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4. Valuation and Risk Models
1. Measures of Financial Risk
1. Introduction
2. Mean-Variance Framework and Efficient Frontier
3. Normal Distribution
4. Value at Risk(VaR)
5. Expected Shortfall (ES)
6. Coherent Risk Measure Properties
7. Non-Coherence of VaR
8. Conclusion
2. Value at Risk (VaR)
1. Introduction
2. Linear and Non-Linear Portfolios
3. Calculating VaR and ES Using Historical Simulation
4. Calculating VaR Using Delta-Normal Approach
5. VaR for Linear Derivatives
6. Limitations of Delta-Normal Method
7. Monte Carlo method Simulation to Calculate VaR
8. Correlation Breakdown for Scenario Analysis
9. Worst-Case Scenario (WCS) Analysis Vs VaR
10. Conclusion
3. Volatility
1. Introduction
2. Deviation of Asset Retrns from Normal Distribution
3. Fat Tails in Return Distribution
4. Conditional and Unconditional Distributions
5. Estimating Conditional Volatility
6. Exponentially Weighted Moving Average (EWMA) Model
7. GARCH (1,1) Model
8. Long Horizon Volatility/VaR
9. Implied Volatility
10. Updating Correlation Estimates
11. Conclusion
4. Credit Ratings
1. Introduction
2. External Rating Scales and Processes
3. Conditional Vs Unconditional Default Probabilities
4. Hazard Rate
5. Recovery Rate
6. Through-The-Cycle Vs Point-In-Time Ratings
7. Alternative Credit Ratings Methods
8. External Vs Internal Ratings
9. Ratings Transition Matrix
10. Credit Ratings and Financial Markets
11. Historical Failures and Challenges of Credit Ratings
12. Conclusion
5. Country Risk
1. Introduction
2. Country's Risk Exposure
3. Composite Measures of Country Risk
4. Sovereign Default
5. Consequences of Sovereign Default
6. Sovereign Default Risk Factors
7. Sovereign Credit Spreads and Credit Default Swaps (CDS)
8. Conclusion
6. Credit Risk
1. Introduction
2. Economic Capital and Regulatory Capital
3. Loan Defaults and Portfolio’s Default Rate
4. Expected Loss (EL)
5. Unexpected Loss (UL)
6. Mean and Standard Deviation of Credit Losses
7. Gaussian Copula Model
8. Vasicek Model for Default Rate Estimation
9. CreditMetrics Model for Economic Capital Estimation
10. Estimating Loan's Contribution using Euler’s theorem
11. Challenges in Calculating Credit Risk for Derivatives
12. Challenges in Quantifying Credit Risk
13. Conclusion
7. Operational Risk
1. Introduction
2. Types of Operational Risk
3. Approaches for Calculating Operational Risk Regulatory Capital
4. Standardized Measurement Approach
5. Loss Distribution Derivation
6. Data Issues in Estimating Loss Distribution
7. Scenario Analysis with Scarce Data
8. Causal Relationships and Operational Risk Management
9. Allocation of Operational Risk Capital
10. Measuring Operational Risk Using Power Law
11. MInsurance against Operational Risk
12. Conclusion
8. Stress Testing
1. Introduction
2. Stress Testing as a Risk Management Tool
3. Considerations and Challenges in Stress Testing
4. Stress Testing and Other Risk Measures
5. Stressed VaR and Stressed ES
6. Stress Testing Governance Responsibilities
7. Policies, Procedures, Validation and Independent Review
8. Basel Stress Testing Principles
9. Conclusion
9. Pricing Conventions, Discounting and Arbitrage
1. Introduction
2. Discount Factor and Discount Function
3. Law of One Price
4. Arbitrage Opportunities for Fixed Income Securities
5. Components of a US Treasury Coupon Bond
6. Replicating Portfolio
7. Clean and Dirty Bond Pricing
8. Day-Count Conventions
9. Conclusion
10. Interest Rates
1. Introduction
2. Impact of Compounding Frequency on Bond Value
3. Spot Rate
4. Forward Rate
5. Par Rate
6. Relationship between Spot, Forward and Par Rates
7. Impact of Maturity on Bond Pricing and Returns
8. Flattening and Steepening of Rate Curves
9. Swaps
10. Overnight Indexed Swaps (OIS)
11. Conclusion
11. Bonds
1. Introduction
2. Gross Vs Net Realized Returns
3. Bond Spread
4. Bond Pricing using Yield-to-Maturity (YTM)
5. Computing Bond's YTM
6. Annuity and Perpetuity
7. Spot Rates and YTM
8. Coupon Effect
9. Decomoposing P&L for a Bond Position
10. Carry Roll-Down
11. Conclusion
12. Duration, Convexity and DV01
1. Introduction
2. One-Factor Interest Rate Model
3. DV01 of a Fixed Income Security
4. Hedging Options using Bonds
5. Effective Duration of a Fixed Income Security
6. DV01 Vs Effective Duration
7. Convexity of a Fixed Income Security
8. Effective Duration and Convexity of a Portfolio
89. Hedging based on Effective Duration and Convexity
10. Barbell and Bullet Investments
11. Conclusion
13. Non Parallel Term Structure Shifts
1. Introduction
2. Principal Components Analysis and Term Structure Movements
3. Key Rate Exposures
4. Key-Rate Shift Analysis
5. Key Rate ‘01 and Key Rate Duration
6. Hedging Key Rate Risks of a Portfolio
7. Key Rates, Partial 01s, and Forward-Bucket 01s
8. Portfolio Volatility Estimation
9. Conclusion
14. Binomial Trees
1. Introduction
2. Valuing Options using Binomial Model
3. Volatility in Binomial Model
4. Convergence in Binomial Model with Time
5. Delta of a Stock Option
6. Expanding Binomial Model
7. Conclusion
15. Black Scholes Merton Model
1. Introduction
2. Lognormal Property of Stock Prices
3. Realized Return and Historical Volatility
4. Assumptions of Black-Scholes-Merton Model
5. Pricing European Options
6. Implied Volatility
7. Effect of Dividends on Early Exercising
8. Extending Options Valuation
9. Warrants
10. Conclusion
16. Options Sensitivities
1. Introduction
2. Option Positions Risks
3. Stop Loss Hedging Strategy
4. Delta Hedging for an Option
5. Delta of an Option
6. Dynamic Aspects of Delta Hedging
7. Delta of a Portfolio
8. Theta, Gamma, Vega and Rho
9. Maintaining Neutral Positions
10. Greeks Relationship
11. Portfolio Insurance
12. Conclusion
