We specify a class of non-linear and non-Gaussian models for which we estimate and forecast the conditional distributions with daily frequency. We use these forecasts to calculate VaR measures for three different equity markets (US, GB and Japan). These forecasts are evaluated on the basis of different statistical performance measures as well as on the basis of their economic costs that go along with the forecasted capital requirements. The results indicate that different performance measures generate different rankings of the models even within one financial market. We also find that for the three markets the improvement in the forecast by non-linear models over linear ones is negligible, while non-gaussian models significantly dominate the gaussian models. / Series: Report Series SFB "Adaptive Information Systems and Modelling in Economics and Management Science"

This project focuses on risk analysis of corporate bond portfolios. We separate the total risk of the portfolio into three parts, which are market risk, credit risk and liquidity risk. The market risk component is quantified by value-at-risk (VaR) determined by change in yield to maturity of the bond portfolio. For the credit risk component, we calculate default probabilities and losses in the event of default and then compute credit VaR. Next, we define a factor called basis which is the difference between the Credit Default Swap (CDS) spread and its corresponding corporate bond yield spread (z-spread or OAS). We quantify the liquidity risk by using the basis. In addition, we also introduce a Fama-French multi-factor model to analyze factor significance to the corporate bond portfolio.

This project focuses on risk analysis of corporate bond portfolios. We divide the total risk of the portfolio into three parts, which are market risk, credit risk and liquidity risk. The market risk component is quantified by value-at-risk (VaR) which is determined by change in yield to maturity of the bond portfolio. For the credit risk component, we calculate default probabilities and losses in the event of default and then compute credit VaR. Next, we define a factor called `basis' which is the difference between the Credit Default Swap (CDS) spread and its corresponding corporate bond yield spread (z-spread or OAS). We quantify the liquidity risk by using the basis. In addition we also introduce a Fama-French multi-factor model to analyze the factor significance to the corporate bond portfolio.

Calculation of the Value at Risk (VaR) measure, of a portfolio, can be done using Monte Carlo simulations of that portfolio's potential losses over a specified period of time. Regulators, such as the US Securities and Exchange Commission, and Exchanges, such as the New York Stock Exchange, establish regulatory capital requirements for firms. These regulations set the amount of capital that firms are required to have on hand to safeguard against market loses that can occur. VaR gives us this specific monetary value set by Regulators and Exchanges. The specific amount of capital on hand must satisfy that, for a given confidence level, a portfolio's loses over a certain period of time, will likely be no greater than the capital required a firm must have on hand. The scenario used will be one of a Risk Manager position in which this manager inherited a portfolio that was set up for a client beginning in April 1992. The portfolio will have to meet certain parameters. The initial portfolio is worth $61,543,328.00. The risk manager will be responsible for the calculation of the Value at Risk measure, at five percent, with a confidence level of 95% and 20 days out from each of the 24 business quarters, over a six year period, starting in 1992 and ending in 1996.

Nos últimos anos, o value-at-risk tem se tornado uma ferramenta amplamente utilizada nas principais instituições financeiras, inclusive no Brasil. Dentre suas vantagens, destaca-se a possibilidade de se resumir em um único número os riscos de mercado incorridos e incorporar neste valor tanto a exposição da instituição quanto a volatilidade do mercado. O objetivo principal deste estudo é verificar a eficácia dos modelos mais conhecidos de value-at-risk - RiskMetrics(TM) e Simulação Histórica - na mensuração dos riscos de mercado de carteiras de renda fixa compostas por instrumentos pré-fixados em reais. No âmbito da alocação de capital para atendimento aos órgãos de regulamentação, o estudo estende-se também ao modelo adotado pelo Banco Central do Brasil. No decorrer do estudo, discute-se ainda as vantagens e desvantagens apresentadas, bem como o impacto que as peculiaridades do mercado brasileiro exercem sobre as hipóteses assumidas em cada um dos modelos. / Value-at-Risk (VaR) has become the primary tool for the systematic measuring and monitoring of market risk in most financial institutions. VaR is a statistical measure that comprises not only the exposure but also the market volatility in a single number. The main purpose of this work is to evaluate the performance of the well-known value-at-risk models - RiskMetrics(TM) and Historical Simulation - in the Brazilian fixed-income market. In the scope of capital allocation related to banking regulation, this study also extends briefly to the model adopted by the Brazilian Central Bank. Additionally, the underlying assumptions of these models are analyzed in the Brazilian financial market context. Also, this study discusses the advantages and disadvantages presented by the RiskMetrics and the Historical Simulation models.

In last few years Value-at-Risk (Var) is a very popular and frequently used risk measure. Risk measure VaR is used in most of the financial institutions. VaR is popular thanks to its simple interpretation and simple valuation. Valuation of VaR is a problem if we assume a few dependent risks. So VaR is estimated in a practice. In presented thesis we study theory of stochastic bounding. Using this theory we obtain bounds for VaR of sum a few dependent risks. In next part of presented thesis we show how we can generalize obtained bounds by theory of copulae. Then we show numerical algorithm, which we can use to evaluate bounds, when exact analytical evaluate isn't possible. In a final part of presented thesis we show our results on practical examples.

Stochastic solvency testing methods have existed for more than 20 years, yet there has been little research conducted in this area, particularly in Australia. This is for a number of reasons, the most pertinent of which being the lack of computing capabilities available in the past to implement more sophisticated techniques. However, recent advances in computing have made stochastic solvency testing possible in practice and have resulted in a trend towards this being done in advanced studies. ¶ The purpose of this thesis is to develop a realistic solvency testing model in a form that can be implemented by Australian Life Insurers, in anticipation that the Australian insurance regulator, APRA, will ultimately follow the world trend and require stochastic solvency testing to be carried out in Australia. The model is constructed from three interconnected stochastic sub-models used to describe the economic environment and the mortality and lapsation experience of the portfolio of policies under consideration. Australian economic and Life Insurance data is used to fit a number of possible sub-models, such as generalised linear models, over-dispersion models and asset models, and the ``best'' model is selected in each case. The selected models are a modified CAS/SOA economic sub-model; either a Poisson or negative binomial (NB1) distribution (depending on the policy type considered) as the mortality sub-model; and a normal-Poisson lapsation sub-model. ¶ Based on tests carried out using this model, it is demonstrated that, for portfolios of level and yearly-renewable term insurance business, the current deterministic solvency capital requirements provide little protection against insolvency. In fact, for the test portfolios of term insurance policies considered, the deterministic capital requirements have levels of sufficiency of less than 2% (on a Value at Risk basis) when compared to the change in capital distribution over a three year time horizon. This is of concern, as yearly-renewable term insurance comprises a significant volume of Life Insurance business in Australia, with there being over 426,000 yearly-renewable term insurance policies on the books of Australian Life Insurers in 1999 and more business expected since then. ¶ A sensitivity analysis shows that the results of the stochastic asset requirement calculations are sensitive to the choice of sub-model used to forecast economic variables and to the choice of formulae used to describe the mean mortality and lapsation rates. The implication of this is that, if APRA were to require Life Insurers to calculate their solvency capital requirements on a stochastic basis, some guidance would need to be provided regarding the components of the solvency testing model used. The model is not, however, sensitive to whether an allowance is made for mortality or lapsation rate over-dispersion, nor to whether dependency relationships between mortality rates, lapsation rates and the economy are allowed for. Thus, over-dispersion and dependency relationships between the sub-models can be ignored in a stochastic solvency testing model without significantly impacting the calculated solvency requirements.

We utilise several asset pricing models that allow for discontinuities in the returns and volatility time series in order to obtain estimates of Value-at-Risk (VaR). The first class of model that we use mixes a continuous diffusion process with discrete jumps at random points in time (Poisson Jump Diffusion Model). We also apply a purely discontinuous model that does not contain any continuous component at all in the underlying distribution (Variance Gamma Model). These models have been shown to have some success in capturing certain characteristics of return distributions, a few being leptokurtosis and skewness. Calibrating these models onto the returns of an index of Australian stocks (All Ordinaries Index), we then use the resulting parameters to obtain daily estimates of VaR. In order to obtain the VaR estimates for the Poisson Jump Diffusion Model and the Variance Gamma Model, we introduce the use of an innovation from option pricing techniques, which concentrates on the more tractable characteristic functions of the models. Having then obtained a series of VaR estimates, we then apply a variety of criteria to assess how each model performs and also evaluate these models against the traditional approaches to calculating VaR, such as that suggested by J.P. Morgan???s RiskMetrics. Our results show that whilst the Poisson Jump Diffusion model proved the most accurate at the 95% VaR level, neither the Poisson Jump Diffusion or Variance Gamma models were dominant in the other performance criteria examined. Overall, no model was clearly superior according to all the performance criteria analysed, and it seems that the extra computational time required to calibrate the Poisson Jump Diffusion and Variance Gamma models for the purposes of VaR estimation do not provide sufficient reward for the additional effort than that currently employed by Riskmetrics.

金融市場的激烈震盪，往往會造成投資大眾與企業的重大損失，甚而危及企業的生存及整體金融市場的穩定與發展。而每當金融市場發生變化時首當其衝者常為金融證券相關產業。證券商所面臨之經營風險雖可區分為市場風險、信用風險、流動性風險、作業風險、法律風險及系統風險等六類，但以市場風險為最主要的風險來源，由近年來國內外多起金融機構的重大損失案例可為證。大型化，國際化及多元化為國內證券商之發展趨勢，由於業務多元化、大型化，將使證券商所持有之金融資產部位增加，業務複雜度、組織運作與管理難度增加，相對的經營風險亦提高。因此適當的風險管理機制，以維持良好的風險管理能力，與適當的資源配置是證券商在致力於追求業務擴展之餘，應加以特別注意的重要事項。 本研究主要在探討國內證券商所面對的經營風險有那些，以及其在風險管理上存在的問題與建議，並對主要的市場風險管理問題尋求解決方案及進行個案分析。風險控管的內涵主要包括：風險管理的組織運作、風險衡量之技術、風險管理之策略、風險管理政策與執行等。除探討一般風險管理之策略運用(風險分散、風險移轉、風險承擔及動態避險等的原理與方法)外，並就近年來頗受注目的，風險值風險衡量管理技術的運用與模型進行研究，包括一般所定義之風險值的說明與實務運用外，進一步討論個別模型（包括歷史模擬法、蒙地卡羅模擬法、變異數-共變異數法及波動度之衡量方式等）的計算方法、特點。而在證券商之現行風險管理政策方面，則著重於證券商風險控管之外部規範與內部制度及其所存在的問題。 而就國內證券商所面對的風險管理問題與對策，本文以為除了必須要注重人才的培育召募及落實管理制度的執行外，還必須要有一具效率的風險管理工具及符合風險管理需要的組織與運作模式。就『有效率的風險管理工具』的問題，由於財務工程的原理與資訊科技的技術，可以幫助企業在市場環境快速變化下，迅速掌握企業在經營各項業務與投資決策時所面臨的風險大小與風險承擔能力進而採取適當的避險策略以規避風險。本文建議以建構『風險值風險管理資訊系統』以為解決對策，而就『符合風險管理需要的組織與運作模式』的問題，本文則建議以建構『專業分工、權力制衡、風控獨立、風險績效衡量』的組織運作模式為解決方案。

在台灣即將加入WTO的前提下，各家券商、銀行等金融業者為了提升本身的競爭力不斷追求利潤最大化以及風險最小化為其首要目標，因此風險控管的重要性便與日遽增，風險管理的方法也不斷推陳出新，在眾多的方法中，如何尋求最適自身的方法，便是各家金融業者刻不容緩研究的課題，風險值（Value at Risk）便是近期發展出來的一種風險控管工具。 　本研究以台灣債券組合為例，建構短期與長期公債的投資組合進行評估，研究方法採用一階、二階常態法、偏態修正法、蒙第卡羅模擬法及歷史資料模擬法，並配合不同的信賴水準、移動視窗及不同的利率期間結構及標準差估計法，對債券投資組合進行比較分析與驗証。在風險值驗證方面，則採用回溯測試與前向測試兩種驗證方法加上統計學上的平均值與變異數兩種方法，分別對上述不同的模型方法作驗證。