1  Cover

      2  Title Page

      3  Copyright

      4  Preface Note

      5  Acknowledgments

      6  Acronyms

      7  CHAPTER 1: Why Perturbation Methods? 1.1 ANALYTIC PRICING OF DERIVATIVES 1.2 IN DEFENCE OF PERTURBATION METHODS NOTE

      8  CHAPTER 2: Some Representative Case Studies 2.1 QUANTO CDS PRICING 2.2 WRONG‐WAY INTEREST RATE RISK 2.3 CONTINGENT CDS PRICING AND CVA 2.4 ANALYTIC INTEREST RATE OPTION PRICING 2.5 EXPOSURE SCENARIO GENERATION 2.6 MODEL RISK 2.7 MACHINE LEARNING 2.8 INCORPORATING INTEREST RATE SKEW AND SMILE NOTE

      9  CHAPTER 3: The Mathematical Foundations 3.1 THE PRICING EQUATION 3.2 PRICING KERNELS 3.3 EVOLUTION OPERATORS 3.4 OBTAINING THE PRICING KERNEL 3.5 CONVOLUTIONS WITH GAUSSIAN PRICING KERNELS 3.6 PROOFS FOR CHAPTER 3 NOTES

      10  CHAPTER 4: Hull–White Short‐Rate Model 4.1 BACKGROUND OF HULL–WHITE MODEL 4.2 THE PRICING KERNEL 4.3 APPLICATIONS 4.4 PROOF OF THEOREM 4.1 NOTES

      11  CHAPTER 5: Black–Karasinski Short‐Rate Model 5.1 BACKGROUND OF BLACK–KARASINSKI MODEL 5.2 THE PRICING KERNEL 5.3 APPLICATIONS 5.4 COMPARISON OF RESULTS 5.5 PROOF OF THEOREM 5.1 5.6 EXACT BLACK–KARASINSKI PRICING KERNEL NOTES

      12  CHAPTER 6: Extension to Multi‐Factor Modelling 6.1 MULTI‐FACTOR PRICING EQUATION 6.2 DERIVATION OF PRICING KERNEL 6.3 EXACT EXPRESSION FOR HULL–WHITE MODEL 6.4 ASYMPTOTIC EXPANSION FOR BLACK–KARASINSKI MODEL 6.5 FORMAL SOLUTION FOR RATES‐CREDIT HYBRID MODEL NOTE

      13  CHAPTER 7: Rates‐Equity Hybrid Modelling 7.1 STATEMENT OF PROBLEM 7.2 PREVIOUS WORK 7.3 THE PRICING KERNEL 7.4 VANILLA OPTION PRICING

      14  CHAPTER 8: Rates‐Credit Hybrid Modelling 8.1 BACKGROUND 8.2 THE PRICING KERNEL 8.3 CDS PRICING NOTES

      15  CHAPTER 9: Credit‐Equity Hybrid Modelling 9.1 BACKGROUND 9.2 DERIVATION OF CREDIT‐EQUITY PRICING KERNEL 9.3 CONVERTIBLE BONDS 9.4 CONTINGENT CDS ON EQUITY OPTION NOTES

      16  CHAPTER 10: Credit‐FX Hybrid Modelling 10.1 BACKGROUND 10.2 CREDIT‐FX PRICING KERNEL 10.3 QUANTO CDS 10.4 CONTINGENT CDS ON CROSS‐CURRENCY SWAPS

      17  CHAPTER 11: Multi‐Currency Modelling 11.1 PREVIOUS WORK 11.2 STATEMENT OF PROBLEM 11.3 THE PRICING KERNEL 11.4