近幾年，風險值已經成為金融機構風險控管的重要工具。它的明確及簡單易懂是其讓人接受的原因，加上巴塞爾銀行監理委員會在1996提出的巴塞爾協定修正，規定銀行將市場風險因素納入考量，並允許銀行自行發展內部模型，以風險值模型衡量市場風險後，各種風險值的估算方法相繼被提出。 本篇論文是使用部分整合自回歸條件變異數（Fractional Integrated Generalized Autoregressive Conditional Heteroskedasticity，簡稱FIGARCH）計算長期利率期貨多空部位的每日風險值。選取的三支長期利率期貨是在芝加哥期貨交易所掛牌的三十年期美國政府債券期貨（TB）、十年期美國政府債券期貨（TN） 與十年期市政債券指數期貨（MNI）。 利率期貨的研究在過去文獻中，甚少被提及。但隨著利率型商品日新月異的發展，以利率期貨避險的需求也與日遽增。尤其在台灣，利率期貨更是今年新登場的期貨商品。因此，我選擇利率期貨作為研究標的，藉由以FIGARCH模型來配適波動性，提供避險者一個估算風險值的方法。 FIGARCH模型係由Baillie、Bollerslev與Mikkelsen於1996所提出，與傳統GARCH模型所不同的是，FIGARCH模型特別適用於描述具有波動性長期記憶（Long Memory）性質的資料。所謂長期記憶性，是指衝擊所造成的持續性是以緩慢的雙曲線速率衰退。而許多市場實證分析均指出，FIGARCH較適合用來描述金融市場上的波動性。此外，本研究的風險值計算，除了一般實務界常用的常態分配以外，還考慮了t分配與偏斜t分配，以捕捉財務資料常見的厚尾與偏斜的特性。 而實證結果顯示，長期利率期貨報酬率的波動性確實存在長期記憶性，所以FIGARCH(1,d,1)模型可以適切地估算長期利率期貨的每日風險值，不論在樣本內或樣本外的風險值計算均優於傳統GARCH(1,1)模型的計算結果。至於各種不同分配的比較，在樣本內的風險值計算，當α=0.05時，常態分配FIGARCH(1,d,1)模型表現較佳；當α=0.025到0.0025時，t分配與偏斜t分配FIGARCH(1,d,1)模型表現較佳，而偏斜t分配FIGARCH又稍微優於t分配FIGARCH(1,d,1)模型。 而樣本外的風險值預測，則有不同的結果，當α=0.05，t分配與偏斜t分配FIGARCH(1,d,1)模型表現較佳；而α=0.01時，常態分配FIGARCH(1,d,1)模型表現較佳。而且t分配與偏斜t分配FIGARCH(1,d,1)模型在α=0.01會出現太過保守的情形，出現失敗率（failure rate）為零，高估風險值。 / Value-at-Risk (VaR) has become the standard measure used to quantify market risk recently, and it is defined as the maximum expected loss in the value of an asset or portfolio, for a given probability α at a determined time period. This article uses the FIGARCH(1,d,1) models to calculate daily VaR for long-term interest rate futures returns for long and short trading positions based on the normal, the Student-t, and the skewed Student-t error distributions. The U.S. Treasury bonds futures, Treasury notes futures, and municipal notes index futures of daily frequency are studied. The empirical results show that returns series for three interest rate futures all have long memory in volatility, and should be modeled using fractional integrated models. Besides, the in-sample and out-of-sample VaR values generated using FIGARCH(1,d,1) models are more accurate than those generated using traditional GARCH(1,1) models. For different distributions among FIGARCH(1,d,1) models, the normal FIGARCH(1,d,1) models are preferred for in-sample VaR computing whenα=0.05, and the Student-t and skewed Student-t models perform better for in-sample VaR computing whenα=0.025-0.0025. Nonetheless, for out-of-sample VaR, the Student-t and skewed Student-t FIGARCH(1,d,1) models perform better in the case α=0.05 while the normal FIGARCH(1,d,1) models perform better in the case α=0.01. The VaR values obtained by the Student-t and skewed Student-t FIGARCH(1,d,1) models are too conservative whenα=0.01.

本文提出了一個新興風險衡量的工具的概念-期望尾端損失值(ETL)，其有別於風險值為百分位數且未考慮報酬分配的尾部風險(Tail Risk)，本研究期望能透過ETL的估計可以更完整表達投資組合所有可能面臨的風險，對於市場風險能更有效控管。 本文實證討論有關VaR與ETL穩定度的部分，VaR雖然在理論上證明無法滿足次可加性這個條件，但是在本研究實證中，即使在分配具厚尾狀況下，VaR仍滿足次加性的性質。這也表示，我們在現實生活中很難因VaR理論上缺乏次可加性，而捨棄VaR這個風險衡量工具，然ETL也有其貢獻性，其較VaR多考慮尾部資訊，可視為風險值外另一參考指標，此為本文貢獻一。 本文實證也探討移動窗口中歷史資料長度的不同，是否造成VaR與ETL估算準確性的差異，本文由實證結果發現：在歷史窗口的資料長度越長(1000日)下，並沒有正確預估VaR與ETL，而本研究中以移動窗口為500日下，使用內部模型較具正確性，故在使用風險值模型時，應謹慎選擇移動窗口之長度，此為本文貢獻二。

The US sub-prime mortgage crisis greatly affected not only the US economy but also other countries in the world. This thesis employs the extreme value theory and Value at Risk (VaR) analysis to assess the impact of the US sub-prime mortgage crisis on various stock markets of the MSCI indexes, including 10 countries and 7 areas. It is reasonable to guess that VaR value should increase after the crisis. The empirical analyses on these indexes conclude that (1) the American market indexes not only do not agree with the guess after the crisis but four American indexes are identical; (2) not all the Asia market indexes consist with the guess; (3) the European market indexes agree with the guess; (4) MSCI AC PACIFIC, NEW ZEALAND, and AUSTRALIA consist with the guess; (5) the behavior for the positive log returns is different from that for the negative returns in some MSCI indexes. Over speaking, the impacts of US sub-prime mortgage crisis on those countries are not the same.

放款的利息收入雖是商業銀行主要之獲利來源, 但借貸行為卻同時使得銀行承受著違約風險。銀行應透過風險管理方法, 計算經濟資本以提列足夠準備來防範預期以及未預期損失。 另外, 若銀行忽略違約行為之間的相關性, 將有可能低估損失的嚴重性。因此, 為了在考量違約相關性下提列經濟資本, 本文由 Merton (1974) 模型出發, 以信用風險因子模型判定放款對象是否違約, 進而決定銀行面對的整體損失為何。 為簡化分析, 本文假設違約損失率 (loss given default) 為 100%。 再者, 為加強相關性, 本文亦將違約傳染性加入因子模型並比較有無傳染性效果時, 模型所計算出的損失孰輕孰重。 而在決定違約與否時, 須利用來自移轉矩陣上的無條件違約機率, 然信評機構所發布之移轉矩陣概遺漏諸多訊息, 依此, 本文以多期連續的移轉矩陣修正之並得到另一不同的無條件違約機率。 最後, 以臺灣的 537 家上市櫃公司作為資產組合, 經由蒙地卡羅模擬得到兩個因子模型的損失分配, 我們發現具有傳染性效果存在時, 預期損失和非預期損失較大且損失分配也較為右偏。 / Despite interest income from loans is a major profit contributor for commercial banks, lending inevitably makes banks bear default risks. For the sake of avoiding expected and unexpected losses, risk management methods ough to be employed by banks to meet the ecomical capital requirement. Besides, loan loss severity may very well be underestimated if the correlation between default events is disregarded. Therefore, in order to calculate economical capital when taking default correlation into account, we start from Merton (1974) model, and identify if loans will be in default via facor models for portfolio credit risk and portfolio losses can then be detemined. To simplify our analysis in this paper, loss given default is assumed to be 100%. To intensify correlation, default contagion is, moreover, introduced to our factor model and we investigate which model results in larger losses as well. When determining default, we have to utilize rating transition matrices to obtain unconditional probability of default. Transition matrices published by credit rating agencies, however, have embedded drawback of insufficient information. We correct this flaw by means of another transition matrix based on continuous-time observations and produce different unconditional probability of default. Through Monte Carlo simulation, loss distributions are calibrated respectively from the two factor models under portfolio of 537 Taiwan listed and OTC companies. We find that expected and unexpected losses are larger and loss distribution is more right-skewed when infectious effects exsit.

The thesis describes commonly used measures of risk, such as volatility, Value at Risk (VaR) and Expected Shortfall (ES), and is tasked with creating models for measuring market risk. It is concerned with the risk over daily and over monthly horizons and shows the shortcomings of a square-root-of-time approach for converting VaR and ES between horizons. Parametric models, geometric Brownian motion (GBM) and GARCH process, and non-parametric models, historical simulation (HS) and some its possible improvements, are presented. The application of these mentioned models is demonstrated using real data. The accuracy of VaR models is proved through backtesting and the results are discussed. Part of this thesis is also a simulation study, which reveals the precision of VaR and ES estimates.

Topic of the master thesis is the Financial Instruments in Bank Accounting. The master thesis looks at bookkeeping and accounting of financial instruments in international financial reporting standards context. The main reporting standards which are discussed in the paper are: IAS 32, IAS 39, IFRS 7 and IFRS 9. In the first part, the reporting standards impact on banks as commercial subjects, legislation of bank operations, financial instruments and accounting in both a national and international context are presented. The focus of master thesis is examined in the second and third sections where financial instruments are discussed in detail and their characteristics, initial recognition, subsequent measurement and accounting are also examined. The next topic is the issue of the reclassification of financial instruments and their impairment is discussed. The forth part of the thesis examines IFRS 7. The standard has claims on the disclosure of financial instruments in both the statement of financial position and statement of comprehensive income. IFRS 7 also has claims on related areas including disclosure of credit, liquidity and market risk. The last part deals with news in the examined area where the main focus is IFRS 9.

This essay investigates how realized variance affects the GARCH-models (GARCH, EGARCH, GJRGARCH) when added as an external regressor. The GARCH models are estimated with three different distributions; Normal-, Student’s t- and Normal inverse gaussian distribution. The results are ambiguous - the models with realized variance improves the model fit, but when applied to forecasting, the models with realized variance are performing similar Value at Risk predictions compared to the models without realized variance.

Este trabalho consiste em um estudo comparativo de diversos modelos para cálculo do Valor em Risco de um portifólio. São comparados modelos que consideram a série univariada de log-retornos do portifólio versus mo- delos multivariados, que consideram as séries de log-retornos de cada ativo que compõe o portifólio e suas correlações condicionais. Além disso, são testados modelo propostos recentemente, que possuem pouca literatura a respeito, como o PS-GARCH e o VARMA-GARCH. Também propomos um novo modelo, que utiliza o resultado acumulado do portifólio nos últimos dias como variável exógena. Os diferentes modelos são avaliados em termos de sua adequação às exigëncias do Acordo de Basileia e seu impacto financeiro, em um período que inclui épocas de alta volatilidade. De forma geral, não foram notadas grandes diferenças de performance entre modelos univariados e multivariados. Os modelos mais complexos mostraram-se mais eficientes, produzindo resultados satisfatórios inclusive em tempos de crise. / The present work consists of a comparative study of several portfolio Value-at-Risk models. Univariate models, which consider only the portfolio log-returns series, are compared to multivariate models, which consider the log-returns series of each asset individually and their conditional correlations. Additionally, recently proposed models such as PS-GARCH and VARMA-GARCH are tested. We also propose a new model that uses past cumulative returns as exogenous variables. All models are evaluated in terms of their compliance to Basel Accord and financial impact, in period that includes high volatility times. In general, univariate and multivariate models performed similarly. More complex models yielded more accurate results, with satisfactory performance including in crisis periods.

Neste trabalho são definidos, discutidos e estimados o Valor em Risco e o Expected Shortfall. Estas são medidas de Risco Financeiro de Mercado muito utilizadas por empresas e investidores para o gerenciamento do risco, aos quais podem estar expostos. O objetivo foi apresentar e utilizar vários métodos e modelos para a estimação dessas medidas e estabelecer qual o modelo mais adequado dentro de determinados cenários. / In this work Value at Risk and Expected Shortfall are defined, discussed and estimated . These are measures heavily used in Financial Market Risk, in particular by companies and investors to manage risk, which they may be exposed. The aim is to present and use several methods and models for estimating those measures and to establish which model is most appropriate in certain scenarios.

The debate on quantitative operational risk modeling has only started at the beginning of the last decade and the best-practices are still far from being established. Estimation of capital requirements for operational risk under Advanced Measurement Approaches of Basel II is critically dependent on the choice of risk measure, which quantifies the risk exposure based on the underlying simulated distribution of losses. Despite its well-known caveats Value-at-Risk remains a predominant risk measure used in the context of operational risk management. We describe several serious drawbacks of Value-at-Risk and explain why it can possibly lead to misleading conclusions. As a remedy we suggest the use of coherent risk measures - and namely the statistic known as Expected Shortfall - as a suitable alternative or complement for quantification of operational risk exposure. We demonstrate that application of Expected Shortfall in operational loss modeling is feasible and produces reasonable and consistent results. We also consider a variety of statistical techniques for modeling of underlying loss distribution and evaluate extreme value theory framework as the most suitable for this purpose. Using stress tests we further compare the robustness and consistency of selected models and their implied risk capital estimates...