This thesis project is an experimental study on how to approach quantitative portfolio credit risk modelling in Venture Debt portfolios. Facing a lack of applicable default data from ArK and publicly available sets, as well as seeking to capture companies that fail to service debt obligations before defaulting per se, we present an approach to risk modeling based on trends in revenue. The main framework revolves around driving a Monte Carlo simulation with Copluas to predict future revenue scenarios across a portfolio of early-stage technology companies. Three models for a random Gaussian walk, a Linear Dynamic System and an Autoregressive Integrated Moving Average (ARIMA) time series are implemented and evaluated in terms of their portfolio Value-at-Risk influence. The model performance confirms that modeling portfolio risk in Venture Debt is challenging, especially due to lack of sufficient data and thus a heavy reliance on assumptions. However, the empirical results for Value-at-Risk and Expected Shortfall are in line with expectations. The evaluated portfolio is still in an early stage with a majority of assets not yet in their repayment period and consequently the spread of potential losses within one year is very tight. It should further be recognized that the scope in terms of explanatory variables for sales and model complexities has been narrowed and simplified for computational benefits, transparency and communicability. The main conclusion drawn is that alternative approaches to model Venture Debt risk is fully possible, and should improve in reliability and accuracy with more data feeding the model. For future research it is recommended to incorporate macroeconomic variables as well as similar company analysis to better capture macro, funding and sector conditions. Furthermore, it is suggested to extend the set of financial and operational explanatory variables for sales through machine learning or neural networks. / Detta examensarbete är en experimentell studie för kvantitativ modellering av kreditrisk i Venture Debt-portföljer. Givet en brist på tillgänlig konkurs-data från ArK samt från offentligt tillgängliga databaser i kombination med ambitionen att inkludera företag som misslyckas med skuldförpliktelser innan konkurs per se, presenterar vi en metod för riskmodellering baserad på trender i intäkter. Ramverket för modellen kretsar kring Monte Carlo-simulering med Copluas för att estimera framtida intäktsscenarier över en portfölj med tillväxtbolag inom tekniksektorn. Tre modeller för en random walk, ett linjärt dynamiskt system och ARIMA- tidsserier implementeras och utvärderas i termer av deras inflytande på portföljens Value-at- Risk. Modellens prestationer bekräftar att modellering av portföljrisk inom Venture Debt är utmanande, särskilt på grund av bristen på tillräckliga data och därmed ett stort beroende av antaganden. Dock är de empiriska resultaten för Value-at-Risk och Expected Shortfall i linje med förväntningarna. Den utvärderade portföljen är fortfarande i ett tidigt skede där en majoritet av tillgångarna fortfarande befinner sig i en amorteringsfri period och följaktligen är spridningen av potentiella förluster inom ett år mycket snäv. Det bör vidare tillkännages att omfattningen i termer av förklarande variabler för intäkter och modellkomplexitet har förenklats för beräkningsfördelar, transparens och kommunicerbarhet. Den främsta slutsatsen som dras är att alternativa metoder för att modellera risker inom Venture Debt är fullt möjliga och bör förbättras i tillförlitlighet och precision när mer data kan matas in i modellen. För framtida arbete rekommenderas det att inkorporera makroekonomiska variabler samt analys av liknande bolag för att bättre fånga makro-, finansierings- och sektorsförhållanden. Vidare föreslås det att utöka uppsättningen av finansiella och operationella förklarande variabler för intäkter genom maskininlärning eller neurala nätverk.

Die Quantilsregression untersucht die Quantilfunktion QY |X (τ ), sodass ∀τ ∈ (0, 1), FY |X [QY |X (τ )] = τ erfu ̈llt ist, wobei FY |X die bedingte Verteilungsfunktion von Y gegeben X ist. Die Quantilsregression ermo ̈glicht eine genauere Betrachtung der bedingten Verteilung u ̈ber die bedingten Momente hinaus. Diese Technik ist in vielerlei Hinsicht nu ̈tzlich: beispielsweise fu ̈r das Risikomaß Value-at-Risk (VaR), welches nach dem Basler Akkord (2011) von allen Banken angegeben werden muss, fu ̈r ”Quantil treatment-effects” und die ”bedingte stochastische Dominanz (CSD)”, welches wirtschaftliche Konzepte zur Messung der Effektivit ̈at einer Regierungspoli- tik oder einer medizinischen Behandlung sind. Die Entwicklung eines Verfahrens zur Quantilsregression stellt jedoch eine gro ̈ßere Herausforderung dar, als die Regression zur Mitte. Allgemeine Regressionsprobleme und M-Scha ̈tzer erfordern einen versierten Umgang und es muss sich mit nicht- glatten Verlustfunktionen besch ̈aftigt werden. Kapitel 2 behandelt den Einsatz der Quantilsregression im empirischen Risikomanagement w ̈ahrend einer Finanzkrise. Kapitel 3 und 4 befassen sich mit dem Problem der h ̈oheren Dimensionalit ̈at und nichtparametrischen Techniken der Quantilsregression. / Quantile regression studies the conditional quantile function QY|X(τ) on X at level τ which satisfies FY |X QY |X (τ ) = τ , where FY |X is the conditional CDF of Y given X, ∀τ ∈ (0,1). Quantile regression allows for a closer inspection of the conditional distribution beyond the conditional moments. This technique is par- ticularly useful in, for example, the Value-at-Risk (VaR) which the Basel accords (2011) require all banks to report, or the ”quantile treatment effect” and ”condi- tional stochastic dominance (CSD)” which are economic concepts in measuring the effectiveness of a government policy or a medical treatment. Given its value of applicability, to develop the technique of quantile regression is, however, more challenging than mean regression. It is necessary to be adept with general regression problems and M-estimators; additionally one needs to deal with non-smooth loss functions. In this dissertation, chapter 2 is devoted to empirical risk management during financial crises using quantile regression. Chapter 3 and 4 address the issue of high-dimensionality and the nonparametric technique of quantile regression.

The global financial crisis that took off in 2007 gave rise to several adjustments of the risk regulation for banks. An extensive adjustment, that is to be implemented in 2019, is the Fundamental Review of the Trading Book (FRTB). It proposes to use Expected Shortfall (ES) as risk measure instead of the currently used Value at Risk (VaR), as well as applying varying liquidity horizons based on the various risk levels of the assets involved. A major difficulty of implementing the FRTB lies within the backtesting of ES. Righi and Ceretta proposes a robust ES backtest based on Monte Carlo simulation. It is flexible since it does not assume any probability distribution and can be performed without waiting for an entire backtesting period. Implementing some commonly used VaR backtests as well as the ES backtest by Righi and Ceretta, yield a perception of which risk models that are the most accurate from both a VaR and an ES backtesting perspective. It can be concluded that a model that is satisfactory from a VaR backtesting perspective does not necessarily remain so from an ES backtesting perspective and vice versa. Overall, the models that are satisfactory from a VaR backtesting perspective turn out to be probably too conservative from an ES backtesting perspective. Considering the confidence levels proposed by the FRTB, from a VaR backtesting perspective, a risk measure model with a normal copula and a hybrid distribution with the generalized Pareto distribution in the tails and the empirical distribution in the center along with GARCH filtration is the most accurate one, as from an ES backtesting perspective a risk measure model with univariate Student’s t distribution with ⱱ ≈ 7 together with GARCH filtration is the most accurate one for implementation. Thus, when implementing the FRTB, the bank will need to compromise between obtaining a good VaR model, potentially resulting in conservative ES estimates, and obtaining a less satisfactory VaR model, possibly resulting in more accurate ES estimates. The thesis was performed at SAS Institute, an American IT company that develops software for risk management among others. Targeted customers are banks and other financial institutions. Investigating the FRTB acts a potential advantage for the company when approaching customers that are to implement the regulation framework in a near future. / Den globala finanskrisen som inleddes år 2007 ledde till flertalet ändringar vad gäller riskreglering för banker. En omfattande förändring som beräknas implementeras år 2019, utgörs av Fundamental Review of the Trading Book (FRTB). Denna föreslår bland annat användande av Expected Shortfall (ES) som riskmått istället för Value at Risk (VaR) som används idag, liksom tillämpandet av varierande likviditetshorisonter beroende på risknivåerna för tillgångarna i fråga. Den huvudsakliga svårigheten med att implementera FRTB ligger i backtestingen av ES. Righi och Ceretta föreslår ett robust ES backtest som baserar sig på Monte Carlo-simulering. Det är flexibelt i den mening att det inte antar någon specifik sannolikhetsfördelning samt att det går att implementera utan att man behöver vänta en hel backtestingperiod. Vid implementation av olika standardbacktest för VaR, liksom backtestet för ES av Righi och Ceretta, fås en uppfattning av vilka riskmåttsmodeller som ger de mest korrekta resultaten från både ett VaR- och ES-backtestingperspektiv. Sammanfattningsvis kan man konstatera att en modell som är acceptabel från ett VaR-backtestingperspektiv inte nödvändigtvis är det från ett ES-backtestingperspektiv och vice versa. I det hela taget har det visat sig att de modeller som är acceptabla ur ett VaR-backtestingperspektiv troligtvis är för konservativa från ett ESbacktestingperspektiv. Om man betraktar de konfidensnivåer som föreslagits i FRTB, kan man ur ett VaR-backtestingperspektiv konstatera att en riskmåttsmodell med normal-copula och en hybridfördelning med generaliserad Pareto-fördelning i svansarna och empirisk fördelning i centrum tillsammans med GARCH-filtrering är den bäst lämpade, medan det från ett ES-backtestingperspektiv är att föredra en riskmåttsmodell med univariat Student t-fördelning med ⱱ ≈ 7 tillsammans med GARCH-filtrering. Detta innebär att när banker ska implementera FRTB kommer de behöva kompromissa mellan att uppnå en bra VaR-modell som potentiellt resulterar i för konservativa ES-estimat och en modell som är mindre bra ur ett VaRperspektiv men som resulterar i rimligare ES-estimat. Examensarbetet genomfördes vid SAS Institute, ett amerikanskt IT-företag som bland annat utvecklar mjukvara för riskhantering. Tänkbara kunder är banker och andra finansinstitut. Denna studie av FRTB innebär en potentiell fördel för företaget vid kontakt med kunder som planerar implementera regelverket inom en snar framtid. / Riskhantering, finansiella tidsserier, Value at Risk, Expected Shortfall, Monte Carlo-simulering, GARCH-modellering, Copulas, hybrida distributioner, generaliserad Pareto-fördelning, extremvärdesteori, Backtesting, likviditetshorisonter, Basels regelverk

本研究之宗旨在於探究中國大陸對亞洲區域內國家的金融市場影響程度之變化。由過去的各國股市日報酬率資料間相關程度與政策改變間的影響結果，來觀察是否未來在兩岸政策更開放下會使中國大陸對台灣的影響程度上升，進而使國際間投資組合的風險分散效果下降。本研究自DataStream選取台灣、香港、中國大陸、泰國、印尼、新加坡、馬來西亞、菲律賓、日本以及美國等十國的股價指數日資料，以對數轉換為日報酬率後年化加以分析。選取時間自1991年7月15日(中國大陸上海證券交易所股價指數公開後)至2008年12月31日。本研究選用的方法為使用風險值(VaR; Value at Risk)的概念來取代傳統的標準差，衡量以該十國所分別組成的各投資組合風險值變動情形；以及由風險值所衍生出的Diversification Benefit與Incremental VaR的結果。發現到僅由亞洲區域國家內組成的投資組合風險分散效果逐漸下降；且效果並不如有納入區域外國家(如美國)的投資組合。接著本研究將Gaussian Copula模型放入VaR中以增加對極端值的捕捉能力，結果發現本研究所選用的指數加權移動平均法所求得之相關係數已可有效反應出各國之間的相依程度，即加入Copula的效果有限。另外藉由Copula所求得之相關係數顯示，台灣、香港對中國大陸之間的相依程度已逐漸上升，並開始出現超越美國之現象，其中又以2005年為上升趨勢的起點。最後本研究以向量自我迴歸模型(VARs)來驗證2005年前後中國大陸股市對其他亞洲區域國家的影響力是否存在結構性的改變；並再佐以變異數拆解之方法來觀察2005年前後各國家之間自發性衝擊對彼此之間的影響程度變化。研究結果發現，透過VARs可證明中國大陸對亞洲區域各國的影響力在2005年後轉變為顯著；僅對美國不存在此一現象。另外變異數拆解的結果也顯示各國之間的相依程度在2005年後有明顯的上升，中國大陸對各國的影響程度亦然。透過本研究之結論，在未來兩岸將簽訂金融監理備忘錄使整合關係提升的環境下，需提醒投資人整合關係的上升將使得以之為標的之投資組合風險分散效果下降，需作為投資策略之考量。 / The object of this research is to find out the trend of dependence and correlation between China and other Asian countries. Based on past information about the relationship between equity markets’ correlation and changes in policies, this research can make suggestions to the foreseeable future of Taiwan and China whose relationship will be more solid due to new policy. The data of this research are gathered from DataStream, which includes Taiwan, Hong Kong, China, Thailand, Indonesia, Singapore, Malaysia, Philippines, Japan and United States. Selected from 1991/07/15 (when the Shanghai SE Composite went public) to 2008/12/31, this research calculates the annualized daily return using natural logarithms of two consecutive daily index prices. This research uses Value at Risk (VaR) to measure the risk exposure of portfolios formed by ten countries, and extends to the use of Diversification Benefit and Incremental VaR. The results found out that the diversification effects of portfolio which includes only Asian countries are decreasing and inferior to the effects when cross region countries are included. The second study of this research is to combine Gaussian Copula Model with VaR to capture the effects of extreme values. Empirical results found out that the VaR using Exponentially Weighted Moving Average method is good enough for analyzing Asian stock markets. The correlation in Copula model suggests that the dependence between Taiwan and China had increased since 2005 and has the increasing trend which might overwhelm the dependence between Taiwan and United States. Final research is about using Vector Autoregressions Model (VARs) to testify is there exist any structural change of dependence before and after 2005, and using Variance Decomposition to observe the relationships between these ten countries. The results found out that there exist structural change in 2005, the post-2005 periods shows that for Asian countries the effect from China are significant and greater than pre-2005 periods.

Cette thèse traite la contribution des méthodes d'ondelettes sur la modélisation des séries temporelles économiques et financières et se compose de deux parties: une partie univariée et une partie multivariée. Dans la première partie (chapitres 2 et 3), nous adoptons le cas univarié. Premièrement, nous examinons la classe des processus longue mémoire non-stationnaires. Une étude de simulation a été effectuée afin de comparer la performance de certaines méthodes d'estimation semi-paramétrique du paramètre d'intégration fractionnaire. Nous examinons aussi la mémoire longue dans la volatilité en utilisant des modèles FIGARCH pour les données de l'énergie. Les résultats montrent que la méthode d'estimation Exact Local Whittle de Shimotsu et Phillips [2005] est la meilleure méthode de détection de longue mémoire et la volatilité du pétrole exhibe une forte évidence de phénomène de mémoire longue. Ensuite, nous analysons le risque de marché des séries de rendements univariées de marchés boursier, qui est mesurée par le risque systématique (bêta) à différents horizons temporels. Les résultats montrent que le Bêta n'est pas stable, en raison de multi-trading stratégies des investisseurs. Les résultats basés sur l'analyse montrent que le risque mesuré par la VaR est plus concentrée aux plus hautes fréquences. La deuxième partie (chapitres 4 et 5) traite l'estimation de la variance et la corrélation conditionnelle des séries temporelles multivariées. Nous considérons deux classes de séries temporelles: les séries temporelles stationnaires (rendements) et les séries temporelles non-stationnaires (séries en niveaux). / This thesis deals with the contribution of wavelet methods on modeling economic and financial time series and consists of two parts: the univariate time series and multivariate time series. In the first part (chapters 2 and 3), we adopt univariate case. First, we examine the class of non-stationary long memory processes. A simulation study is carried out in order to compare the performance of some semi-parametric estimation methods for fractional differencing parameter. We also examine the long memory in volatility using FIGARCH models to model energy data. Results show that the Exact local Whittle estimation method of Shimotsu and Phillips [2005] is the better one and the oil volatility exhibit strong evidence of long memory. Next, we analyze the market risk of univariate stock market returns which is measured by systematic risk (beta) at different time horizons. Results show that beta is not stable, due to multi-trading strategies of investors. Results based on VaR analysis show that risk is more concentrated at higher frequency. The second part (chapters 4 and 5) deals with estimation of the conditional variance and correlation of multivariate time series. We consider two classes of time series: the stationary time series (returns) and the non-stationary time series (levels). We develop a novel approach, which combines wavelet multi-resolution analysis and multivariate GARCH models, i.e. the wavelet-based multivariate GARCH approach. However, to evaluate the volatility forecasts we compare the performance of several multivariate models using some criteria, such as loss functions, VaR estimation and hedging strategies.

保險公司清償能力一直是保險監理的重心，在所有現行的制度中風險基礎資本是最重要的，但此項制度仍有其缺點，因此其他動態分析模型被許多學者所提出，如涉險值及情境分析。雖然這些動態分析模型被學者所偏好，但監理機關仍須對這些模型的精確程度加以了解，這也是本篇論文所要研究的目的。 基於此，本篇論文以模擬方式及經濟模型加以分析風險基礎資本、情境分析及涉險值等方法的破產預測的相對精確性。其中風險基礎資本完全採用現有NAIC的年報資料，情境分析及涉險值則採用我們所建立的模型，基於此也可以確認現有監理制度是否有缺失。 我們的結果發現風險基礎資本的預測能力很低，動態模型-情境分析及涉險值皆優於風險基礎資本，且在不同動態模型中涉險值的預測能力較好。因此可知被學者所偏好的動態分析模型應是未來保險監理的方向希望藉由本篇提供監理機關一個參考的依據。 / Solvency prediction of insurers has been the focus of insurance regulation. Among the solvency regulation systems, risked-based capital (RBC) is the most important but RBC still has some drawbacks. Thus, the dynamic financial analyses-scenario analysis and Value at Risk have been developed to be the regulation tool. Although, the scholars prefer the dynamic financial analysis, the regulators still want to make sure the accuracy of dynamic financial analysis. That is the purpose of our paper. Therefore, we use the simulation result and the econometric model to analyze the relative effectiveness of RBC, scenario and Value at Risk (VaR). The RBC is from the annual statement and the scenario and VaR come from our simulation model. Our result shows that the RBC has very low explanatory power, the dynamic financial analysis is better than RBC, and VaR outperform scenario analysis. Thus, we conclude that VaR is the way to go for property-casualty insurance regulators.

本文首次提出應用新的模擬方法：定態(stationary) bootstrap來估計涉險值(Value-at-Risk, 以下簡稱VaR)。VaR是衡量投資組合市場風險(market risk)的工具，由於1990年代以來國際間對市場風險管理的重視，且VaR較傳統風險衡量指標容易瞭解，又考慮整個投資組合資產間相關性降低風險的效果，加上VaR可作為企業內控、主管機關監督、以及投資人評估企業營運狀況等指標，故已廣為實務界及學界所接受。目前幾種主要衡量VaR的方法，包括變異數—共變數法、歷史模擬法、蒙地卡羅模擬法、classical bootstrap法以及壓力測試法等，各有其假設限制及優缺點。其中，classical bootstrap在衡量VaR時，使用的假設比較少，似乎非常適合衡量VaR。但是classical bootstrap會割裂了資料自我相關的性質，較適用於獨立且相同分配的樣本。我們在本文中介紹修正classical bootstrap的方法：移動區塊(moving block) bootstrap以及定態bootstrap，並利用統計模擬的方式證明定態bootstrap適合用於時間序列資料，對於捕捉真實分配的能力很強。接著我們選取11檔上市公司股票建構投資組合，並利用classical bootstrap以及定態bootstrap來衡量1999年共266個交易日的VaR。實證結果支持定態bootstrap能夠正確地衡量VaR，且其結果與classical bootstrap有明顯的不同。定態bootstrap法是個比較合理的衡量VaR方法，因此，我們建議風險管理者可採用定態bootstrap 衡量VaR。

本篇文章將採用長期記憶模型之一的HYGARCH模型，搭配1985年廣場協議後的日圓匯率期貨資料來估計日圓期貨匯率買入和放空部位的日報酬風險值，探討控管日圓匯率期貨在使用上的風險。為了更準確地計算風險值，本文採用常態分配、學生t分配以及偏態學生t分配來作模型估計以及風險值之計算。 本文實證的結果將有兩方面的貢獻：首先，實證結果顯示當我們採用厚尾分配估計風險值時，樣本內風險值的估計誤差會與信賴水準的高低呈正比的現象，證明在極端的風險值估計上，厚尾分配均有較佳的表現。其次，與其他使用HYGARCH模型研究日圓匯率的文章相較，本文在風險控管層面上所提供的偏態學生t分配，於估計風險值時，比起只考慮厚尾的對稱學生t分配將來得更為有效，其不但在估計誤差上較小，而且根據Kupiec檢定法，其在樣本內的風險值估計也有較好的表現。此外，本文也將多方證明此資料的偏態分配屬於右偏。 / In order to manage the exposure of the dollar/yen futures returns with regarding the long memory behavior in volatility, we use the HYGARCH(1,d,1) model with the data after the Plaza Accord to compute daily Value-at-Risk (VaR) of long and short trading positions. To take into account the fat-tail situation in financial time series, we estimate the model under the normal, Student-t, and skewed Student-t distributions. The contribution of this article is twofold. First, the empirical results show that the bias of in-sample VaR increases as the confidence level increases when VaR is calculated with a fat-tail distribution. Second, we provide a better distribution, the skewed Student-t innovation, for estimating the HYGARCH model for the Japanese yen in respect of risk management because the bias under the skewed Student-t innovation is smaller than that under the Student-t distribution, and in-sample VaR of the models with a skewed Student-t distribution outperforms based on Kupiec test. In addition, we get the innovation skewed to the right through the in-sample VaR analysis.

許多公司在發行公司債的時候，會給此公司債一個可提前贖回的特性，此種公司債稱為可贖回公司債(Callable Bond)，用來規避利率變動風險的金融商品也與我們熟知的利率交換不同，稱為可取消利率交換(Cancelable Swap)。其實可取消利率交換可以拆解成百慕達利率交換選擇權(Bermudan Swaption)加上利率交換，由於利率交換之評價較簡單也有市場一致的評價方法，因此百慕達利率交換選擇權便成為評價的重點。 評價的部分，由於百慕達式的商品有提前履約的特性，造成其封閉解不存在，因此需要利用其他的近似解或是數值方法來求它的價格。由於本文採用BGM(1997)的市場利率模型(Libor Market Model)，其高維度的性質導致數狀方法與有限差分法使用起來較無效率，因此本文選擇使用蒙地卡羅法做為評價的方法，同時利用Longstaff and Schwartz(2001)的最小平方蒙地卡羅法(Least Squares Monte Carlo Method)來解決提前履約的問題。 最後，本文將採用2種利率波動度假設與2種不同利率間相關係數的假設，共4種組合，在歐式利率交換選擇權的市場波動度下進行校準，使用校準出來的參數進行評價來得到4種價格。再進行商品的敏感度分析(Sensitivity Analysis)和風險值(Value at Risk)的計算。

Shorter product life cycles and rapid product obsolescence provide increasing incentives to introduce newproducts to markets more quickly. As a consequence of rapidly changing market conditions, firms focus onimproving their new product development processes to reap the benefits of early market entry. Researchershave analyzed market entry, but have seldom provided quantitative approaches for the product rolloverproblem. This research builds upon the literature by using established optimization methods to examine howfirms can minimize their net loss during the rollover process. Specifically, our work explicitly optimizes thetiming of removal of old products and introduction of new products, the optimal strategy, and the magnitudeof net losses when the market entry approval date of a new product is unknown. In the first paper, we use theconditional value at risk to optimize the net loss and investigate the effect of risk perception of the manageron the rollover process. We compare it to the minimization of the classical expected net loss. We deriveconditions for optimality and unique closed-form solutions for single and dual rollover cases. In the secondpaper, we investigate the rollover problem, but for a time-dependent demand rate for the second producttrying to approximate the Bass Model. Finally, in the third paper, we apply the data-driven optimizationapproach to the product rollover problem where the probability distribution of the approval date is unknown.We rather have historical observations of approval dates. We develop the optimal times of rollover and showthe superiority of the data-driven method over the conditional value at risk in case where it is difficult to guessthe real probability distribution