Financial Risk Management
The Basle Market Risk Charges Following P. Jorion, Financial Risk Management Chapter 32
Daniel HERLEMONT
Introduction Market Charges was introduced in 1996, implemented beginning 1998 2 Methods the Standardized approach Internal Models Approach (IMA)
Summary of the presentation Standardized approach Internal Models Approach (IMA) Stress Testing Backtesting Daniel HERLEMONT
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The Standardized Approach Guidelines to compute Interest rates risk Exchange risk Equity risk Commodity risk
The bank's total risk is computed as the summation of the 4 categories ignoring correlations !!!
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The Standardized Approach - Interest Rate Risk
Provide a robust measure of interest rate risk taking into account Systematic/Market risk duration basis risk across maturities
Specific/Idiosyncratic risk
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The Standardized Approach - Market Interest Rate Risk
Market risk is defined via Maturity Bands
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Exemple
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Example
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Example
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Specific Interest Risk Charge
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The Standardized Approach - Equity Risk As for Interest Risk, Equity Risk is split into The Specific Risk defined as The Gross equity positions = the sum of absolute value of all long and short positions The net equity positions: General (or Systematic) Risk
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The Standardized Approach - Currency Risk Spot and forward positions for currency, including Gold
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Commodity Risk Have greater volatilities than currency and Gold 3 approaches Internal Model Approach (see hereafter) Maturity ladder approach: similar to the interest rate approach Simplified approach: risk charge is 15% of the net exposure 3% of the gross exposure
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Commodity Risk - Maturity Approach - bands
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Option Risk
3 approaches Simplified Intermediate Delta-plus method Scenarios approach
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Option Risk - Simplified Approach Charge is the minimum of the MRC for underlying asset or the value of the option
typically for long call position, the worst loss is the premium Daniel HERLEMONT
Option Risk - The Intermediate Approach - Delta-Plus Method
decomposition of option into "Greeks", then factored into the standard risk charge for the relevant category (e.g. currency for currency options) Additional charges for gamma and vega risk
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The Market Risk Charge (MRC) The bank MRC is obtained be a summation of risk across different types of risk i on each day t
Standardized model pro easy to implement robust to model mispecification
Standardized model cons risk classification is arbitrary for instance 8% charge is applied to currency or equity without regard to their volatilities
leads to very conservative: charge is added up without considering diversification effects Implicitly, this approach is the worst case scenario that assumes that the worst loss will occur at the same time across all sources of risk. Daniel HERLEMONT
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The Internal Model Approach (IMA) Rely on Internal Risk Management of the Bank for the first time Regulation recognized that bank had developed trustable risk management systems if this approach lead to lower Capital Charge, Banks have incentives to develop sophisticated and more accurate models However, need to be approved by Regulation sound and sufficient details on the VAR and diversification models at qualitative and quantitative levels
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The Internal Model Approach (IMA) - Qualitative Requirements
Independant Risk Control Unit The bank must a risk control that is independent of trading and reports to senior management, to minize conflicts of interests
Back testing Involvement senior sufficient resources
Use of limits Stress Testing Compliance (to a documented set of policies) Independent Review Daniel HERLEMONT
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The Internal Model Approach (IMA) - Quantitative Requirements
Requirement on risk factors : at least 6 factors for yield curve risk + separate risk factors to model spread risk for equity, the model should at least consist of beta mapping on an index, a more detailed approach could consist in adding industry factors, as well as individual risk factor modeling for active trading in commodity, the model should account for for movements in the spot plus convenient yields bank should also capture the non linear price characteristics of options (gamma, vega , ...) Correlation within broad risk categories are recognized explicitly Daniel HERLEMONT
The Internal Model Approach (IMA) - VAR Market Risk Charge = VAR Shall be computed every day for a10 days horizon Bank can use a daily VAR and scale it using the square root time rule
with a 99% confidence level with an observation period based on at least one year moving window of historical data shall be set at the higher of the previous day's VAR, or the average over the 60 business days, times a multiplicative factor k determined by regulator (in the range of 3 to 4) to prevent model misspecifications
a plus factor is added (depending on the performance of the model)
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Stress Testing Stress Testing can be described as a process to identify and manage situations that could cause extraordinary losses Tools Scenarios Analysis Stressing Models Policy Response Daniel HERLEMONT
Stress Testing - Scenarios Analysis Evaluating the portfolios under various states of the world evaluating the impact changing evaluation models volatilities and correlations
Scenarios requiring no simulations analyzing large past losses
Scenarios requiring simulations running simulations of the current portfolio subject to large historical shocks e.g. 1987 crash, etc ...
Bank specific scenario driven by the current position of the bank rather than historical simulaltion
Much more subjective than VAR Can help to identify undetected weakness in the bank's portfolio Daniel HERLEMONT
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Backtesting Internal Models are allowed because they can be verified Verification is the process of checking the model is adequate Tools Stress Testing Inspections and reviews Backtesting Definition of Backtesting: Statistical testing that consist of checking whether actual trading losses are in line with the VAR forecasts Daniel HERLEMONT
Backtesting - Measuring Exceptions The Basle backtesting framework consists in recording daily exception of the 99% VAR voer the last year Even though capital requirements are based on 10 days VAR, backtesting uses a daily interval, which entails more observations On average, one would expect 1% of 250 or 2.5 instances of exceptions over the last year Too many exceptions indicate that either the model is understating VAR the Bank is unlucky How to decide ? Statistical inference Daniel HERLEMONT
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The penalty zones
recall of k definition
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Backtesting Possible cause and remedies of the "Yellow" zone Basic Integrity of the model Deficient model accuracy Intra day trading Bad luck
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Type I and II errors in practice With 5 exceptions or more, the probability of type I error is about 10.8%. This is the probability of penalizing a bank that has a correct model but excessive exceptions due to bad luck ...
On hte other side ... with 4 exceptions and an actual 97% coverage, the probability of type II error is about 5.7. This is the probability of accepting a bad model due to good luck ... Daniel HERLEMONT
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