High-dimensional GARCH process segmentation with an application to Value-at-Risk

Models for financial risk often assume that underlying asset returns are stationary. However, there is strong evidence that multivariate financial time series entail changes not only in their within-series dependence structure, but also in the cross-sectional dependence among them. In particular, the stressed Value-at-Risk of a portfolio, a popularly adopted measure of market risk, cannot be gauged adequately unless such structural breaks are taken into account in its estimation. We propose a method for consistent detection of multiple change points in high-dimensional GARCH panel data set where both individual GARCH processes and their correlations are allowed to change over time. We prove its consistency in multiple change point estimation, and demonstrate its good performance through simulation studies and an application to the Value-at-Risk problem on a real dataset. Our methodology is implemented in the R package segMGarch, available from CRAN

Fundamental review of the trading book: impact assessment on banks capital requirements under the internal models approach

This study assesses the impact of the FRTB on bank’s regulatory capital requirements for market risk, considering the Internal Models Approach. To this end, the capital requirement based on the current approach is compared with the capital requirement required with the implementation of the FRTB, through the analysis of a stylized portfolio. In order to assess whether the asset structure of the portfolio affects this result, as sensitivity analysis was also carried out, by changing the relative weights of some asset classes on the portfolio in relation to the baseline scenario. The results of this investigation show that the overall Expected Shortfall, as a standalone measure, implies a higher market risk capital charge when compared to the sum of the Value at Risk and Stressed Value at Risk measures. Both the diversifiable and non-diversifiable components of the Expected Shortfall contribute to such increase, being the latter the main responsible. Regarding the market risk capital requirement considering the computation of all measures over the preceding 60 business days and the effect of the multiplication factor inherent to each regulation, the market risk capital requirement is higher under the current regulation for the baseline scenario and for the scenario with an increase in equity positions. For the scenario with an increase in bonds positions, the market risk capital requirement is higher under the FRTB, yet in a slight way.Este estudo avalia o impacto do FRTB nos requisitos de capital regulamentar dos bancos para risco de mercado, considerando a Abordagem de Modelos Internos. Para tal, o requisito de capital baseado na abordagem atual é comparado com o requisito de capital exigido com a implementação do FRTB, através da análise de uma carteira estilizada. De modo a avaliar se a estrutura de ativos da carteira afeta o resultado desta comparação, foi também efetuada uma análise de sensibilidade, através da alteração dos pesos relativos de algumas classes de ativos na carteira em relação ao cenário de base. Os resultados desta investigação evidenciam que o Expected Shortfall, por si só, implica um requisito de capital para risco de mercado mais elevado quando comparado com a soma das medidas Value at Risk e Stressed Value at Risk. Ambas as componentes diversificável e não diversificável do Expected Shortfall contribuem para tais aumentos, sendo esta última a principal responsável. Em relação ao requisito de capital para risco de mercado considerando o cálculo destas três medidas nos últimos 60 dias anteriores e o efeito do fator de multiplicação inerente a cada regulamentação, este é superior no âmbito da regulamentação atual para o cenário de base e para o cenário com um aumento nas posições de ações. Para o cenário com um aumento nas posições de obrigações, o requisito de capital é superior no âmbito do FRTB, embora de forma ligeira

The Spectral Stress VaR (SSVaR)

URL des Documents de travail : http://centredeconomiesorbonne.univ-paris1.fr/documents-de-travail/Documents de travail du Centre d'Economie de la Sorbonne 2015.52 - ISSN : 1955-611XOne of the key lessons of the crisis which began in 2007 has been the need to strengthen the risk coverage of the capital framework. In response, the Basel Committee in July 2009 completed a number of critical reforms to the Basel II framework which will raise capital requirements for the trading book and complex securitisation exposures, a major source of losses for many international active banks. One of the reforms is to introduce a stressed value-at-risk (VaR) capital requirement based on a continuous 12-month period of significant financial stress (Basel III (2011) [1]. However the Basel framework does not specify a model to calculate the stressed VaR and leaves it up to the banks to develop an appropriate internal model to capture material risks they face. Consequently we propose a forward stress risk measure “spectral stress VaR” (SSVaR) as an implementation model of stressed VaR, by exploiting the asymptotic normality property of the distribution of estimator of VaR p. In particular to allow SSVaR incorporating the tail structure information we perform the spectral analysis to build it. Using a data set composed of operational risk factors we fit a panel of distributions to construct the SSVaR in order to stress it. Additionally we show how the SSVaR can be an indicator regarding the inner model robustness for the bank

Непараметрический метод вычисления величины условной напряженности при наличии риска

We consider the Value at Risk (VaR) of a portfolio under stressed conditions. In practice, the stressed VaR (sVaR) is commonly calculated using the data set that includes the stressed period. It tells us how much the risk amount increases if we use the stressed data set. In this paper, we consider the VaR under stress scenarios. Technically, this can be done by deriving the distribution of profit or loss conditioned on the value of risk factors. We use two methods; the one that uses the linear model and the one that uses the Hermite expansion discussed by Marumo and Wolff (2013, 2016). Numerical examples shows that the method using the Hermite expansion is capable of capturing the non-linear effects such as correlation collapse and volatility clustering, which are often observed in the markets.Рассматривается оценка рисковой стоимости в условиях напряженности. На практике напряженная величина риска обычно рассчитывается с использованием набора данных, включающего напряженный период. Это говорит о том, насколько возрастает риск, если мы используем данные в условиях напряженности. В данной работе мы рассматриваем величину риска (VaR) при напряженных сценариях. Технически это можно сделать, получив распределение прибыли или убытка, обусловленное величиной факторов риска. Мы используем два метода: один, который использует линейную модель, и другой, который использует распределение по Эрмиту, рассмотренный Марумо и Вольфом (2013, 2016). Численные примеры показывают, что метод распределения по Эрмету способен фиксировать нелинейные эффекты, такие как корреляционный коллапс и кластеризация волатильности, которые часто наблюдаются на рынках

Preparing for Basel IV : why liquidity risks still present a challenge to regulators in prudential supervision (II)

Whilst the predecessor (Part I) to this paper addresses criticisms and challenges which have arisen in response to recent Basel Committee's initiatives aimed at addressing capital and liquidity standards, the present paper highlights further measures which are being introduced by the Basel Committee to address such criticisms and challenges. As well as presenting and drawing attention to proposals which could serve as means of addressing challenges presented by liquidity risks, Part I of the paper concludes with the result that market based regulation is an essential and vital tool in the Basel Committee's efforts to address some of the challenges presented by liquidity risks. The present paper highlights the Basel Committee's acknowledgement of this conclusion. Furthermore, it draws attention to other areas which are considered to constitute fertile substrates for purposes of future research. This paper will also illustrate why the potential of banking regulations and disclosure requirements to impact risk taking levels is not only dependent on certain factors such as the dissemination of information to appropriate recipients, appropriate volume of disseminated information, when to disseminate such information, but also on other factors such as ownership structures and effective corporate governance measures aimed fostering monitoring, supervision and accountability.liquidity risks; systemic risks; capital; standards; Basel III; moral hazard; disclosure; information; Liquidity Coverage Ratio (LCR); Net Stable Funding Ratio (NSFR); accountability; corporate governance

Preparing for Basel IV – Why Liquidity Risks Still Present a Challenge to Regulators in Prudential Supervision.

This paper considers and assesses various explanations attributed as principal factors of the recent Financial Crisis. In particular, it focuses on two principal regulatory tools which constitute the basis of the framework promulgated by recent Basel Committee's initiatives, that is, Basel III. These two regulatory tools being capital and liquidity requirements. Various conclusions have been put forward to explain what triggered the recent Financial Crisis. This paper aims to explain why the Basel Committee's liquidity requirements and present proposals aimed at addressing liquidity risks, still represent a very modest milestone in efforts aimed at addressing challenges in prudential regulation and supervision. Even though problems attributed to capital adequacy requirements are considered by many authorities to have triggered the recent Crisis, the paper will highlight how runs on banks are triggered by liquidity crises and that liquidity risks cannot be isolated from systemic risks. In so doing, it will incorporate the roles assumed by information asymmetries and market based regulation – hence elaborate on how market based regulation could serve to address problems which trigger liquidity risks. Imperfect knowledge being a factor which is contributory to liquidity crises and bank runs, and market based regulation being essential in facilitating disclosure - since the Basel Committee's focus on banks and prudential supervision cannot on its own, address the challenges encountered in the present regulatory environment. Furthermore, it will address measures and proposals which could serve as bases for future regulatory reforms - as well as criticisms and challenges still encountered by recent Basel Committee initiatives

Preparing for Basel IV: why liquidity risks still present a challenge to regulators in prudential supervision

This paper considers and assesses various explanations attributed as principal factors of the recent Financial Crisis. In particular, it focuses on two principal regulatory tools which constitute the basis of the framework promulgated by recent Basel Committee's initiatives, that is, Basel III. These two regulatory tools being capital and liquidity requirements. Various conclusions have been put forward to explain what triggered the recent Financial Crisis. This paper aims to explain why the Basel Committee's liquidity requirements and present proposals aimed at addressing liquidity risks, still represent a very modest milestone in efforts aimed at addressing challenges in prudential regulation and supervision. Even though problems attributed to capital adequacy requirements are considered by many authorities to have triggered the recent Crisis, the paper will highlight how runs on banks are triggered by liquidity crises and that liquidity risks cannot be isolated from systemic risks. In so doing, it will incorporate the roles assumed by information asymmetries and market based regulation – hence elaborate on how market based regulation could serve to address problems which trigger liquidity risks. Imperfect knowledge being a factor which is contributory to liquidity crises and bank runs, and market based regulation being essential in facilitating disclosure - since the Basel Committee's focus on banks and prudential supervision cannot on its own, address the challenges encountered in the present regulatory environment. Furthermore, it will address measures and proposals which could serve as bases for future regulatory reforms - as well as criticisms and challenges still encountered by recent Basel Committee initiatives.capital; liquidity; Basel III; Basel Committee; lender of last resort; banks; insurance; securities; information asymmetry; market based regulation; bail outs; disclosure; moral hazard; Dodd Frank Act; Financial Crisis

Reverse stress testing: Identifying weaknesses to prevent failures

This dissertation uses a methodology for attributing a stock portfolio most likely negative scenarios given a pre-defined loss. Using an extensive dataset spanning from 2007 through 2019, we calculated stock returns and their sample covariance matrix is estimated to obtain the portfolio Value at Risk (VaR). Due to idiosyncratic risk, we aggregate the returns into their corresponding indices to obtain the systematic component (the one explained by the market) and, afterwards, the Systematic Value at Risk was determined. Backward induction is then applied. Considering that returns follow a multivariate normal distribution, we derive the main scenario which could lead to the calculated VaR or even to a worst loss – the decision is up to the user. Reverse Stress Testing should be used as a framework, otherwise the risk manager could simply recalculate the VaR for different confidence intervals and investigate the evolution of the corresponding risk factors. Thus, the objective is to find multiple plausible scenarios –not only the most probable one. Principal component analysis (PCA) is applied to identify additional, less likely scenarios. These scenarios are linked to the basis scenario, which ensures plausibility. The relative likelihood is then defined manually as 0.1, meaning the central scenario is ten times more likely than the less likely one. Consequently, four scenarios were generated along with the calculation of their corresponding likelihoods. Overall, we identify the most probable loss scenarios for our portfolio given an input loss. Additionally, we explore the methodology further to determine scenarios under market extreme volatility events.Esta dissertação aplica uma metodologia que identifica as perdas mais prováveis de uma carteira de ações, considerando como input uma perda definida. Através da utilização de um extenso conjunto de dados correspondentes ao período de 2007 até 2019, são calculados os retornos das ações e a matriz de variâncias-covariâncias é estimada de forma a obter o Value at Risk (VaR). Devido ao risco idiossincrático, os retornos foram agregados em função dos índices correspondentes, a fim de obter uma componente sistemática, i.e., explicada pelo mercado, procedendo-se ao cálculo do Systematic VaR. Invertendo o processo, e considerando que os retornos seguem uma distribuição normal multivariada, obtém-se um cenário central que dá origem ao Systematic VaR calculado, ou caso o utilizador entenda, uma perda superior. Posteriormente, o objetivo passará por encontrar diversos cenários plausíveis – e não apenas o mais provável. O método Principal Component Analysis (PCA) permitirá a obtenção de cenários menos prováveis. Estes encontram-se relacionados ao cenário mais provável através de verosimilhança, o que garante a plausibilidade dos cenários gerados. A verosimilhança relativa é definida manualmente como 0.1, refletindo um cenário central dez vezes mais provável que o menos provável. Assim, foram gerados quatro cenários, juntamente com o cálculo das respetivas verosimilhanças. Em suma, identificamos os cenários de perda mais prováveis para a carteira em questão, considerando uma perda como input. Adicionalmente, exploramos a metodologia de forma a determinar outros cenários em contexto de extrema volatilidade no mercado