Value-at-Risk Training Course

Newly revised and updated in light of the global credit crisis, the course provides up-to-date covering of the latest strategies and techniques for VaR analysis.

This intensive course outlines and illustrates a framework for measuring Value-at-Risk (VaR) and demonstrates how it could be used to generate the types of measures that align with current regulatory recommendations.  This is done in the context of equity, fixed income and interest rate derivative products.

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VaR: Overview, Risk Capital & Regulatory Developments

• Motivation - Risk profile of derivatives portfolio
• Risk governance measurement – Common conceptual framework
• Headline disasters – Control & poor risk measurement
• Basel II: Three Pillars & revisions to Basel II
• Solvency II - Scenario analysis & stress testing
• Banking regulators and back testing - Tier capital

Computer Workshop 1: Understanding total risk (volatility) measures

VaR Methodologies

• Historical simulation (empirical, non-parametric)
• Variance/CoVariance Matrix (Parametric)
• Monte Carlo simulation
• Lattice-Tree approach

Historical Simulation (VaR/S)

• Principle assumptions
• Calibrating the empirical model – Accuracy, extensions (weights)
• Revaluation issues in portfolio (one-day vs ten-day VaR)
• Incorporating volatility updating - EWMA, GARCH (1,1)
• Bootstrap method
• Extreme Value Theory (EVT) - Estimating tails, power law
• Expected Tail Loss (ETL) - Fitting Johnson SU distribution

Computer Workshop 2: Historical simulation - Value-at-Risk reports

Variance-Covariance (Correlation) Matrix (VaR/P)

• Principle assumptions
• Estimate volatilities (EWMA, GARCH) and correlations
• Cash flow mapping (Bucketing, Gridding) algorithm
• Portfolio aggregation
• Advantages and issues

Computer Workshop 3: Variance-CoVariance (Riskmetrics) computations

VaR–Measuring Market Risk: Variance/Covariance Analysis

• Equity portfolio, treasury portfolio, derivatives portfolio
• Market risk
• Variance-covariance matrices
• VaR of equity portfolio
• Effect of correlation on overall risk
• Do VaRs add? Conditional VaR
• VaR of fixed income sector
• VaR of derivatives (options)
• Quadratic model: Delta, Gamma measures
• Cornish-Fisher expansion
• Non-normal assumptions

Computer Workshop 4: Variance-Covariance VaR reports for equity, fixed-income and derivatives trading portfolios

VaR–Monte Carlo Simulation: Cash Market Portfolio

• Underlying principles
• Modelling equity price process
• Box-Muller transformation
• Polar rejection method

Computer Workshop 5

• Monte Carlo simulation - Value-at-risk equity reports
• Box-Muller transformation
• Polar rejection method

VaR–Monte Carlo Simulation: Options Portfolio

• Applied to options portfolio
• Why returns are less than expected
• Risk-neutral (Martingale) insights
• VaR/S versus VaR/P results

Computer Workshop 6:

• Monte Carlo simulation applied to options portfolio
• Appropriate use of Black–Scholes/Merton option pricing model

VaR–Monte Carlo Simulation: Correlated Assets Portfolio

• Multiple assets portfolios
• Modelling correlated stock price processes
• Independent price processes
• Perfectly correlated price processes
• Imperfectly correlated price processes
• Cholesky decomposition

Computer Workshop 7

• Monte Carlo simulation applied to multiple assets portfolios
• Modelling correlation
• Cholesky decomposition

Global Description of Risk: VaR

• A framework for implementation
• Key features of VaR system modules
  - Review of recent regulatory developments
  - Interest rate risk framework
  - Market and credit risk
  - BIS Basel system of risk management
  - Measuring interest rate risk
  - Shortcomings of duration approaches 

A Sophisticated Approach to Measuring Interest Rate Risk

• Accounting for movements in (stochastic) yield curves
  - Level (inflation)
  - Steepness (monetary policy)
  - Curvature (mean reversion)
  - Simulation analysis
  - Modelling of a wide range of yield curve behaviour

A Two-Factor Approach for Interest Rate Derivatives Flowchart of Risk Management System

• Stochastic yield curve builder
• Derivative contracts converter
• Valuation module: gridding (mapping) option pricing models
• Risk analyser (PVBP analysis)

Step-by-Step Worked Example – Actual Implementation in a Leading Bank

• Principal Component Analysis (PCA) for extracting two factors
• Estimating volatility and correlation between factors
• Estimating mean reversion coefficient
• Generation of stochastic term structures of interest rates
• State-by-state interest rate scenarios analysis
• Valuing books of cash flows/derivatives over holding period
• Valuing interest rate options and swaptions

Computer Workshop 8:

• Building one-factor stochastic yield curve model
• Effects and implications for VaR analysis and reports

Stochastic Two-Factor Model

• Inputs - Current yield curve
• Interest rate factors - Short rate and long rate
• Inputs - Volatilities, correlation, mean reversion
• Worked example using real term structure
• VaR toolkit
  - Current yield curve builder mathematics
  - Money market
  - Swap market
  - Futures market
  - Linear stripping
  - Geometric interpolation
• Generation of interest rate scenarios
• State-by-state interest rate scenarios analysis

Computer Workshop 9

• Building two-factor stochastic yield curve model
• Effects and implications for VaR analysis and reports

Value-at-Risk Reports: Swap, Cash, Bond Book

• Worked example using real swap book
• VaR toolkit - Swap principal method valuation mathematics
• VaR toolkit - Gridding and bucketing mathematics

Computer Workshop 10: Value-at-Risk for portfolios of linear risk cash flow instruments: cash, bonds and swaps

Value-at-Risk Reports: Interest Rate Options

• Worked example using real interest rate cap book
• VaR toolkit: Black (1976) valuation mathematics

Computer Workshop 11: Value-at-Risk for portfolios of non-linear risk cash flow instruments: interest rate options (caps and floors)

Value-at-Risk, PVBP and Risk Management

• VaR and risk management hedging

Credit Risk Losses and Credit VaR

• Estimating credit losses: default probability, recovery rates
• M-KMV Vasicek and Merton structural models
• CreditMetrics: correlation and time horizon

Computer Workshop 12

• Structural models of credit VaR
• CreditMetrics VaR

This cutting-edge training programme will provide you invaluable practical information on:

• VaR risk capital & regulatory developments
• Key issues in risk governance, risk management and risk audits
• Historical simulation methodologies and issues
• VaRCoVaR methods and issues, expected tail-loss (conditional VaR)
• Monte Carlo simulation analytics and issues
• Importance of multi-factor term-structure models
• Auditing a risk management hedging system of a derivatives book