Market Risk Capital Requirements Research Articles

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.

Market risk management in a post-Basel II regulatory environment

We propose a novel method of Mean-Capital Requirement portfolio optimization. The optimization is performed using a parallel framework for optimization based on the Nondominated Sorting Genetic Algorithm II. Capital requirements for market risk include an additional stress component introduced by the recent Basel 2.5 regulation. Our optimization with the Basel 2.5 formula in the objective function produces superior results to those of the old (Basel II) formula in stress scenarios in which the correlations of asset returns change considerably. These improvements are achieved at the expense of reduced cardinality of Pareto-optimal portfolios. This reduced cardinality (and thus portfolio diversification) in periods of relatively low market volatility may have unintended consequences for banks’ risk exposure.

Reducing Basel III Capital Requirements with Dynamic Conditional Correlation and Monte Carlo Simulation

Value-at-Risk (VaR) and Conditional-Value-at-Risk (CVaR) are popular risk measure in portfolio optimisation and market regulations. However, so far little research has been done on how these risk measures reduce the Basel III market risk capital requirements. This paper analyses the efficiency of empirical, parametric and simulation based VaR and CVaR optimised portfolios on the regulatory capital requirements. Furthermore, we show how the Population-Based Incremental Learning algorithm can be used to solve the constraint optimisation problems. We find that the parametric and empirical distribution assumption generate similar results and neither of them clearly outperforms the other. Our results indicate that portfolios optimised with a multivariate Dynamic Conditional Correlation simulation approach reduce the capital requirements by about 11%.

Market Risk Management in a Post-Basel II Regulatory Environment

We propose a novel method of Mean-Capital Requirement portfolio optimization. The optimization is performed using a parallel framework for optimization based on the Non-dominated Sorting Genetic Algorithm II. Capital requirements for market risk include an additional stress component introduced by the recent Basel 2.5 regulation. Our optimization with the Basel 2.5 formula in the objective function produces superior results to those of the old (Basel II) formula in stress scenarios in which the correlations of asset returns change considerably. These improvements are achieved at the expense of reduced cardinality of Pareto-optimal portfolios. This reduced cardinality (and thus portfolio diversification) in periods of relatively low market volatility may have unintended consequences for banks’ risk exposure.

Incremental Default Risk (IDR): Modeling Framework for the 'Basel 4' 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.

Minimizing Basel III Capital Requirements with Unconditional Coverage Constraint

SummaryThe new Basel III framework increases the banks’ market risk capital requirements. In this paper, we introduce a new risk management approach based on the unconditional coverage test to minimize the regulatory capital requirements. Portfolios optimized with our new minimum capital constraint successfully reduce the Basel III market risk capital requirements. In general, portfolios with value‐at‐risk and conditional‐value‐at‐risk objective functions and underlying empirical distribution yield better portfolio risk profiles and have lower capital requirements. For the optimization we use the threshold‐accepting heuristic and the common trust‐region search method.

Portfolio Optimization Under Solvency II: Implicit Constraints Imposed by the Market Risk Standard Formula

We consider the issue of optimizing an insurance company's asset allocation in the context of portfolio theory when the firm needs to adhere to the market risk capital requirements of Solvency II. The discussion starts with a brief review of the standard formula and the introduction of a parsimonious partial internal model. Subsequently, we estimate empirical risk-return profiles for the main asset classes held by insurers and run a quadratic optimization program to derive nondominated frontiers with budget, short-sale, and investment constraints. We then compute the respective capital charges under both solvency models and identify those efficient portfolio compositions that are permitted for an exogenously given amount of equity. Finally, we consider a systematically selected set of inefficient portfolios and check their admissibility, too. Our results document that the standard formula is unable to distinguish investments on the basis of risk-return profiles and does hence not produce economically sensible results. Therefore, the introduction of Solvency II in its current form might cause severe asset management biases in the European insurance sector.

Portfolio Optimization Under Solvency II: Implicit Constraints Imposed by the Market Risk Standard Formula

AbstractWe optimize a life insurance company's asset allocation in the context of classical portfolio theory when the firm needs to adhere to the market risk capital requirements of Solvency II. The discussion starts with a brief review of the standard formula and the introduction of a parsimonious partial internal model. Subsequently, we estimate empirical risk–return profiles for the main asset classes held by European insurers and run a quadratic optimization program to derive nondominated frontiers with budget, short‐sale, and investment constraints. We then compute the capital charges under both solvency models and identify those efficient portfolio compositions that are permitted for an exogenously given amount of equity. Finally, we consider a systematically selected set of inefficient portfolios and check their admissibility, too. Our results show that the standard formula suffers from severe shortcomings that interfere with economically sensible asset management decisions. Therefore, the introduction of Solvency II in its current form is likely to have an adverse impact on certain parts of the European insurance sector.

Cash Flow at Risk: A Tool for Financial Planning

Abstract The company's cash levels can vary considerably over time depending on, payment and collection cycle. Made full and timely payment of sufficient operating capital to keep and disruption of operations, it is important to predict cash levels correctly.Cash Flow at Risk; as well as financial strategies and long-term investment planning based on the scientific basis of creation, it provides an assessment of capital structure. Through different scenarios that may occur rarely even considers events. Through Cash Flow at Risk calculations on a specific date how much cash levels may fall within the confidence interval, how can rise under favorable market conditions can be analyzed. As a result of this analysis, to meet the level of cash payments, the probability of occurrence of certain changes in the cash flow, working capital requirements for market risk are determined in consideration of cash planning is done.The purpose of the study is to evaluate the risks that may arise due to the deviation of cash flows. In this context, based on 2014 budget of a sample business, cash flow at risk will be calculated. To manage the liquidity risk of sample business, an analysis will be carried out in two different scenarios whether to use or not to use a credit.

Volatility Forecasts: Do Volatility Estimators and Evaluation Methods Matter?

This study investigates the volatility forecasting abilities of return‐based and range‐based estimators for two stock indices and two individual stocks in the U.S. stock market. The forecasting performances are evaluated by two robust statistical loss functions, and further by financial applications in risk management and option pricing. Consistent with previous studies, the range‐based volatility forecasts outperform in terms of statistical evaluation, value‐at‐risk calculation, and option pricing. However, return‐based volatility forecasts prove superior in the evaluation of market risk capital requirements. © 2013 Wiley Periodicals, Inc. Jrl Fut Mark 34:1077–1094, 2014

Capital requirements for market risks

PurposeThe financial crisis has led the Basel Committee to improve the system of capital requirements for market risks. This paper aims to investigate the effects of different models to estimate the market risk in the management of the trading book. The study takes into account the events occurring in the financial markets and the new prudential rules.Design/methodology/approachThe author compares different models and proposes an opportunity cost function able to evaluate the cost related to capital requirements. He identified seven asset classes and studies the effects of different models for estimating VaR simulating financial portfolios with increasing risk. The series consists of the daily return from 01/01/2002 to 06/30/2012.FindingsThe results show that it is possible to identify a wide area between aggressive and conservative approach where the bank management must choose. The regulation does not encourage intermediaries to the use of complex models that could better evaluate the risk in financial markets. The revision of the market risk framework increases the capital requirement and reduces the incentive to use models with more predictive power for regulatory purposes.Originality/valueThe work differs from previous contributions for three characteristics: first, it uses a set of extended data and more consistent with the actual operation. Secondly, the author presents an opportunity cost function in order to evaluate the estimation models. Third, he calculates the effect of stressed‐VaR after a year and a half of adoption.

IRC and CRM: Modelling Framework for the ‘Basel 2.5’ Risk Measures

This paper presents a modelling framework for the Incremental Risk Charge (IRC) and Comprehensive Risk Measure (CRM) as the new capital requirements for market risks in a bank's trading book (‘Basel 2.5’). Both are Value-at-Risk-type measures projecting losses over a one-year capital horizon at a 99.9% confidence level and are applicable to credit flow and credit correlation instruments, respectively. With no consensus on industry standards for suitable internal models as yet, the article discusses selected risk factor models to derive simulation-based loss distributions and the associated risk figures. Example calculations and implementation aspects complement the discussion.

Will Solvency II Market Risk Requirements Bite? The Impact of Solvency II on Insurers' Asset Allocation

The European insurance industry is among the largest institutional investors in Europe. Therefore, major reallocations in their investment portfolios due to the new risk-based economic capital requirements introduced by Solvency II would cause significant disruptions in European capital markets and corporate financing. This paper studies whether the new regulatory capital requirements for market risk are a binding constraint for European insurers by comparing the required regulatory capital of the Solvency II standard model with the required rating capital of the Standard & Poor's rating model for market risk for a fictitious, but representative, European-based life insurer. The results show that for a comparable level of confidence, the rating model requires more than 68% more capital than the standard model for the same market risks. Hence, Solvency II seems not to be a binding capital constraint for market risk and thus would not significantly influence the insurance companies' investment strategies. Horing, D. (2012), Will Solvency II market risk requirements bite? The impact of Solvency II on insurers' asset allocation, The Geneva Papers advance online publication 11 July, doi:10.1057/gpp.2012.31

Will Solvency II Market Risk Requirements Bite? The Impact of Solvency II on Insurers’ Asset Allocation

The European insurance industry is among the largest institutional investors in Europe. Therefore, major reallocations in their investment portfolios due to the new risk-based economic capital requirements introduced by Solvency II would cause significant disruptions in European capital markets and corporate financing. This paper studies whether the new regulatory capital requirements for market risk are a binding constraint for European insurers by comparing the required market risk capital of the Solvency II standard model with the Standard & Poor's rating model for a fictitious, but representative, European-based life insurer. The results show that for a comparable level of confidence, the rating model requires 68 per cent more capital than the standard model for the same market risks. Hence, Solvency II seems not to be a binding capital constraint for market risk and thus would not significantly influence the insurance companies’ investment strategies.

Pitfalls in backtesting Historical Simulation VaR models

Historical Simulation (HS) and its variant, the Filtered Historical Simulation (FHS), are the most popular Value-at-Risk forecast methods at commercial banks. These forecast methods are traditionally evaluated by means of the unconditional backtest. This paper formally shows that the unconditional backtest is always inconsistent for backtesting HS and FHS models, with a power function that can be even smaller than the nominal level in large samples. Our findings have fundamental implications in the determination of market risk capital requirements, and also explain Monte Carlo and empirical findings in previous studies. We also propose a data-driven weighted backtest with good power properties to evaluate HS and FHS forecasts. A Monte Carlo study and an empirical application with three US stocks confirm our theoretical findings. The empirical application shows that multiplication factors computed under the current regulatory framework are downward biased, as they inherit the inconsistency of the unconditional backtest.

Pitfalls in Backtesting Historical Simulation VAR Models

Historical Simulation (HS) and its variant, the Filtered Historical Simulation (FHS), are the most widely used Value-at-Risk forecast methods at commercial banks. These forecast methods are traditionally evaluated by means of the unconditional backtest. This paper formally shows that the unconditional backtest is always inconsistent for backtesting HS and FHS models, with a power function that can be even smaller than the nominal level in large samples. Our findings have fundamental implications in the determination of market risk capital requirements, and also explain Monte Carlo and empirical findings in previous studies. We also propose a data-driven weighted backtest with good power properties to evaluate HS and FHS forecasts. Finally, our theoretical findings are confirmed in a Monte Carlo simulation study and an empirical application with three U.S. stocks. The empirical application shows that multiplication factors computed under the current regulatory framework are downward biased, as they inherit the inconsistency of the unconditional backtest.

Practical implications of higher moments in risk management

In this paper the out-of-sample prediction of Value-at-Risk by means of models accounting for higher moments is studied. We consider models differing in terms of skewness and kurtosis and, in particular, the GARCHDSK model, which allows for constant and dynamic skewness and kurtosis. The issue of VaR prediction performance is approached first from a purely statistical viewpoint, studying the properties concerning correct coverage rates and independence of VaR violations. Then, financial implications of different VaR models, in terms of market risk capital requirements, as defined by the Basel Accord, are considered. Our results, based on the analysis of eight international stock indexes, highlight the presence of conditional skewness and kurtosis, in some case time-varying, and point out that asymmetry plays a significant role in risk management.

A Formalized Hybrid Portfolio Replication Technique Applied to Participating Life Insurance Portfolios

The practice of portfolio replication has proven its applicability to market risk management in complete markets through the appropriate modeling of a range of non-linear financial instruments. Replicating portfolios provide an intuitive and operational framework for explaining financial risks of life insurance companies as financial instruments with analytical formula encompassing instruments’ non-linearities, path dependency and specific sensitivities capture financial risks. Carrying out the market risk calculation for life insurance companies requires the replicating portfolio technique as the plan calculation referred to as ‘stochastic in stochastic’ requires immense computational power. For each of the real-world scenarios, the market-consistent values of assets and liabilities on the basis of the replicating portfolio technique are therefore determined. This article presents an enhanced replicating portfolio framework that is of utmost importance for the generation of market risk capital requirements applied to life insurance portfolios embedding options and guarantees. While the classic replication technique requires approximations and expert judgments as there is no clear-cut, easy answer for finding an optimal replicating portfolio providing a superior replication power (i.e. a portfolio composed of a finite number of financial vanilla instruments in an arbitrage-free context out of which the cash-flows best replicate the magnitude and timing of liabilities over the projection term), the proposed approach relies on a formalized framework that leads to build optimal replicating portfolios for participating life insurance business. This paper derives the principles behind the portfolio replication technique and provides explanations and justifications on the parameterization of replicating portfolios via a practical application case. The approach adopted is a hybrid model that combines a 'pure' portfolio replication technique and the curve fitting approach. As a result, the quality of replicating portfolios in extreme capital market environments is tested by means of a comparison with the results of a brute force revaluation incorporating a large range of sensitivities such as EEV, QIS 5 and extreme scenario (close to the economic capital driven scenario) sensitivities. In order to determine the weights of financial instruments, the ordinary least square technique is used to find the best possible portfolio composition that replicates liability cash flows in several market conditions at either the present or terminal value of the projection. Additional enhancement techniques such as a particular adjustment within the singular value decomposition and a scenario filter are introduced to better fit the weights of selected instruments with liability moves. An example of calibration strategy that leads to an optimal replicating portfolio is broadly described in this paper.

Capital Requirements for Latin American Banks in Relation to Their Market Risks: The Relevance of the Basle 1996 Amendment to Latin America

Banks' market or 'trading' risks have increased noticeably over the past years, largely as a result of the growth of liquid assets on banks' balance sheets and the increase in banks' off-balance sheet activities. Well-publicized bank failures and significant capital losses have focussed further attention on these developments. In January 1996, the Basle Committee recommended the imposition of capital charges related to banks` trading risks, and the European Community's Capital Adequacy Directive (CAD) came into force on January 1st, adopting, in part, the Basle Amendment. The G10 countries are committed to full implementation of these recommendations by the end of 1997. This paper reviews the main features of the Basle Amendment, which allows banks a choice between a 'standardized methodology' and the use of their own internal models, subject to the authorization of the relevant supervisor and a set of parameter values. The relevance of this regulation for Latin America is analysed in the light of the region's characteristics. We suggest that these characteristics increase rather than diminish the importance of the implementation of market risk capital requirements in Latin America.

The Incremental Risk Capital Charge - A Challenge for Risk Managers

In responding to the global financial crisis, regulators and industry observers particularly noted that several banks posted losses in their trading books that were considerably greater than their own estimates computed using standard VaR methodology. Some of these losses exceeded those regulatory capital requirements for market risk. In the Basel III framework, the Basel Committee on Banking Supervision responded by proposing to increase the capital requirements for market risk for banks that model specific risk in the trading book through an additional capital requirement based on a stressed market risk VaR estimate complemented by an Incremental Risk Capital (IRC) charge.