Perturbation methods in credit derivatives : strategies for efficient risk management /: strategies for efficient risk management. (2021)

• Record Type: Book
• Further Information: Note: Colin Turfus.
• Authors: Turfus, Colin
• Contents: Preface xiii Acknowledgments xvii Acronyms xix 1 Why Perturbation Methods? 1 1.1 Analytic Pricing of Derivatives 1 1.2 In Defence of Perturbation Methods 3 2 Some Representative Case Studies 7 2.1 Quanto CDS Pricing 7 2.2 Wrong-Way Interest Rate Risk 8 2.3 Contingent CDS Pricing and CVA 9 2.4 Analytic Interest Rate Option Pricing 9 2.5 Exposure Scenario Generation 10 2.6 Model Risk 11 2.7 Machine Learning 12 2.8 Incorporating Interest Rate Skew and Smile 13 3 The Mathematical Foundations 15 3.1 The Pricing Equation 15 3.2 Pricing Kernels 18 3.2.1 What Is a Kernel? 18 3.2.2 Kernels in Financial Engineering 20 3.2.3 Why Use Pricing Kernels? 20 3.3 Evolution Operators 21 3.4 Obtaining the Pricing Kernel 25 3.4.1 Example – The Black-Scholes Pricing Kernel 31 3.4.2 Example – Mean-Reverting Diffusion 32 3.5 Convolutions with Gaussian Pricing Kernels 35 3.6 Proofs for Chapter 3 39 3.6.1 Proof of Theorem 3.2 39 3.6.2 Proof of Lemma 3.1 41 4 Hull-White Short Rate Model 43 4.1 Background of Hull-White Model 44 4.2 The Pricing Kernel 45 4.3 Applications 46 4.3.1 Zero Coupon Bond Pricing 46 4.3.2 LIBOR Pricing 47 4.3.3 Caplet Pricing 49 4.3.4 European Swaption Pricing 50 4.3.5 CMS Index Representation 51 4.4 Proof of Theorem 4.1 52 4.4.1 Preliminary Results 52 4.4.2 Turn the Handle! 54 5 Black-Karasinski Short Rate Model 57 5.1 Background of Black-Karasinski Model 57 5.2 The Pricing Kernel 59 5.3 Applications 61 5.3.1 Zero Coupon Bond Pricing 61 5.3.2 Caplet Pricing 63 5.3.3 European Swaption Pricing 67 5.4 Comparison of Results 67 5.5 Proof of Theorem 5.1 71 5.5.1 Preliminary Result 71 5.5.2 Turn the Handle! 72 5.6 Exact Black-Karasinski Pricing Kernel 74 6 Extension to Multi-Factor Modelling 77 6.1 Multi-Factor Pricing Equation 77 6.2 Derivation of Pricing Kernel 81 6.2.1 Preliminaries 81 6.2.2 Full Solution Using Operator Expansion 82 6.3 Exact Expression for Hull-White Model 83 6.4 Asymptotic Expansion for Black-Karasinski Model 87 6.5 Formal Solution for Rates-Credit Hybrid Model 91 7 Rates-Equity Hybrid Modelling 95 7.1 Statement of Problem 95 7.2 Previous Work 96 7.3 The Pricing Kernel 97 7.3.1 Main Result 97 7.4 Vanilla Option Pricing 100 8 Rates-Credit Hybrid Modelling 101 8.1 Background 101 8.1.1 Black-Karasinski as a Credit Model 101 8.1.2 Analytic Pricing of Rates-Credit Hybrid Products 102 8.1.3 Mathematical Definition of the Model 103 8.1.4 Pricing Credit-Contingent Cash Flows 103 8.2 The Pricing Kernel 104 8.3 CDS Pricing 110 8.3.1 Risky Cash Flow Pricing 110 8.3.2 Protection Leg Pricing 113 8.3.3 Defaultable LIBOR Pricing 114 8.3.4 Defaultable Capped LIBOR Pricing 119 8.3.5 Contingent CDS with IR Swap Underlying 120 9 Credit-Equity Hybrid Modelling 127 9.1 Background 127 9.2 Derivation of Credit-Equity Pricing Kernel 129 9.2.1 Pricing Equation 129 9.2.2 Pricing Kernel 130 9.2.3 Asymptotic Expansion 132 9.3 Convertible Bonds 133 9.4 Contingent CDS on Equity Option 136 10 Credit-FX Hybrid Modelling 139 10.1 Background 139 10.2 Credit-FX Pricing Kernel 140 10.3 Quanto CDS 141 10.3.1 Domestic Currency Fixed Flow 141 10.3.2 Foreign Currency Fixed Flow 142 10.3.3 Foreign Currency LIBOR Flow 143 10.3.4 Foreign Currency Notional Protection 143 10.4 Contingent CDS on Cross-Currency Swaps 145 11 Multi-Currency Modelling 151 11.1 Previous Work 151 11.2 Statement of Problem 152 11.3 The Pricing Kernel 153 11.3.1 Main Result 153 11.3.2 Derivation of Multi-Currency Pricing Kernel 157 11.4 Inflation and FX Options 159 12 Rates-Credit-FX Hybrid Modelling 161 12.1 Previous Work 161 12.2 Derivation of Rates-Credit-FX Pricing Kernel 162 12.2.1 Pricing Equation 162 12.2.2 Pricing Kernel 163 12.3 Quanto CDS Revisited 170 12.3.1 Domestic Currency Fixed Flow 170 12.3.2 Foreign Currency Fixed Flow 171 12.3.3 Foreign Currency Notional Protection 174 12.4 CCDS on Cross-Currency Swaps Revisited 175 13 Risk-Free Rates 181 13.1 Background 181 13.2 Hull-White Kernel Extension 183 13.3 Applications 184 13.3.1 Compounded Rates Payment 184 13.3.2 Caplet Pricing 185 13.3.3 European Swaption Pricing 187 13.3.4 Average Rate Options 187 13.4 Black-Karasinski Kernel Extension 189 13.5 Applications 190 13.5.1 Compounded Rates Payment 190 13.5.2 Caplet Pricing 191 13.6 A Note on Term Rates 195 14 Multi-Curve Framework 197 14.1 Background 197 14.2 Stochastic Spreads 200 14.3 Applications 201 14.3.1 LIBOR Pricing 201 14.3.2 LIBOR Caplet Pricing 202 14.3.3 European Swaption Pricing 206 15 Scenario Generation 209 15.1 Overview 209 15.2 Previous Work 210 15.3 Pricing Equation 213 15.4 Hull-White Rates 214 15.4.1 Two-Factor Pricing Kernel 214 15.4.2 m-Factor Extension 217 15.5 Black-Karasinski Rates 218 15.5.1 Two-Factor Pricing Kernel 218 15.5.2 Asymptotic Expansion 219 15.5.3 m-Factor Extension 221 15.5.4 Representative Calculations 222 15.6 Joint Rates-Credit Scenarios 224 16 Model Risk Management Strategies 227 16.1 Introduction 227 16.2 Model Risk Methodology 229 16.2.1 Previous work 229 16.2.2 Proposed framework 232 16.2.3 Calibration to CDS market 234 16.3 Applications 235 16.3.1 Interest rate swap extinguisher 235 16.3.2 Contingent CDS 236 16.4 Conclusions 238 Bibliography 239 Index 247
• Publisher Details: Chichester, West Sussex, United Kingdom : John Wiley & Sons, Ltd
• Publication Date: 2021
• Copyright Date: 2021
• Extent: 1 online resource (xvi, 233 pages), illustrations
• Subjects: 332.64/57; Credit derivatives; Financial risk management; Credit derivatives; Financial risk management; Electronic books
• Languages: English
• ISBNs: 9781119610168; 1119610168; 9781119609599; 1119609593; 1119609623; 9781119609629
• Related ISBNs: 9781119609612
• Notes: Note: Includes bibliographical references and index.; Note: Description based on online resource; title from digital title page (viewed on January 14, 2021).
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.