Quantitative Concepts in Treasury and Asset-Liability Management

Study of Risk management requires understanding of a number of statistical concepts. Some of them are listed in this article.

How Banks can Lose Money

lMarket Risk
lCredit Risk
lOperating Risk

lManaging Risk at Macro Level
–Capital
–Risk Limit
–Liabilities
–Assets
–Equity Capital

lRisk
lProbability of Default
   Estimating probabilities of default - FRB NY Staff report - 2004
lEconomic Capital
lRisk Adjusted Performance
lRisk Adjusted Return on Capital (RAROC)
lExpected Return – Actual Return




lProbability Density
lCumulative Probability
lMean
lStandard Deviation
lSkew
lKurtosis

Standard Probability Distributions
lNormal distribution
lLog-normal distribution
lBeta distribution

lConfidence Intervals
lConfidence levels
lPercentiles
lCorrelation and covariance
lRandom Processes


Traded Instruments
lYield curve
lYield to Maturity
lDuration
lForward Rate Agreement
lFutures
lSwap
lOption
Options
lValue of Option
lBlack Scholes Model
lImplied Volatility

Risk Measurement for Options
lDelta
lGamma
lVega
lRho
lTheta


Market Risk Measurement
lDuration
lSensitivity analysis for equities
lStress testing
lScenario testing
lCapital Asset Pricing Model
lSharpe Ratio
lTreynor Ratio



lValue at Risk

Three Approaches to Calculate VAR
lParametric VaR
lHistorical Simulation

lMonte Carlo Simulation

Value at Risk Contribution
lVaRC is constructed so that the sum of VaRC for all subportfolios equals the total VaR for the portfolio.


VaR Testing Methodologies
lSoftware installation test
lProfit and Loss reconciliation test
lModeled-probability-distribution back-test


Approaches for Assessing Extreme Events
lJump diffusion
lHistorical Simulation
lAdjustments to Monte Carlo Simulation
lExtreme Value Theory


Liquidity Risk
lClose out Days
lUsing Close-out time to quantify Liquidity Risk
lSimulation based techniques to Quantify Liquidity Risk
lUsing the Bid-Ask spread to Assess Liquidity Risk


Management of Market Risk
lLimits on market risks
lInventory Age Limits
lConcentration Limits
lStop-loss Limits
lLimits on Position Size
lPrinciples for Setting Limits
–Setting VaR Limits

Asset Liability Management
lBanks use three alternative approaches to measure ALM interest-rate risk
–Gap reports
–Rate-shift scenarios
–Simulation methods similar to Monte Carlo VaR

Gap Reports
lContractual Maturity Gap Reports
lRepricing Gap Reports
lEffective Maturity Gap Reports

lEstimating Economic Capital based on Gap Reports

lModels to create Interest-rate Scenarios Randomly


Funds-Transfer Pricing
lTraditional Transfer Pricing
lMatched-Funds-Transfer Pricing
lTransfer Pricing for Indeterminate-Maturity Transfer Pricing

Credit Risk
lExposure at Default
lLoss in the Event of Default
lProbability of Default


Mitigating Counterparty Credit Risk
lRequiring collateral
lSettling according to the market-to-market
lEarly settlement in the event of a downgrade
lUsing a SPV
lA netting master agreement
lCounterparty exposure limits
lPricing for Credit Risk


Risk Measurement for a Single Credit Facility
lDetermining Losses due to Default
lDetermining Losses due to both Default and Downgrades.
lDetermining Default Probabilities over Multiple Years


Estimating Parameter Values for Single Facilities
lExpert credit Grading
lQuantitative Scores based on Customer Data
–Discriminant Analysis
–Logistic Regression
–Equity based credit scoring

Estimating the Exposure at Default
lEstimating the Losses at Default


Modeling Techniques to Measure Portfolio Credit Risk
lCovariance model
lActuarial model
lMerton based simulation model
lMacroeconomic default model
lMacroeconomic cash-flow model

lStandardized approach
lInternal Ratings-Based Approach


Measuring Operating Risk
lQualitative approaches
lStructural Approaches
lActuarial Approaches


Regulatory Capital for Operating Risks
lThe basic indicator approach
lThe standardised approach
lThe internal measurement approach

lInter-risk correlation in a Bank

Reference
Fundamentals of Risk Measurement
By Chris Marrison
Tata McGraw-Hill, New Delhi, 2005
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