Читать книгу Perturbation Methods in Credit Derivatives - Colin Turfus - Страница 2
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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 INFLATION AND FX OPTIONS NOTE
18 CHAPTER 12: Rates‐Credit‐FX Hybrid Modelling 12.1 PREVIOUS WORK 12.2 DERIVATION OF RATES‐CREDIT‐FX PRICING KERNEL 12.3 QUANTO CDS REVISITED 12.4 CCDS ON CROSS‐CURRENCY SWAPS REVISITED
19 CHAPTER 13: Risk‐Free Rates 13.1 BACKGROUND 13.2 HULL–WHITE KERNEL EXTENSION 13.3 APPLICATIONS 13.4 BLACK–KARASINSKI KERNEL EXTENSION 13.5 APPLICATIONS 13.6 A NOTE ON TERM RATES NOTES
20 CHAPTER 14: Multi‐Curve Framework 14.1 BACKGROUND 14.2 STOCHASTIC SPREADS 14.3 APPLICATIONS
21 CHAPTER 15: Scenario Generation 15.1 OVERVIEW 15.2 PREVIOUS WORK 15.3 PRICING EQUATION 15.4 HULL–WHITE RATES 15.5 BLACK–KARASINSKI RATES 15.6 JOINT RATES‐CREDIT SCENARIOS NOTES
22 CHAPTER 16: Model Risk Management Strategies 16.1 INTRODUCTION 16.2 MODEL RISK METHODOLOGY 16.3 APPLICATIONS 16.4 CONCLUSIONS NOTES
23 CHAPTER 17: Machine Learning 17.1 TRENDS IN QUANTITATIVE FINANCE RESEARCH 17.2 FROM PRICING MODELS TO MARKET GENERATORS 17.3 SYNERGIES WITH PERTURBATION METHODS NOTES
24 Bibliography
25 Index
List of Tables
1 Chapter 15TABLE 15.1 Model parameters used in USD rates evolution
List of Illustrations
1 Chapter 5FIGURE 5.1 Black–Karasinski prices for maturity cap with 6m LIBOR tenorFIGURE 5.2 Black–Karasinski prices for caps with different maturitiesFIGURE 5.3 Dependence of Black–Karasinski prices for 5y caps on volatility l...FIGURE 5.4 Dependence of Black–Karasinski prices for 5y caps on volatility m...FIGURE 5.5 Dependence of ATM Black–Karasinski prices for 5y caps on IR curve...
2 Chapter 8FIGURE 8.1 Prices for maturity CDSFIGURE 8.2 Correlation impact on prices for maturity IR swap extinguisher...FIGURE 8.3 Correlation impact on prices for IR swap extinguisher with delaye...FIGURE 8.4 IR volatility impact on prices for IR swap extinguisher with dela...FIGURE 8.5 Prices for a CCDS on a 10y IR swap underlying
3 Chapter 10FIGURE 10.1 Pricing of counterparty risk protection on a cross‐currency swap...
4 Chapter 15FIGURE 15.1 USD rates evolution: Scenario 1FIGURE 15.2 USD rates evolution: Scenario 2FIGURE 15.3 USD rates evolution: Scenario 3FIGURE 15.4 Comparison of 1st and 2nd order results for
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