Оглавление
Colin Turfus. Perturbation Methods in Credit Derivatives
Table of Contents
List of Tables
List of Illustrations
Guide
Pages
Perturbation Methods in Credit Derivatives. Strategies for Efficient Risk Management
Preface
Note
Acknowledgments
Acronyms
CHAPTER 1 Why Perturbation Methods? 1.1 ANALYTIC PRICING OF DERIVATIVES
1.2 IN DEFENCE OF PERTURBATION METHODS
NOTE
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
CHAPTER 3 The Mathematical Foundations. 3.1 THE PRICING EQUATION
3.2 PRICING KERNELS. 3.2.1 What Is a Kernel?
3.2.2 Kernels in Financial Engineering
3.2.3 Why Use Pricing Kernels?
3.3 EVOLUTION OPERATORS
3.3.1 Time‐Ordered Exponential
3.3.2 Magnus Expansion
3.4 OBTAINING THE PRICING KERNEL
3.4.1 Duhamel–Dyson Expansion Formula
3.4.2 Baker–Campbell–Hausdorff Expansion Formula
3.4.3 Exponential Expansion Formula
3.4.4 Exponentials of Derivatives
3.4.5 Example – The Black–Scholes Pricing Kernel
3.4.6 Example – Mean‐Reverting Diffusion
3.5 CONVOLUTIONS WITH GAUSSIAN PRICING KERNELS
3.6 PROOFS FOR CHAPTER 3
3.6.1 Proof of Theorem 3.2
3.6.2 Proof of Lemma 3.1
NOTES
CHAPTER 4 Hull–White Short‐Rate Model
4.1 BACKGROUND OF HULL–WHITE MODEL
4.2 THE PRICING KERNEL
4.3 APPLICATIONS. 4.3.1 Zero Coupon Bond Pricing
4.3.2 LIBOR Pricing
4.3.3 Caplet Pricing
4.3.4 European Swaption Pricing
4.4 PROOF OF THEOREM 4.1. 4.4.1 Preliminary Results
4.4.2 Turn the Handle!
NOTES
CHAPTER 5 Black–Karasinski Short‐Rate Model
5.1 BACKGROUND OF BLACK–KARASINSKI MODEL
5.2 THE PRICING KERNEL
5.3 APPLICATIONS
5.3.1 Zero Coupon Bond Pricing
5.3.2 Caplet Pricing
5.3.3 European Swaption Pricing
5.4 COMPARISON OF RESULTS
5.5 PROOF OF THEOREM 5.1. 5.5.1 Preliminary Result
5.5.2 Turn the Handle!
5.6 EXACT BLACK–KARASINSKI PRICING KERNEL
NOTES
CHAPTER 6 Extension to Multi‐Factor Modelling. 6.1 MULTI‐FACTOR PRICING EQUATION
6.2 DERIVATION OF PRICING KERNEL. 6.2.1 Preliminaries
6.2.2 Full Solution Using Operator Expansion
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
CHAPTER 7 Rates‐Equity Hybrid Modelling. 7.1 STATEMENT OF PROBLEM
7.2 PREVIOUS WORK
7.3 THE PRICING KERNEL. 7.3.1 Main Result
7.4 VANILLA OPTION PRICING
CHAPTER 8 Rates‐Credit Hybrid Modelling. 8.1 BACKGROUND. 8.1.1 Black–Karasinski as a Credit Model
8.1.2 Analytic Pricing of Rates‐Credit Hybrid Products
8.1.3 Mathematical Definition of the Model
8.1.4 Pricing Credit‐Contingent Cash Flows
8.2 THE PRICING KERNEL
8.3 CDS PRICING
8.3.1 Risky Cash Flow Pricing
8.3.2 Protection Leg Pricing
8.3.3 Defaultable LIBOR Pricing
8.3.4 Defaultable Capped LIBOR Pricing
8.3.5 Contingent CDS with IR Swap Underlying
NOTES
CHAPTER 9 Credit‐Equity Hybrid Modelling. 9.1 BACKGROUND
9.2 DERIVATION OF CREDIT‐EQUITY PRICING KERNEL. 9.2.1 Pricing Equation
9.2.2 Pricing Kernel
9.2.3 Asymptotic Expansion
9.3 CONVERTIBLE BONDS
9.4 CONTINGENT CDS ON EQUITY OPTION
NOTES
CHAPTER 10 Credit‐FX Hybrid Modelling. 10.1 BACKGROUND
10.2 CREDIT‐FX PRICING KERNEL
10.3 QUANTO CDS
10.3.1 Domestic Currency Fixed Flow
10.3.2 Foreign Currency Fixed Flow
10.3.3 Foreign Currency LIBOR Flow
10.3.4 Foreign Currency Notional Protection
10.4 CONTINGENT CDS ON CROSS‐CURRENCY SWAPS
CHAPTER 11 Multi‐Currency Modelling
11.1 PREVIOUS WORK
11.2 STATEMENT OF PROBLEM
11.3 THE PRICING KERNEL. 11.3.1 Main Result
11.3.2 Derivation of Multi‐Currency Pricing Kernel
11.4 INFLATION AND FX OPTIONS
NOTE
CHAPTER 12 Rates‐Credit‐FX Hybrid Modelling. 12.1 PREVIOUS WORK
12.2 DERIVATION OF RATES‐CREDIT‐FX PRICING KERNEL. 12.2.1 Pricing Equation
12.2.2 Pricing Kernel
12.3 QUANTO CDS REVISITED
12.3.1 Domestic Currency Fixed Flow
12.3.2 Foreign Currency Fixed Flow
12.3.3 Foreign Currency Notional Protection
12.4 CCDS ON CROSS‐CURRENCY SWAPS REVISITED
CHAPTER 13 Risk‐Free Rates. 13.1 BACKGROUND
13.2 HULL–WHITE KERNEL EXTENSION
13.3 APPLICATIONS. 13.3.1 Compounded Rates Payment
13.3.2 Caplet Pricing
13.3.3 European Swaption Pricing
13.3.4 Average Rate Options
13.4 BLACK–KARASINSKI KERNEL EXTENSION
13.5 APPLICATIONS. 13.5.1 Compounded Rates Payment
13.5.2 Caplet Pricing
13.6 A NOTE ON TERM RATES
NOTES
CHAPTER 14 Multi‐Curve Framework. 14.1 BACKGROUND
14.2 STOCHASTIC SPREADS
14.3 APPLICATIONS. 14.3.1 LIBOR Pricing
14.3.2 LIBOR Caplet Pricing
14.3.3 European Swaption Pricing
CHAPTER 15 Scenario Generation. 15.1 OVERVIEW
15.2 PREVIOUS WORK
15.3 PRICING EQUATION
15.4 HULL–WHITE RATES. 15.4.1 Two‐Factor Pricing Kernel
15.4.2 m‐Factor Extension
15.5 BLACK–KARASINSKI RATES. 15.5.1 Two‐Factor Pricing Kernel
15.5.2 Asymptotic Expansion
15.5.3 m‐Factor Extension
15.5.4 Representative Calculations
15.6 JOINT RATES‐CREDIT SCENARIOS
NOTES
CHAPTER 16 Model Risk Management Strategies. 16.1 INTRODUCTION
16.2 MODEL RISK METHODOLOGY. 16.2.1 Previous Work
16.2.2 Proposed Framework
16.2.3 Calibration to CDS Market
16.3 APPLICATIONS
16.3.1 Interest Rate Swap Extinguisher
16.3.2 Contingent CDS
16.4 CONCLUSIONS
NOTES
CHAPTER 17 Machine Learning. 17.1 TRENDS IN QUANTITATIVE FINANCE RESEARCH. 17.1.1 Some Recent Trends
17.1.2 The Arrival of Machine Learning
17.2 FROM PRICING MODELS TO MARKET GENERATORS
17.3 SYNERGIES WITH PERTURBATION METHODS
17.3.1 Asymptotics as Control Variates
17.3.2 Data Representation
NOTES
Bibliography
Index
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