Quantitative Risk Management Tools

Trading Market Risk Requirements

In December 2011 we received model approvals, from the BaFin, for the stressed value-at-risk, incremental risk charge and comprehensive risk measure models. These are additional methods we use to measure market risk exposures.

  • Stressed value-at-risk: calculates a stressed value-at-risk measure based on a continuous one year period of significant market stress.
  • Incremental Risk Charge: captures default and credit migration risks in addition to the risks already captured in value-at-risk for credit-sensitive positions in the trading book.
  • Comprehensive Risk Measure: captures incremental risk for the correlation trading portfolio calculated using an internal model subject to qualitative minimum requirements as well as stress testing requirements.
  • Market Risk Standardized Approach: calculates regulatory capital for securitizations and nth-to-default credit derivatives.

Stressed value-at-risk, incremental risk charge and the comprehensive risk measure are calculated for all relevant portfolios. The results from the models are used in the ongoing risk management of the bank, as well as for defining regulatory capital.

Stressed Value-at-Risk

We calculate a stressed value-at-risk measure using a 99 % confidence level and a holding period of one day. For regulatory purposes, the holding period is ten days.

Our stressed value-at-risk calculation utilizes the same systems, trade information and processes as those used for the calculation of value-at-risk. The only difference is that historical market data from a period of significant financial stress (i.e., characterized by high volatilities) is used as an input for the Monte Carlo Simulation. The time window selection process for the stressed value-at-risk calculation is based on the identification of a time window characterized by high levels of volatility and extreme movements in the top value-at-risk contributors. The results from these two indicators (volatility and number of outliers) are combined using chosen weights intended to ensure qualitative aspects are also taken into account (i.e., inclusion of key crisis periods).

Incremental Risk Charge

The incremental risk charge is based on our own internal model and is intended to complement the value-at-risk modeling framework. It represents an estimate of the default and migration risks of unsecuritized credit products over a one-year capital horizon at a 99.9 % confidence level, taking into account the liquidity horizons of individual positions or sets of positions. We use a Monte Carlo Simulation for calculating incremental risk charge as the 99.9 % quantile of the portfolio loss distribution and for allocating contributory incremental risk charge to individual positions. The model captures the default and migration risk in an accurate and consistent quantitative approach for all portfolios. Important parameters for the incremental risk charge calculation are exposures, recovery rates and default probabilities, ratings migrations, maturity, and liquidity horizons of individual positions.

We calculate the incremental risk charge on a weekly basis. The charge is determined as the higher of the most recent 12 week average of incremental risk charge and the most recent incremental risk charge.

The contributory incremental risk charge of individual positions, which is calculated by expected shortfall allocation, provides the basis for identifying risk concentrations in the portfolio.

Liquidity horizons are conservatively set to the time required to sell a position or to hedge all material relevant price risks in a stressed market. Liquidity horizons are specified at product level and reflect our actual practice and experience during periods of systematic and idiosyncratic stresses. We have defined the sets of positions used for applying liquidity horizons in a way that meaningfully reflects the differences in liquidity for each set. Market risk managers who specialize in each product type determine liquidity horizons, with a liquidity horizon floor of three-months. Liquidity horizons are regularly reviewed so that the act of selling or hedging, in itself, would not materially affect the price. As at year-end 2014, for regulatory RWA calculation all liquidity horizons have been conservatively set to 12 months while we review the selection methodology. Default and rating migration probabilities are defined by rating migration matrices which are calibrated on historical external rating data. Taking into account the trade-off between granularity of matrices and their stability we apply a global corporate matrix and a sovereign matrix comprising the seven main rating bands. Accordingly, issue or issuer ratings from the rating agencies Moody’s, S&P and Fitch are assigned to each position.

To quantify a loss due to rating migration, a revaluation of a position is performed under the new rating. The probability of joint rating downgrades and defaults is determined by the migration and rating correlations of the incremental risk charge model. These correlations are specified through systematic factors that represent geographical regions and industries and are calibrated on historical rating migration and equity time series. The simulation process incorporates a rollover strategy that is based on the assumption of a constant level of risk. This assumption implies that positions that have experienced default or rating migration over their liquidity horizon are re-balanced at the end of their liquidity horizon to attain the initial level of risk. Correlations between positions with different liquidity horizons are implicitly specified by the dependence structure of the underlying systematic and idiosyncratic risk factors, helping to ensure that portfolio concentrations are identified across liquidity horizons. In particular, differences between liquidity horizons and maturities of hedges and hedged positions are recognized.

Direct validation of the incremental risk charge through back-testing methods is not possible. The charge is subject to validation principles such as the evaluation of conceptual soundness, ongoing monitoring, process verification and benchmarking and outcome analysis. The validation of the incremental risk charge methodology is embedded in the validation process for our credit portfolio model, with particular focus on the incremental risk charge specific aspects. Model validation relies more on indirect methods including stress tests and sensitivity analyses. Relevant parameters are included in the annual validation cycle established in the current regulatory framework. The incremental risk charge is part of the quarterly group-wide stress test using the stress testing functionality within our credit engine. Stressed incremental risk charge figures are reported on group level and submitted to the Stress Test Working Group (STWG) and the Portfolio Risk Committee (PRC).

Comprehensive Risk Measure

The comprehensive risk measure for the correlation trading portfolio is based on our own internal model. We calculate the comprehensive risk measure based on a Monte Carlo Simulation technique to a 99.9 % confidence level and a capital horizon of one year. Our model is applied to the eligible correlation trading positions where typical products include collateralized debt obligations, nth-to-default credit default swaps, and commonly traded index- and single-name credit default swaps. Re-securitizations or products which reference retail claims or real estate exposures are not eligible. Furthermore, trades subject to the comprehensive risk measure have to meet minimum liquidity standards to be eligible. The model incorporates concentrations of the portfolio and nonlinear effects via a full revaluation approach.

Comprehensive risk measure is designed to capture defaults as well as the following risk drivers: interest rates, credit spreads, recovery rates, foreign exchange rates and base correlations, index-to-constituent and base correlation basis risks.

Comprehensive risk measure is calculated on a weekly basis. Initially, the eligible trade population within the correlation trading portfolio is identified. Secondly, the risk drivers of the P&L are simulated over a one year time horizon. The trade population is then re-valued under the various Monte Carlo Simulation scenarios and the 99.9 % quantile of the loss distribution is extracted.

The market and position data are collected from front office systems and are subject to quality control. The comprehensive risk measure figures are closely monitored and play a significant role in the management of the correlation trading portfolio. We use three years of historical market data to estimate the risk drivers to the comprehensive risk measure.

In our comprehensive risk measure model the liquidity horizon is set to 12 months, which equals the capital horizon.

In order to maintain the quality of our comprehensive risk measure model we continually monitor the potential weaknesses of this model. Backtesting of the trade valuations and the propagation of single risk factors is carried out on a monthly basis and a quarterly recalibration of parameters is performed. In addition, a series of stress tests have been defined on the correlation trading portfolio where the shock sizes link into historical distressed market conditions.

Model validation is performed by an independent team and reviews, but is not limited to, the above mentioned backtesting, the models which generate risk factors, appropriateness and completeness of risk factors, the Monte Carlo Simulation stability, and performs sensitivity analyses.

For regulatory reporting purposes, the comprehensive risk measure represents the higher of the internal model spot value at the reporting dates, their preceding 12-week average calculation, and the floor, where the floor is equal to 8 % of the equivalent capital charge under the standardised approach securitization framework.

Market Risk Standardized Approach

Market Risk Management monitors exposures and addresses risk issues and concentrations for certain exposures under the specific Market Risk Standardized Approach (“MRSA”). We use the MRSA to determine the regulatory capital charge for the interest rate risk of nth-to-default credit default swaps and for the correlation trading portfolio securitization positions which are not eligible for the comprehensive risk measure. For these positions we assign all retained securitization positions that are unrated or rated below BB a risk weight of 1,250 percent to the exposure.

We also use the MRSA to determine the regulatory capital charge for longevity risk as set out in CRR/CRD 4 regulations. Longevity risk is the risk of adverse changes in life expectancies resulting in a loss in value on longevity linked policies and transactions. For risk management purposes, stress testing and economic capital allocations are also used to monitor and manage longevity risk.

Furthermore, certain types of investment funds require a capital charge under the MRSA. For risk management purposes, these positions are also included in our internal reporting framework.

Validation of Front Office models

An independent team validates front office models that are used for official pricing and risk management of trading positions. The key objectives of model validation are to:

  • Assess and validate the logical and conceptual soundness (model design and construction) of models in line with their design objectives and purpose (for front office models this would be valuation and risk sensitivities);
  • Assess appropriateness and accuracy of implementation methodology; and
  • Assess the appropriateness of the model for the intended products to be priced and risk managed, identifying potential limitations and conditions for use.

Trading Market Risk Management Framework at Postbank

Market risk arising from Postbank has been included in our reporting since 2010. Since the domination agreement between Deutsche Bank and Postbank became effective in September 2012, aggregate market risk limits for Postbank are set by Deutsche Bank according to our market risk limit framework. Postbank’s Head of Market Risk Management has a functional reporting line into our Market Risk Management organization and acts based upon delegated authority with respect to monitoring, reporting and managing market risk exposure according to market risk limits allocated to Postbank.

Sub limits are allocated by the Postbank Market Risk Committee to the individual operating business units. Deutsche Bank is represented by a senior member of Market Risk Management on the Postbank Market Risk Committee. The market risk economic capital limits allocated to specific business activities define the level of market risk that is reasonable and desirable for Postbank from an earnings perspective.

Market risk at Postbank is monitored on a daily basis using a system of limits based on value-at-risk. In addition, Postbank’s Market Risk Committee has defined sensitivity limits for the trading and banking book as well as for key sub-portfolios. Postbank also performs scenario analyses and stress tests in addition to the value-at-risk calculations. The assumptions underlying the stress tests are reviewed and validated on an ongoing basis.

Value-at-Risk at Postbank

Postbank also uses the value-at-risk concept to quantify and monitor the market risk it assumes. Value-at-risk is calculated using a Monte Carlo Simulation. The risk factors taken into account in the value-at-risk include interest rates, equity prices, foreign exchange rates, and volatilities, along with risks arising from changes in credit spreads. Correlation effects between the risk factors are derived from equally-weighted historical data.

Postbank’s trading book value-at-risk is currently not consolidated into the value-at-risk of the remaining Group. However, it is shown separately in the internal value-at-risk report.

We also apply the MRSA for the determination of the regulatory capital charge for Postbank’s trading market risk.