Table of Contents
1 Cover
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