the risk level of the investment. / Användningen av volatilitetshanterande strategier har fått ökad uppmärksamhet under de senaste åren. Därför undersöker detta arbete avkastningen och risken hos en portfölj som använder en sådan strategi på den svenska aktiemarknaden. Investeringsstrategin är baserad på prognosen av volatilitet. Olika modeller för volatilitetsprediktion utvärderas för olika tidsintervall för att hitta modellen med högst precision. Denna studie finner att en GARCH(1,1) modell som omanpassar sig månadsvis resulterar i den mest exakta prediktionen. Med hänsyn till risk och avkastning så är resultaten för volatilitetsstrategin tvetydiga i jämförelse med en köp-och-behåll strategi. Volatilitetsstrategin är endast fördelaktig när ett fast volatilitetsmål används då transaktionskostnader inkorporeras. Med avseende på fördelningsegenskaper, så visar en volatilitetsstrategi med ett rörligt volatilitetsmål på egenskaper hos en fördelning med lättare svansar, i jämförelse med köp-och-behåll portföljen. För det fasta volatilitetsmålet så är fördelningsegenskaperna inkoherenta. Volatilitetsstrategin är inte fördelaktig för investeraren under en kortare period med hög volatilitet. Detta examensarbete ger underlag för användandet av en volatilitetshanterande strategi med ett fast volatilitetsmål för att uppnå en högre avkastning i relation till referensportföljen. Det bevisar dock inte att en högre avkastning går att uppnå utan att öka risken hos portföljen.

Time series forecasting and volatility forecasting is a particularly active research field within financial mathematics. More recent studies extend well-established forecasting methods with machine learning. This thesis will evaluate and compare the standard Generalized Autoregressive Conditional Heteroskedasticity (GARCH) model and some of its extensions to a proposed Long Short-Term Memory (LSTM) model on historic data from five Swedish stocks. It will also explore hybrid models that combine the two techniques to increase prediction accuracy over longer horizons. The results show that the predictability increases when switching from univariate GARCH and LSTM models to hybrid models combining them both. Combining GARCH, Glosten, Jagannathan, and Runkle GARCH (GJR-GARCH), and Fractionally Integrated GARCH (FIGARCH) yields the most accurate result with regards to mean absolute error and mean square error. The forecasting errors decreased with 10 to 50 percent using the hybrid models. Comparing standard GARCH to the hybrid models, the biggest gains were seen at the longest horizon, while comparing the LSTM to the hybrid models, the biggest gains were seen for the shorter horizons. In conclusion, the prediction ability increases using the hybrid models compared to the regular models. / Tidsserieprognostisering, och volatilitetsprognostiering i synnerhet, är ett växande fält inom finansiell matamatik som kontinereligt står inför implementation av nya tekniker. Det som en gång startade med klassiksa tidsseriemodeller som ARCH har nu utvecklats till att dra fördel av maskininlärning och neurala nätverk. Detta examensarbetet uvärderar och jämför Generalized Autoregressive Conditional Heteroskedasticity (GARCH) modeller och några av dess vidare tillämpningar med Long Short-Term Memory (LSTM) modeller på fem svenska aktier. ARbetet kommer även gå närmare inpå hybridmodeller som kombinerar dessa två tekniker för att öka tillförlitlig prognostisering under längre tidshorisonter. Resultaten visar att förutsägbarheten ökar genom att byta envariata GARCH och LSTM modeller till hybridmodeller som kombinerar båda delarna. De mest korrekta resultaten kom från att kombinera GARCH, Glosten, Jagannathan, och Runkle GARCH (GJR-GARCH) och Fractionally Integrated GARCH (FIGARCH) modeller med ett LSTM nätverk. Prognostiseringsfelen minskade med 10 till 50 procent med hybridmodellerna. Specifikt, vid jämförelse av GARCH modellerna till hybridmodellerna sågs de största förbättringarna för de längre tidshorisonterna, medans jämförelse mellan LSTM och hybridmodellerna sågs den mesta förbättringen hos de kortare tidshorisonterna. Sammanfattningsvis öker prognostiseringsförmågan genom användning av hybridmodeller i jämförelse med standardmodellerna.

Numerous studies have documented the existence of nonlinearity within various financial time series. But how important of a finding is this? This dissertation examines this issue from a number of perspectives. First, is the nonlinearity that has been found a statistical anomaly that is isolated to a few of the more widely known financial time series or is nonlinearity a statistical regularity inherent in such series? Second, even if nonlinearity is pervasive, does this finding have any practical relevance for finance practitioners or academics? Using the relatively financially isolated but nonetheless well-traded Taiwan Stock Exchange as a case study, it is found that virtually all of the stocks trading on this exchange exhibit nonlinearity. The pervasiveness of nonlinearity within this market, combined with earlier results from other markets, suggests that nonlinearity is an inherent aspect of financial time series. Furthermore, closer examination of the time-paths of various measures of this nonlinearity via both windowed testing and recursive testing and parameter estimation reveals an additional complication, the possibility of nonstationarity. The serial dependency structures, especially for the nonlinear dependencies, do not appear to be constant, but instead appear to exhibit a number of brief episodes of extremely strong dependencies, followed by longer stretches of relatively quiet behavior. On average, though, these nonlinearities appear with sufficient strength to be significant for the full sample. Continuing on to examine the relevance of such nonlinearities for empirical work in finance, a variety of conditionally heteroskedastic models were fit to the returns for a subsample Taiwanese stocks, the Taiwanese stock index, and stock indices for other stock markets, including New York, London, Tokyo, Hong Kong, and Singapore. In a majority of cases, such models appear to be successful at filtering out the extant nonlinearity from these series of returns; however, a variety of indicators suggest that these models are not statistically well-specified for these returns, calling into question the inferences obtained from these models. Furthermore, a comparison of the various conditionally heteroskedastic models with each other and with a dynamic linear regression model reveals that, for many of the data series, the inferences obtained from these models regarding the day-of-the-week effect and the extant autocorrelation within the data varied from model to model. This finding suggests the importance of adequately accounting for nonlinear serial dependencies (and of ensuring data stationarity) when studying financial time series, even when other empirical aspects of the data are the focus of attention. / Ph. D.

One basic assumption of the celebrated Black-Scholes-Merton PDE model for pricing derivatives is that the volatility is a constant. However, the implied volatility plot based on real data is not constant, but curved exhibiting patterns of volatility skews or smiles. Since the volatility is not observable, various stochastic volatility models have been proposed to overcome the problem of non-constant volatility. Although these methods are fairly successful in modeling volatilities, they still rely on the implied volatility approach for model implementation. To avoid such circular reasoning, we propose a new class of stochastic volatility models based on directly observable volatility proxies and derive the corresponding option pricing formulas. In addition, we propose a new GARCH (1,1) model, and show that this discrete-time stochastic volatility process converges weakly to Heston's continuous-time stochastic volatility model. Some Monte Carlo simulations and real data analysis are also conducted to demonstrate the performance of our methods.

Romaine lettuce and leafy greens have been at the center of food safety concerns over the last several years. More specifically, romaine lettuce has been directly linked to seven(7) foodborne illness outbreaks and resulted in five(5) recalls over the eight(8) years period of January 1, 2012, to December 31, 2019. This paper estimates the effects that these food safety events have had on the price returns of romaine lettuce utilizing a series of Generalized Autoregressive Conditional Heteroskedasticity (GARCH) models. Importantly, the GARCH models allowed us to capture the effects of the recall and illness outbreaks on both the returns and volatility of the romaine price series. We find that three (3) of the seven (7) illness outbreaks resulted in marked increases in the price returns - between 4.1% and 9.6%. Conversely, three (3) of the five (5) recalls reduced price returns - between 30% and 57%. However, the volatility is not found to be significantly nor to affect the price volatility significantly. We conclude that recalls serve as a market correction in the romaine lettuce market. Consequently, a continued focus on increasing traceability with in the romaine lettuce market will help to reduce price fluctuation and limit the number of illnesses resulting from outbreaks. / Master of Science / Romaine lettuce and leafy greens have been at the center of food safety concerns over the last several years. More specifically, romaine lettuce has been directly linked to 7 foodborne illness outbreaks and resulted in 5 recalls over the eight years, January 1, 2012, to December 31, 2019. This paper estimates the effects that these food safety events have had on the price returns of romaine lettuce. It was found that 3 of the seven illness outbreaks resulted in marked increases in the price returns - between 4.1% and 9.6% while, 3 of the 5 recalls reduced price returns - between 30% and 57%. However, the volatility is not found to be significantly nor to affect the price volatility significantly. It is concluded that recalls serve as a market correction in the romaine lettuce market. A continued focus on increasing traceability with in the romaine lettuce market will help to reduce price fluctuation and limit the number of illnesses resulting from outbreaks.

本研究目的在於探討韓國、巴西與俄羅斯等實施外匯管制的國家，其上市本國貨幣匯率期貨對該國外匯市場之影響。及小型開放經濟的紐西蘭，在CME上市的美元/紐幣匯率期貨後，對該國外匯市場之影響。以加入虛擬變數單變量GARCH模型探討匯率期貨成立期間對匯率現貨的波動性是否會產生影響；以雙變量GARCH模型探討匯率期貨波動是否會對匯率現貨波動造成影響。 研究期間乃以各國引入匯率期貨契約的基準日之下，前後各兩年的匯率日報酬率資料。實證結果顯示： 一、韓國、巴西與俄羅斯，其開放匯率期貨交易後反而會降地現貨市場的波動，但小型開放經濟的紐西蘭，在CME上市的美元/紐幣匯率期貨後，會增加現貨市場的波動。 二、以上四個國家其外匯現貨市場的波動並不會受外匯期貨市場波動的影響。 / The objective of this study is to evaluate the impact upon foreign exchange markets for exchange control countries as Korea, Brazil, and Russia when foreign exchange futures was introduced, and small-scale open economy as New Zealand when foreign exchange futures was introduced in CME. This study was an application of univariate and bivariate GARCH models to investigate the effect of foreign exchange futures trading and volatility on spot market volatility. This study utilized the daily foreign exchange rate return series based on foreign exchange futures introduced with the former and latter two years. The empirical results are as follows: 1. The spot volatility decreases significantly after foreign exchange futures trading in Korea, Brazil, and Russia. The spot volatility increases significantly after foreign exchange futures trading in New Zealand. 2. The futures volatility does not affect the spot volatility in Korea, Brazil, Russia, and New Zealand.

本文以次貸風暴期間英國金融服務管理局的限制放空政策為研究對象，探討該政策對股票報酬率、股票波動度之影響。本研究將研究期間分為限制放空期間、允許放空期間，並將英國金融服務管理局公布的限制放空名單劃分為銀行業、財務顧問業、壽險業、產險業，利用GJR模型分析限制放空政策對不同產業影響的差異性。 實證結果證明，除少數銀行類股在限制放空期間的股價報酬率顯著低於允許放空期間，大部分限制放空個股的報酬率在兩期間並無顯著差異，然而限制放空期間幾乎所有研究樣本的股票波動度卻顯著提高。顯見政府限制放空政策不一定能有效抑制股價跌幅，卻會加劇股票波動性，加劇市場震盪。 / UK’s Financial Service Authority banned short selling on financial stocks during subprime crisis. This paper investigates the effects of short-selling restrictions on stocks’ return and volatility in the United Kingdom. After dividing the sample period into banned and no-banned period and classifying the samples into banking, financial consulting, life insurance and nonlife insurance industries, we explore the impact of short-selling restrictions using GJR-GARCH models on individual firms in different industries. We find that stock returns of most samples in the short-selling banned period are not significantly different from the ones in the no-banned period except for a few stocks in the banking industry. However, we also find that stock volatility is significantly higher in short-selling banned period for most samples. Our results show that short-selling restrictions imposed by the U.K. government have only limited effects on stock return, but have significantly alleviated stock volatility.

Black-Litterman är en allokeringsmodell som gör det möjligt att förena historiska avkastningar med personliga övertygelser om framtida avkastningar från en enskild investerare. Denna studie jämför två kvantitativa metoder i framtagande av felskattningen för framtida prognoser i syfte att kunna minska Black-Littermans subjektivitet. Tidigare litteratur har testat dessa metoder enskilt men aldrig ställt dem mot varandra. De metoder som undersöks använder varianser proportionella mot varianser i marknadsjämvikten, samt varianser från residualer i en faktormodel. Resultatet visar att tillämpandet av varianser framtagna av en GARCH (1,1)-modell är den metod som genererar högst avkastning, samt ger upphov till en fördelning av tillgångar som bidrar till lägst marknadskänslighet. Utifrån denna studie rekommenderas därmed tillämpningen av varianser från residualer i en faktormodel som tillägg för att minska modellens godtycklighet. / The Black-Litterman allocation model unifies historical returns with investor personal views of future returns. The study compares two quantitative methods for the estimation of uncertainty in future views with the goal to mitigate the subjectivity of the Black-Litterman model. Previous literature have investigated and tested these methods independently but a comparison has never been made between them. The two methods consist of using variances in proportion to the variances of market equilibrium and operating the residual variance of a factor model. Results show that the usage of variances estimated by a GARCH (1,1) will generate the highest average returns with an allocation distribution that contributes to least market sensitivity. Furthermore, the study recommends the implementation of variances from residuals with the addition of a factor model to diminish the subjectivity of the Black-Litterman model.

Cette thèse de doctorat est composée de trois chapitres, un article et deux papiers et est principalement liée au domaine de l’économétrie financière empirique. Elle analyse la dépendance et le lien entre les marchés financiers et les marchés de matières premières, en particulier celui de l’énergie. Les distributions et corrélations des variables appartenant aux deux marchés sont étudiées afin de déterminer leurs effets les uns sur les autres et d’analyser leurs tendances pour donner un meilleur aperçu de leurs comportements vis-à-vis des crises et des événements brusques en économie. Ces variables sont représentées par certains indices financiers (SP500, Euro stoxx 50, Msci China) ainsi que par les principaux indices de matières premières (SP GSCI, Brent Oil,Gaz naturel, Metaux precieux). Nous choisissons de modéliser leur corrélation dans le temps et de prendre en compte la non-linéarité et l’instabilité qui peuvent les affecter. Pour cela, l’approche fonction copule a été employée pour modéliser d’une manière efficace leurs distributions. Dans le premier chapitre, nous examinons la dépendance et les co-mouvements entre les prix des émissions de dioxyde de carbone et les indices énergétiques comme le charbon, le gaz naturel, le Brent oil et l’indice énergétique global. Le deuxième chapitre analyse les interactions et relations entre le marché pétrolier et deux principaux marchés financiers en Europe et aux États-Unis représentés par l’Euro stoxx 50 et le SP500. Dans le dernier chapitre, on analyse la dépendance multivariée entre les indices de matière première de différents secteurs avec des indices financiers en utilisant le modèle de la copule Regular Vine. / This Ph.D. thesis is composed by three chapters and is mainly related to theempirical financial econometrics field. It analysis the dependence and correlationbetween the financial markets and the commodity markets specially energy.Variables from both markets are studied to determine their effects on each othersand to analyse their trends to giva a better insight to their co-movements.These variables are represented by some of the major equities (SP500, Eurostoxx 50, Msci China) as well as major commodities indices (SP GSCI commodity,Brent Oil, Natural Gas, Precious metals). We choose to model theircorrelation dynamically and take into account any non-linearity and stylisedfacts into the nature of their dependencies. For that, the copula approach wasused to model efficiently the correlated joint distributions of the studied variables.In the first paper, we examine the dependence and co-movements between theprices of the carbon dioxide emissions and energy commodities (coal, naturalgas, Brent oil and SP GSCI energy index). The dependence between thereturns was modeled by a particular class of dynamic copula, the StochasticAutoregressive Copula (SCAR). The second chapter analysis the interactions and co-movements between the oilmarket and two major stock markets in Europe and the US (the Euro stoxx 50and the SP500). Both the dynamic and the markov (regime switching) copulawere chosen to better understand the link between the two. In The last paper, I study the multivariate dependence between commoditiesfrom different sectors with some major equities using the Regular Vine copula model.