Market Risk Capital Requirements Research Articles

A comparison of market risk measures from a twofold perspective: accurate and loss function

Under the new regulation based on Basel solvency framework, known as Basel III and Basel IV, financial institutions must calculate the market risk capital requirements based on the Expected Shortfall (ES) measure, replacing the Value at Risk (VaR) measure. In the financial literature, there are many papers dedicated to compare VaR approaches but there are few studies focusing in comparing ES approaches. To cover this gap, we have carried out a comprenhensive comparative of VaR and ES models applied to IBEX-35 stock index. The comparison has been carried out from a twofold perspective: accurate risk measure and loss functions. The results indicate that the method based on the conditional Extreme Value Theory (EVT) is the best in estimating market risk, outperforming Parametric method and Filter Historical Simulation.

Fuelling fire sales? Prudential regulation and crises: evidence from the Italian market

The ECB announcement to reduce capital requirements for market risk to smooth pro-cyclicality, published in April 2020, is a good starting point to discuss the impact of regulation on individual banks on the stability of the whole banking and financial system.A large number of theoretical articles and a few empirical papers back the existence of an amplification effect on market volatility caused by the use of risk management measures (e.g. value-at-risk, VaR, for market risk) for regulatory purposes. However, to the best of my knowledge, no paper has empirically investigated the direct relation between the level of tightness of VaR risk limits and market volatility.In this article, I show that market volatility is positively related to past values of the measure of the tightness of the market risk limit, with an overshooting process of adjustment toward equilibrium. The analysis is limited to Italy. The empirical results, based on a unique dataset of VaR values and on other publicly available market data, are in line with the theoretical findings and are novel empirical evidence. They open the way to additional research on how to manage the channels of transmission of the amplification and overshooting effects from the risk management measure to systemic variables, to avoid unintended consequences of the application of individual supervision measures on the whole system.

Banks' Backtesting Exceptions during the COVID-19 Crash: Causes and Consequences

Banks' numerous and simultaneous backtesting exceptions in March 2020, during the COVID-19-related market crash, would have amplified their already-large spike in market risk capital requirements in the absence of regulatory intervention. This note provides background on how backtesting exceptions affect capital requirements generally, the source of those exceptions during the COVID-19 crash, and how regulators exercised discretion to mitigate the unintended capital increase.

Modeling of EUR-MAD and USD-MAD Exchange Rates

Currency Risk can be very problematic for our companies, so it is important for Moroccan companies exposed to currency risk to be able to measure this exposure in order to manage it properly. The objective of this paper is to estimate the foreign exchange risk EUR / MAD and USD / MAD according to Basel II recommendations on capital requirements for market risks. To quantify the potential capital loss on foreign exchange risk, the experts use the VAR (Value At Risk) model to determine the potential loss that could impact the firm's performance. We applied the VAR concept to estimate the foreign exchange risk of the Moroccan Dirham against the Euro and then against the US Dollar. Three standard VAR calculation models most used by risk managers (historical method, parametric method and Monte Carlo simulation) were studied and then applied to a historical exchange rate EUR / MAD and USD / MAD over the period from 02/01/2017 to 31/12/2018 and on a database of 520 observations. Our study revealed that the Monte Carlo simulation method recorded the highest value of the VaR which is established at 281.170 DH against the parametric method which is limited to 204.100 DH. The average of the three methods is around 246.170 DH which represents a loss percentage of 0.91% of the total value of the portfolio. However, to complete this study, we believe that it is wise to use stress testing and backtesting tests which make it possible to validate this VaR model and to meet the standards set by the Basel Committee. With a confidence level of 99%, we found three exceedances of the losses compared to the values ​​of the average VaR. For a 95% confidence level, we have 16 exceedances. The maximum loss corresponds to the date of: 24/08/2017, explained by the sharp drop in the EUR / MAD rate, from 11.235 to 11.156 DH.

FRTB and Fat Tails

We calculate the probability of returns exceeding a multiple of Expected Shortfall for fat-tailed portfolios. Our results show that, taken in isolation, the Basel 3 FRTB Market Risk capital requirements are insufficient to prevent a large number of insolvencies. The impact of applying a cutoff to the tail distribution is also examined.

Applying the Pre-Commitment Approach to bottom-up stress tests: A new old story

The Pre-Commitment Approach (PCA) to capital requirements was developed and promoted by the US Federal Reserve in the 1990s. The proposal was conceived as an alternative to the market-risk capital requirements based on internal models then under discussion, and eventually adopted, by the Basel Committee. Notwithstanding the Fed continued to support the PCA, the idea was abandoned, probably because it was considered too optimistic to allow banks determine the level of capital. In this paper, we study the possibility to adapt the PCA as to work as a complementary (and not alternative) tool applied to the banking book Prudential Regulation. In particular, we explore the application of this approach to a well-known issue in the context of the Stress tests: the top-down vs bottom-up debate. We focus on bottom-up stress tests and suggest creating a system of monetary penalties (charges) proportional to the difference between the expected and the realised losses of a portfolio. The charges would aim to induce model developers to reveal their best forecasts. We show that this approach can be seen as an adaptation of the pre-commitment approach (PCA) but also as an application of the penalty criterion proposed by the Italian mathematician de Finetti as the foundation of the subjectivist definition of probability. We explain how the PCA could be adapted to bottom-up stress testing and provide a practical example of the application of our proposal to the banking book. What emerges is that the PCA can indeed mitigate banks’ incentives to provide underestimated measures of risk under the adverse scenario and thus better align the incentives of banks and supervisors.

The impact of liquidity on portfolio value-at-risk forecasts

ABSTRACTHistorical crisis events have highlighted the insufficiency of Value-at-Risk (VaR) as a measure of market risk because such metric does not take liquidity into account. Unlike previous studies analyzing with only a single asset, we examine the impact of liquidity on computing VaR forecasts from a portfolio level. To this end, we use multivariate GARCH-t and GJR-GARCH-t models, as compared with univariate models, to seize the liquidity property embedded in individual stock returns and evaluate their accuracy and efficiency in computing VaR forecasts for portfolios with different liquidity levels.The empirical results indicate that computing portfolio VaR forecasts with multivariate models outperform the univariate models for full and subsample periods in terms of accuracy and efficiency evaluations, in particular for less-liquid portfolios. These results suggest the importance of liquidity in computing portfolio VaR forecasts. Ignorance of the impact of liquidity in computing portfolio VaR forecasts might result in inadequate coverage and insufficient market risk capital requirements.

Recent Issues in the Implementation of the New Basel Minimum Capital Requirements for Market Risk

The Basel Committee suggested new ways of dealing with market risk in banks’ trading and banking books, in its October 2013 consultative paper, and subsequent versions published thereafter, for revised market risk framework FRTB. The Basel Committee estimates that the new rules will result in an approximate median capital increase of 22% and a weighted average capital increase of 40% (BCBS 2016), compared with the current framework. Budget reports on FRTB implementation range from costs of 5-million USD to 250-million USD. Key changes can be found in the internal model approach, in the standard rules and in the approval process. Significant changes introduced by the FRTB include stricter separation of the trading and banking book. Regardless of whether they use standardized or internal models, banks will need to review their portfolios to determine if existing classifications of instruments and desks as trading or banking book are still applicable, or whether a revision of desk structure is needed. In its article ‘Critical appraisal of the Basel fundamental review of the trading book regulation’ (Orgeldinger 2017) the theoretical foundations of the internal model approach IMA were analysed and the criticisms for FRTB risk models were investigated. A recent onslaught of rules is rendering the existing timeline for implementation practically impossible. In this article we present and critically evaluate different approaches to implement the new rules suggested by academics and major consulting companies.

Computation of market risk measures with stochastic liquidity horizon

The Basel Committee of Banking Supervision has recently set out the revised standards for minimum capital requirements for market risk. The Committee has focused, among other things, on the two key areas of moving from Value-at-Risk (VaR) to Expected Shortfall (ES) and considering a comprehensive incorporation of the risk of market illiquidity by extending the risk measurement horizon. The estimation of the ES for several trading desks and taking into account different liquidity horizons is computationally very involved. We present a novel numerical method to compute the VaR and ES of a given portfolio within the stochastic holding period framework. Two approaches are considered, the delta–gamma approximation, for modelling the change in value of the portfolio as a quadratic approximation of the change in value of the risk factors, and some of the state-of-the-art stochastic processes for driving the dynamics of the log-value change of the portfolio like the Merton jump–diffusion model and the Kou model. Central to this procedure is the application of the SWIFT method developed for option pricing, that appears to be a very efficient and robust Fourier inversion method for risk management purposes.

Market Risk and Volatility Weighted Historical Simulation after Basel III

Regulatory capital requirements for market risk, also known as the Fundamental Review of the Trading Book (FRTB), were disclosed by the Basel Committee on January 2016. This major overhaul of the Basel 2.5 framework challenges risk model specification and backtesting. Given the prevalence of historical simulation approach within large financial institutions, we focus on the Filtered (Volatility Weighted) Historical Simulation (VWHS) approach associated with a EWMA volatility filter. Volatility dynamics is then directed by a single parameter. We discuss how this decay parameter, chosen within a reasonable range, at banks’ discretion, impacts capital metrics, backtesting statistics, as prescribed by the Basel Committee, and fouls the regulatory benchmarking of internal risk models. We show a trade-off between the resilience of risk models to periods of turmoil and the magnitude of capital metrics. Under the new regulatory rules, this would favour plain historical simulation, as compared with filtered or volatility weighed historical simulation. Understanding why, might be helpful for regulated banks, regarding the management of their market risk models, and supervisors involved in internal model approval.

Model Risk in FRTB: The Case of the Default Risk Charge

The recent Fundamental Review of the Trading Book (FRTB) resulted in revised standards for capital requirements for market risks in a bank’s trading book. As part of the ruleset, default risk needs to be measured and capitalized through a dedicated Default Risk Charge (DRC). With the DRC as an extreme tail risk measure at 99.9% confidence level for portfolio default losses at a one-year horizon, there is inherent model risk associated with the reflection of joint defaults. Wilkens and Predescu (2017) proposed an overall framework for modeling the DRC that is based on a Gaussian factor copula model to capture the coincidence of defaults. This paper assesses the resulting model risk by analyzing alternative copulas (Gaussian, Student t, and Clayton) and the influence on the DRC figures with the help of a set of example portfolios. The copula choice can affect the DRC considerably, especially for directional and less diversified portfolios; the influence on typical larger-scale, diversified portfolios is much less pronounced. The uncertainty arising from the calibration of any copula from only a few data points – as implied by the regulation – is at least of equal importance as the selection of the dependence model itself.

Model risk in the Fundamental Review of the Trading Book: the case of the Default Risk Charge

The recent Fundamental Review of the Trading Book (FRTB) resulted in revised standards for capital requirements for market risks in a bank’s trading book. As part of the ruleset, default risk needs to be measured and capitalized through a dedicated Default Risk Charge (DRC). With the DRC as an extreme tail risk measure at 99.9% confidence level for portfolio default losses at a one-year horizon, there is inherent model risk associated with the reflection of joint defaults. Wilkens and Predescu (2017) proposed an overall framework for modeling the DRC that is based on a Gaussian factor copula model to capture the coincidence of defaults. This paper assesses the resulting model risk by analyzing alternative copulas (Gaussian, Student t, and Clayton) and the influence on the DRC figures with the help of a set of example portfolios. The copula choice can affect the DRC considerably, especially for directional and less diversified portfolios; the influence on typical larger-scale, diversified portfolios is much less pronounced. The uncertainty arising from the calibration of any copula from only a few data points – as implied by the regulation – is at least of equal importance as the selection of the dependence model itself.

A Statistical Study of the Revised FRTB's P&L Attribution Tests

One of the key challenges implied by the upcoming regulatory framework for minimum market risk capital requirements, known as FRTB (Fundamental Review of Trading Book), is the PL attribution (PLA) tests. PLA tests constitute a game-changer in the way risk engine and models are assessed for effectiveness and accuracy by regulators to base the qualification for the ‘internal model approach’ for market risk capital. The initial design of these tests, however, has raised concerns from the industry that pointed to a punitive behavior and room for improvements. In this context, the Basel Committee has proposed a completely revamped test design in their March 2018’s Consultative Document. In this paper, we first provide a formal statistical analysis of the performances and the behavior of this newly proposed PLA test as compared to the old one. Our findings suggest that although the revised test design addresses many of the raised concerns, there are still some improvement opportunities, particularly in what relates to the conceptual treatment of hedged portfolios. We also provide a detailed statistical study to orient the selection of the homogeneous PLs distributions test to be retained among the offered alternatives.

The Role of the Skewed Distributions in the Framework of Extreme Value Theory (EVT)

In this paper, we analyze the role of the heavy tail and skewed distribution in market risk estimation (Value at Risk (VaR)). In particular, we are interested in knowing if in the framework of the conditional extreme value theory, the estimation of the volatility model below heavy tail and skewed distribution contributes to improve the VaR estimation respect to these obtained from a symmetric distribution. The study has been carried out for six individual assets belonging to the digital sector: ADP, Amazon, Cerner, Apple, Microsoft and Telefonica. The analysis period runs from January 1st, 2008 to the end of December 2013. Although the evidence found is a little bit weak, the results obtained seem to indicate that the heavy tail and skewed distribution outperforms the symmetric distribution both in terms of accuracy VaR estimations as in terms of firm’s loss function. Furthermore, the market risk capital requirements fixed on the base of the VaR estimations are also lowest below a skewed distribution.

Basel Committee on Banking Supervision Consultative Document Simplified alternative to the standardised approach to market risk capital requirements - June 2017

Basel Committee on Banking Supervision Consultative Document Simplified alternative to the standardised approach to market risk capital requirements - June 2017

Critical Analysis of the New Basel Minimum Capital Requirements for Market Risk

In its October 2013’s consultative paper for a revised market risk framework (FRTB), and subsequent versions published thereafter, the Basel Committee suggests new ways of dealing with market risk in banks’ trading and banking books. The Basel Committee estimates that the new rules will result in an approximate median capital increase of 22% and a weighted average capital increase of 40% [1], compared with the current framework. Key changes can be found in the internal model approach, in the standard rules and in the scope/approval process. Among the significant changes that are being introduced by the FRTB is a stricter separation of the trading book and banking book. Regardless of whether they use standardised or internal models, banks will need to review their portfolios to determine if existing classifications of instruments and desks as trading book or banking book are still applicable or whether a revision of desk structure is needed. In this article, we analyse the theoretical foundations of the internal model approach (IMA), which are the stressed expected shortfall, liquidity adjustments, default & migration risk and non-modellable risk factors. We thoroughly investigate the criticisms for Internal Risk Model (IMA) and the introduction of a standardised floor, the sensitivity based approach (SBA) with Delta, Vega and Curvature, shock scenarios and the aggregation with asymmetric correlation and reflection of basis/default risk.

An application of extreme value theory in estimating liquidity risk

The last global financial crisis (2007–2008) has highlighted the weaknesses of value at risk (VaR) as a measure of market risk, as this metric by itself does not take liquidity risk into account. To address this problem, the academic literature has proposed incorporating liquidity risk into estimations of market risk by adding the VaR of the spread to the risk price. The parametric model is the standard approach used to estimate liquidity risk. As this approach does not generate reliable VaR estimates, we propose estimating liquidity risk using more sophisticated models based on extreme value theory (EVT). We find that the approach based on conditional extreme value theory outperforms the standard approach in terms of accurate VaR estimates and the market risk capital requirements of the Basel Capital Accord.

Default risk charge: modeling framework for the “Basel” risk measure

Revised standards for capital requirements for market risks in a bank’s trading book have been issued as a result of the Fundamental Review of the Trading Book. Under the new standards, default risk needs to be measured and capitalized through a dedicated Default Risk Charge (DRC). While quantitative impact studies are ongoing and banks are preparing for these regulatory changes, this paper is the first to present a modeling framework for the DRC measure that projects losses over a one-year capital horizon at a 99.9% confidence level. The article discusses selected risk factor models to derive simulation-based loss distributions and the associated default risk figures. Model properties, implementation aspects and a comparison to the Standardised Approach for default risk are explored through the use of example portfolios.

Compliance of Basel III Norms: Comparison of selected Nationalised, Private and Foreign Banks

Paper compares compliance of BASEL III norms as given by RBI by selected nationalized, private and foreign banks. There are three categories of banks in India-Public, Private and Foreign banks. Nine banks, three in each category were selected. Data related to 3 factors of Basel III norms i.e., Capital Adequacy requirements, Supervisory Review and Market Discipline for past 10 years i.e.3 years for Basel I norms, 6 years before and 3 years after the adoption of Basel III norms was collected. It was found out that significant difference was observed in case of Tier 1 capital under Basel II and Basel III norms because the capital of the banks had to be raised in order to meet the requirements of new capital adequacy norms. Significant difference was also observed in case of CRAR of the nationalised and private sector banks. Total capital adequacy ratio of the banks was mainly affected by risk weighted assets of the banks. The more the risk weighted assets of the bank the higher is the capital to risk weighted assets ratio (CRAR). The credit risk capital requirements of private sector banks, market risk capital requirements of nationalised banks and operational risk capital requirements of private sector banks witnessed significant differences under Basel II norms and Basel III norms.

Computation of Market Risk Measures with Stochastic Liquidity Horizon

The Basel Committee of Banking Supervision has recently set out the revised standards for minimum capital requirements for market risk. The Committee has focused, among others, on the two key areas of moving from Value-at-Risk (VaR) to Expected Shortfall (ES) and considering a comprehensive incorporation of the risk of market illiquidity by extending the risk measurement horizon. The estimation of the ES for several trading desks and taking into account different liquidity horizons is computationally very involved. We present a novel numerical method to compute the VaR and ES of a given portfolio within the stochastic holding period framework. Two approaches are considered, the delta-gamma approximation, for modelling the change in value of the portfolio as a quadratic approximation of the change in value of the risk factors, and some of the state-of-the-art stochastic processes for driving the dynamics of the log-value change of the portfolio like the Merton jump-diffusion model and the the Kou model. Central to this procedure is the application of the SWIFT method developed for option pricing, that appears to be a very efficient and robust Fourier inversion method for risk management purposes.