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Perturbation Methods in Credit Derivatives

Release Date: 2021/03/01
ISBN: 9781119609612
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Stress-test financial models and price credit instruments with confidence and efficiency using the perturbation approach taught in this expert volume

Perturbation Methods in Credit Derivatives: Strategies for Efficient Risk Management offers an incisive examination of a new approach to pricing credit-contingent financial instruments. Author and experienced financial engineer Dr. Colin Turfus has created an approach that allows model validators to perform rapid benchmarking of risk and pricing models while making the most efficient use possible of computing resources.

The book provides innumerable benefits to a wide range of quantitative financial experts attempting to comply with increasingly burdensome regulatory stress-testing requirements, including:

  • Replacing time-consuming Monte Carlo simulations with faster, simpler pricing algorithms for front-office quants
  • Allowing CVA quants to quantify the impact of counterparty risk, including wrong-way correlation risk, more efficiently
  • Developing more efficient algorithms for generating stress scenarios for market risk quants
  • Obtaining more intuitive analytic pricing formulae which offer a clearer intuition of the important relationships among market parameters, modelling assumptions and trade/portfolio characteristics for traders

The methods comprehensively taught in Perturbation Methods in Credit Derivatives also apply to CVA/DVA calculations and contingent credit default swap pricing.

Table of Contents

  1. Cover
  2. Title Page
  3. Copyright
  4. Preface
    1. Note
  5. Acknowledgments
  6. Acronyms
  7. CHAPTER 1: Why Perturbation Methods?
    1. 1.1 ANALYTIC PRICING OF DERIVATIVES
    2. 1.2 IN DEFENCE OF PERTURBATION METHODS
    3. NOTE
  8. CHAPTER 2: Some Representative Case Studies
    1. 2.1 QUANTO CDS PRICING
    2. 2.2 WRONG‐WAY INTEREST RATE RISK
    3. 2.3 CONTINGENT CDS PRICING AND CVA
    4. 2.4 ANALYTIC INTEREST RATE OPTION PRICING
    5. 2.5 EXPOSURE SCENARIO GENERATION
    6. 2.6 MODEL RISK
    7. 2.7 MACHINE LEARNING
    8. 2.8 INCORPORATING INTEREST RATE SKEW AND SMILE
    9. NOTE
  9. CHAPTER 3: The Mathematical Foundations
    1. 3.1 THE PRICING EQUATION
    2. 3.2 PRICING KERNELS
    3. 3.3 EVOLUTION OPERATORS
    4. 3.4 OBTAINING THE PRICING KERNEL
    5. 3.5 CONVOLUTIONS WITH GAUSSIAN PRICING KERNELS
    6. 3.6 PROOFS FOR CHAPTER 3
    7. NOTES
  10. CHAPTER 4: Hull–White Short‐Rate Model
    1. 4.1 BACKGROUND OF HULL–WHITE MODEL
    2. 4.2 THE PRICING KERNEL
    3. 4.3 APPLICATIONS
    4. 4.4 PROOF OF THEOREM 4.1
    5. NOTES
  11. CHAPTER 5: Black–Karasinski Short‐Rate Model
    1. 5.1 BACKGROUND OF BLACK–KARASINSKI MODEL
    2. 5.2 THE PRICING KERNEL
    3. 5.3 APPLICATIONS
    4. 5.4 COMPARISON OF RESULTS
    5. 5.5 PROOF OF THEOREM 5.1
    6. 5.6 EXACT BLACK–KARASINSKI PRICING KERNEL
    7. NOTES
  12. CHAPTER 6: Extension to Multi‐Factor Modelling
    1. 6.1 MULTI‐FACTOR PRICING EQUATION
    2. 6.2 DERIVATION OF PRICING KERNEL
    3. 6.3 EXACT EXPRESSION FOR HULL–WHITE MODEL
    4. 6.4 ASYMPTOTIC EXPANSION FOR BLACK–KARASINSKI MODEL
    5. 6.5 FORMAL SOLUTION FOR RATES‐CREDIT HYBRID MODEL
    6. NOTE
  13. CHAPTER 7: Rates‐Equity Hybrid Modelling
    1. 7.1 STATEMENT OF PROBLEM
    2. 7.2 PREVIOUS WORK
    3. 7.3 THE PRICING KERNEL
    4. 7.4 VANILLA OPTION PRICING
  14. CHAPTER 8: Rates‐Credit Hybrid Modelling
    1. 8.1 BACKGROUND
    2. 8.2 THE PRICING KERNEL
    3. 8.3 CDS PRICING
    4. NOTES
  15. CHAPTER 9: Credit‐Equity Hybrid Modelling
    1. 9.1 BACKGROUND
    2. 9.2 DERIVATION OF CREDIT‐EQUITY PRICING KERNEL
    3. 9.3 CONVERTIBLE BONDS
    4. 9.4 CONTINGENT CDS ON EQUITY OPTION
    5. NOTES
  16. CHAPTER 10: Credit‐FX Hybrid Modelling
    1. 10.1 BACKGROUND
    2. 10.2 CREDIT‐FX PRICING KERNEL
    3. 10.3 QUANTO CDS
    4. 10.4 CONTINGENT CDS ON CROSS‐CURRENCY SWAPS
  17. CHAPTER 11: Multi‐Currency Modelling
    1. 11.1 PREVIOUS WORK
    2. 11.2 STATEMENT OF PROBLEM
    3. 11.3 THE PRICING KERNEL
    4. 11.4 INFLATION AND FX OPTIONS
    5. NOTE
  18. CHAPTER 12: Rates‐Credit‐FX Hybrid Modelling
    1. 12.1 PREVIOUS WORK
    2. 12.2 DERIVATION OF RATES‐CREDIT‐FX PRICING KERNEL
    3. 12.3 QUANTO CDS REVISITED
    4. 12.4 CCDS ON CROSS‐CURRENCY SWAPS REVISITED
  19. CHAPTER 13: Risk‐Free Rates
    1. 13.1 BACKGROUND
    2. 13.2 HULL–WHITE KERNEL EXTENSION
    3. 13.3 APPLICATIONS
    4. 13.4 BLACK–KARASINSKI KERNEL EXTENSION
    5. 13.5 APPLICATIONS
    6. 13.6 A NOTE ON TERM RATES
    7. NOTES
  20. CHAPTER 14: Multi‐Curve Framework
    1. 14.1 BACKGROUND
    2. 14.2 STOCHASTIC SPREADS
    3. 14.3 APPLICATIONS
  21. CHAPTER 15: Scenario Generation
    1. 15.1 OVERVIEW
    2. 15.2 PREVIOUS WORK
    3. 15.3 PRICING EQUATION
    4. 15.4 HULL–WHITE RATES
    5. 15.5 BLACK–KARASINSKI RATES
    6. 15.6 JOINT RATES‐CREDIT SCENARIOS
    7. NOTES
  22. CHAPTER 16: Model Risk Management Strategies
    1. 16.1 INTRODUCTION
    2. 16.2 MODEL RISK METHODOLOGY
    3. 16.3 APPLICATIONS
    4. 16.4 CONCLUSIONS
    5. NOTES
  23. CHAPTER 17: Machine Learning
    1. 17.1 TRENDS IN QUANTITATIVE FINANCE RESEARCH
    2. 17.2 FROM PRICING MODELS TO MARKET GENERATORS
    3. 17.3 SYNERGIES WITH PERTURBATION METHODS
    4. NOTES
  24. Bibliography
  25. Index
  26. End User License Agreement
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