Machine generated contents note: pt. I Theory and Practice of Model Risk Management -- 1.Understanding Model Risk -- 1.1.What Is Model Risk? -- 1.1.1.The Value Approach -- 1.1.2.The Price Approach -- 1.1.3.A Quant Story of the Crisis -- 1.1.4.A Synthetic View on Model Risk -- 1.2.Foundations of Modelling and the Reality of Markets -- 1.2.1.The Classic Framework -- 1.2.2.Uncertainty and Illiquidity -- 1.3.Accounting for Modellers -- 1.3.1.Fair Value -- 1.3.2.The Liquidity Bubble and the Accountancy Boards -- 1.3.3.Level 1, 2, 3... go? -- 1.3.4.The Hidden Model Assumptions in `vanilla' Derivatives -- 1.4.What Regulators Said After the Crisis -- 1.4.1.Basel New Principles: The Management Process -- 1.4.2.Basel New Principles: The Model, The Market and The Product -- 1.4.3.Basel New Principles: Operative Recommendations -- 1.5.Model Validation and Risk Management: Practical Steps -- 1.5.1.A Scheme for Model Validation -- 1.5.2.Special Points in Model Risk Management --

Contents note continued: 1.5.3.The Importance of Understanding Models -- 2.Model Validation and Model Comparison: Case Studies -- 2.1.The Practical Steps of Model Comparison -- 2.2.First Example: The Models -- 2.2.1.The Credit Default Swap -- 2.2.2.Structural First-Passage Models -- 2.2.3.Reduced-Form Intensity Models -- 2.2.4.Structural vs Intensity: Information -- 2.3.First Example: The Payoff. Gap Risk in a Leveraged Note -- 2.4.The Initial Assessment -- 2.4.1.First Test: Calibration to Liquid Relevant Products -- 2.4.2.Second Test: a Minimum Level of Realism -- 2.5.The Core Risk in the Product -- 2.5.1.Structural Models: Negligible Gap Risk -- 2.5.2.Reduced-Form Models: Maximum Gap Risk -- 2.6.A Deeper Analysis: Market Consensus and Historical Evidence -- 2.6.1.What to Add to the Calibration Set -- 2.6.2.Performing Market Intelligence -- 2.6.3.The Lion and the Turtle. Incompleteness in Practice -- 2.6.4.Reality Check: Historical Evidence and Lack of it --

Contents note continued: 2.7.Building a Parametric Family of Models -- 2.7.1.Understanding Model Implications -- 2.8.Managing Model Uncertainty: Reserves, Limits, Revisions -- 2.9.Model Comparison: Examples from Equity and Rates -- 2.9.1.Comparing Local and Stochastic Volatility Models in Pricing Equity Compound and Barrier Options -- 2.9.2.Comparing Short Rate and Market Models in Pricing Interest Rate Bermud an Options -- 3.Stress Testing and the Mistakes of the Crisis -- 3.1.Learning Stress Test from the Crisis -- 3.1.1.The Meaning of Stress Testing -- 3.1.2.Portfolio Stress Testing -- 3.1.3.Model Stress Testing -- 3.2.The Credit Market and the `Formula that Killed Wall Street' -- 3.2.1.The CDO Payoff -- 3.2.2.The Copula -- 3.2.3.Applying the Copula to CDOs -- 3.2.4.The Market Quotation Standard -- 3.3.Portfolio Stress Testing and the Correlation Mistake -- 3.3.1.From Flat Correlation Towards a Realistic Approach --

Contents note continued: 3.3.2.A Correlation Parameterization to Stress the Market Skew -- 3.4.Payoff Stress and the Liquidity Mistake -- 3.4.1.Detecting the Problem: Losses Concentrated in Time -- 3.4.2.The Problem in Practice -- 3.4.3.A Solution. From Copulas to Real Models -- 3.4.4.Conclusions -- 3.5.Testing with Historical Scenarios and the Concentration Mistake -- 3.5.1.The Mapping Methods for Bespoke Portfolios -- 3.5.2.The Lehman Test -- 3.5.3.Historical Scenarios to Test Mapping Methods -- 3.5.4.The Limits of Mapping and the Management of Model Risk -- 3.5.5.Conclusions -- 4.Preparing for Model Change, Rates and Funding in the New Era -- 4.1.Explaining the Puzzle in the Interest Rates Market and Models -- 4.1.1.The Death of a Market Model: 9 August 2007 -- 4.1.2.Finding the New Market Model -- 4.1.3.The Classic Risk-free Market Model -- 4.1.4.A Market Model with Stable Default Risk -- 4.1.5.A Market with Volatile Credit Risk -- 4.1.6.Conclusions --

Contents note continued: 4.2.Rethinking the Value of Money: The Effect of Liquidity in Pricing -- 4.2.1.The Setting -- 4.2.2.Standard DVA: Is Something Missing? -- 4.2.3.Standard DVA plus Liquidity: Is Something Duplicated? -- 4.2.4.Solving the Puzzle -- 4.2.5.Risky Funding for the Borrower -- 4.2.6.Risky Funding for the Lender and the Conditions for Market Agreement -- 4.2.7.Positive Recovery Extension -- 4.2.8.Two Ways of Looking at the Problem: Default Risk or Funding Benefit? The Accountant vs the Salesman -- 4.2.9.Which Direction for Future Pricing? -- pt. II Snakes in the Grass: Where Model Risk Hides -- 5.Hedging -- 5.1.Model Risk and Hedging -- 5.2.Hedging and Model Validation: What is Explained by P&L Explain? -- 5.2.1.The Sceptical View -- 5.2.2.The Fundamentalist View and Black and Scholes -- 5.2.3.Back to Reality -- 5.2.4.Remarks: Recalibration, Hedges and Model Instability -- 5.2.5.Conclusions: from Black and Scholes to Real Hedging --

Contents note continued: 5.3.From Theory to Practice: Real Hedging -- 5.3.1.Stochastic Volatility Models: SABR -- 5.3.2.Test Hedging Behaviour Leaving Nothing Out -- 5.3.3.Real Hedging for Local Volatility Models -- 5.3.4.Conclusions: the Reality of Hedging Strategies -- 6.Approximations -- 6.1.Validate and Monitor the Risk of Approximations -- 6.2.The Swaption Approximation in the Libor Market Model -- 6.2.1.The Three Technical Problems in Interest Rate Modelling -- 6.2.2.The Libor Market Model and the Swaption Market -- 6.2.3.Pricing Swaptions -- 6.2.4.Understanding and Deriving the Approximation -- 6.2.5.Testing the Approximation -- 6.3.Approximations for CMS and the Shape of the Term Structure -- 6.3.1.The CMS Payoff -- 6.3.2.Understanding Convexity Adjustments -- 6.3.3.The Market Approximation for Convexity Adjustments -- 6.3.4.A General LMM Approximation -- 6.3.5.Comparing and Testing the Approximations -- 6.4.Testing Approximations Against Exact. Dupire's Idea --

Contents note continued: 6.4.1.Perfect Positive Correlation -- 6.4.2.Perfect Negative Correlation -- 6.5.Exercises on Risk in Computational Methods -- 6.5.1.Approximation -- 6.5.2.Integration -- 6.5.3.Monte Carlo -- 7.Extrapolations -- 7.1.Using the Market to Complete Information: Asymptotic Smile -- 7.1.1.The Indetermination in the Asymptotic Smile -- 7.1.2.Pricing CMS with a Smile: Extrapolating to Infinity -- 7.1.3.Using CMS Information to Transform Extrapolation into Interpolation and Fix the Indetermination -- 7.2.Using Mathematics to Complete Information: Correlation Skew -- 7.2.1.The Expected Tranched Loss -- 7.2.2.Properties for Interpolation -- 7.2.3.Properties for Turning Extrapolation into Interpolation -- 8.Correlations -- 8.1.The Technical Difficulties in Computing Correlations -- 8.1.1.Correlations in Interest Rate Modelling -- 8.1.2.Cross-currency Correlations -- 8.1.3.Stochastic Volatility Correlations -- 8.2.Fundamental Errors in Modelling Correlations --

Contents note continued: 8.2.1.The Zero-correlation Error -- 8.2.2.The 1-Correlation Error -- 9.Calibration -- 9.1.Calibrating to Caps/Swaptions and Pricing Bermudans -- 9.1.1.Calibrating Caplets -- 9.1.2.Understanding the Term Structure of Volatility -- 9.1.3.Different Parameterizations -- 9.1.4.The Evolution of the Term Structure of Volatility -- 9.1.5.The Effect on Early-Exercise Derivatives -- 9.1.6.Reducing Our Indetermination in Pricing Bermudans: Liquid European Swaptions -- 9.2.The Evolution of the Forward Smiles -- 10.When the Payoff is Wrong -- 10.1.The Link Between Model Errors and Payoff Errors -- 10.2.The Right Payoff at Default: The Impact of the Closeout Convention -- 10.2.1.How Much Will be Paid at Closeout, Really? -- 10.2.2.What the Market Says and What the ISDA Says -- 10.2.3.A Quantitative Analysis of the Closeout -- 10.2.4.A Summary of the Findings and Some Conclusions on Payoff Uncertainty -- 10.3.Mathematical Errors in the Payoff of Index Options --

Contents note continued: 10.3.1.Too Much Left Out -- 10.3.2.Too Much Left In -- 10.3.3.Empirical Results with the Armageddon Formula -- 10.3.4.Payoff Errors and Armageddon Probability -- 11.Model Arbitrage -- 11.1.Introduction -- 11.2.Capital Structure Arbitrage -- 11.2.1.The Credit Model -- 11.2.2.The Equity Model -- 11.2.3.From Barrier Options to Equity Pricing -- 11.2.4.Capital-structure Arbitrage and Uncertainty -- 11.3.The Cap-Swaption Arbitrage -- 11.4.Conclusion: Can We Use No-Arbitrage Models to Make Arbitrage? -- 12.Appendix -- 12.1.Random Variables -- 12.1.1.Generating Variables from Uniform Draws -- 12.1.2.Copulas -- 12.1.3.Normal and Lognormal -- 12.2.Stochastic Processes -- 12.2.1.The Law of Iterated Expectation -- 12.2.2.Diffusions, Brownian Motions and Martingales -- 12.2.3.Poisson Process -- 12.2.4.Time-dependent Intensity -- 12.3.Useful Results from Quantitative Finance -- 12.3.1.Black and Scholes (1973) and Black (1976) -- 12.3.2.Change of Numeraire.