{"product_id":"perturbation-methods-in-credit-derivatives-9781119609612","title":"Perturbation Methods in Credit Derivatives","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e\u003cb\u003eStress-test financial models and price credit instruments with confidence and efficiency using the perturbation approach taught in this expert volume\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003ci\u003ePerturbation Methods in Credit Derivatives: Strategies for Efficient Risk Management\u003c\/i\u003e offers an incisive examination of a new approach to pricing credit-contingent financial instruments. Author and experienced financial engineer Dr. Colin Turfus has created an approach that allows model validators to perform rapid benchmarking of risk and pricing models while making the most efficient use possible of computing resources.\u003c\/p\u003e \u003cp\u003eThe book provides innumerable benefits to a wide range of quantitative financial expertsattempting to comply with increasingly burdensome regulatory stress-testing requirements, including:\u003c\/p\u003e \u003cul\u003e \u003cli\u003eReplacing time-consuming Monte Carlo simulations with faster, simpler pricing algorithms for front-office quants\u003c\/li\u003e \u003cli\u003eAllowing CVA quants to quantify the impact of counterparty risk, includ\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cp\u003ePreface xi\u003c\/p\u003e \u003cp\u003eAcknowledgments xv\u003c\/p\u003e \u003cp\u003eAcronyms xvi\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 1 Why Perturbation Methods? 1\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1.1 Analytic Pricing of Derivatives 1\u003c\/p\u003e \u003cp\u003e1.2 In Defence of Perturbation Methods 3\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 2 Some Representative Case Studies 8\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1 Quanto CDS Pricing 8\u003c\/p\u003e \u003cp\u003e2.2 Wrong-Way Interest Rate Risk 9\u003c\/p\u003e \u003cp\u003e2.3 Contingent CDS Pricing and CVA 10\u003c\/p\u003e \u003cp\u003e2.4 Analytic Interest Rate Option Pricing 10\u003c\/p\u003e \u003cp\u003e2.5 Exposure Scenario Generation 11\u003c\/p\u003e \u003cp\u003e2.6 Model Risk 11\u003c\/p\u003e \u003cp\u003e2.7 Machine Learning 12\u003c\/p\u003e \u003cp\u003e2.8 Incorporating Interest Rate Skew and Smile 13\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 3 The Mathematical Foundations 14\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.1 The Pricing Equation 14\u003c\/p\u003e \u003cp\u003e3.2 Pricing Kernels 16\u003c\/p\u003e \u003cp\u003e3.2.1 What Is a Kernel? 16\u003c\/p\u003e \u003cp\u003e3.2.2 Kernels in Financial Engineering 18\u003c\/p\u003e \u003cp\u003e3.2.3 Why Use Pricing Kernels? 19\u003c\/p\u003e \u003cp\u003e3.3 Evolution Operators 20\u003c\/p\u003e \u003cp\u003e3.3.1 Time-Ordered Exponential 21\u003c\/p\u003e \u003cp\u003e3.3.2 Magnus Expansion 22\u003c\/p\u003e \u003cp\u003e3.4 Obtaining the Pricing Kernel 23\u003c\/p\u003e \u003cp\u003e3.4.1 Duhamel–Dyson Expansion Formula 24\u003c\/p\u003e \u003cp\u003e3.4.2 Baker–Campbell–Hausdorff Expansion Formula 24\u003c\/p\u003e \u003cp\u003e3.4.3 Exponential Expansion Formula 25\u003c\/p\u003e \u003cp\u003e3.4.4 Exponentials of Derivatives 26\u003c\/p\u003e \u003cp\u003e3.4.5 Example – The Black–Scholes Pricing Kernel 28\u003c\/p\u003e \u003cp\u003e3.4.6 Example – Mean-Reverting Diffusion 30\u003c\/p\u003e \u003cp\u003e3.5 Convolutions with Gaussian Pricing Kernels 32\u003c\/p\u003e \u003cp\u003e3.6 Proofs for Chapter 3 36\u003c\/p\u003e \u003cp\u003e3.6.1 Proof of Theorem 3.2 36\u003c\/p\u003e \u003cp\u003e3.6.2 Proof of Lemma 3.1 38\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 4 Hull–White Short-Rate Model 40\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1 Background of Hull–White Model 41\u003c\/p\u003e \u003cp\u003e4.2 The Pricing Kernel 42\u003c\/p\u003e \u003cp\u003e4.3 Applications 43\u003c\/p\u003e \u003cp\u003e4.3.1 Zero Coupon Bond Pricing 43\u003c\/p\u003e \u003cp\u003e4.3.2 LIBOR Pricing 44\u003c\/p\u003e \u003cp\u003e4.3.3 Caplet Pricing 45\u003c\/p\u003e \u003cp\u003e4.3.4 European Swaption Pricing 47\u003c\/p\u003e \u003cp\u003e4.4 Proof of Theorem 4.1 48\u003c\/p\u003e \u003cp\u003e4.4.1 Preliminary Results 48\u003c\/p\u003e \u003cp\u003e4.4.2 Turn the Handle! 49\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 5 Black–Karasinski Short-Rate Model 52\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5.1 Background of Black–Karasinski Model 52\u003c\/p\u003e \u003cp\u003e5.2 The Pricing Kernel 54\u003c\/p\u003e \u003cp\u003e5.3 Applications 56\u003c\/p\u003e \u003cp\u003e5.3.1 Zero Coupon Bond Pricing 56\u003c\/p\u003e \u003cp\u003e5.3.2 Caplet Pricing 58\u003c\/p\u003e \u003cp\u003e5.3.3 European Swaption Pricing 61\u003c\/p\u003e \u003cp\u003e5.4 Comparison of Results 62\u003c\/p\u003e \u003cp\u003e5.5 Proof of Theorem 5.1 65\u003c\/p\u003e \u003cp\u003e5.5.1 Preliminary Result 65\u003c\/p\u003e \u003cp\u003e5.5.2 Turn the Handle! 66\u003c\/p\u003e \u003cp\u003e5.6 Exact Black–Karasinski Pricing Kernel 67\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 6 Extension to Multi-Factor Modelling 70\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e6.1 Multi-Factor Pricing Equation 70\u003c\/p\u003e \u003cp\u003e6.2 Derivation of Pricing Kernel 73\u003c\/p\u003e \u003cp\u003e6.2.1 Preliminaries 73\u003c\/p\u003e \u003cp\u003e6.2.2 Full Solution Using Operator Expansion 74\u003c\/p\u003e \u003cp\u003e6.3 Exact Expression for Hull–White Model 75\u003c\/p\u003e \u003cp\u003e6.4 Asymptotic Expansion for Black–Karasinski Model 78\u003c\/p\u003e \u003cp\u003e6.5 Formal Solution for Rates-Credit Hybrid Model 82\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 7 Rates-Equity Hybrid Modelling 86\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e7.1 Statement of Problem 86\u003c\/p\u003e \u003cp\u003e7.2 Previous Work 86\u003c\/p\u003e \u003cp\u003e7.3 The Pricing Kernel 87\u003c\/p\u003e \u003cp\u003e7.3.1 Main Result 87\u003c\/p\u003e \u003cp\u003e7.4 Vanilla Option Pricing 90\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 8 Rates-Credit Hybrid Modelling 92\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e8.1 Background 92\u003c\/p\u003e \u003cp\u003e8.1.1 Black–Karasinski as a Credit Model 92\u003c\/p\u003e \u003cp\u003e8.1.2 Analytic Pricing of Rates-Credit Hybrid Products 93\u003c\/p\u003e \u003cp\u003e8.1.3 Mathematical Definition of the Model 94\u003c\/p\u003e \u003cp\u003e8.1.4 Pricing Credit-Contingent Cash Flows 94\u003c\/p\u003e \u003cp\u003e8.2 The Pricing Kernel 95\u003c\/p\u003e \u003cp\u003e8.3 CDS Pricing 101\u003c\/p\u003e \u003cp\u003e8.3.1 Risky Cash Flow Pricing 101\u003c\/p\u003e \u003cp\u003e8.3.2 Protection Leg Pricing 103\u003c\/p\u003e \u003cp\u003e8.3.3 Defaultable LIBOR Pricing 105\u003c\/p\u003e \u003cp\u003e8.3.4 Defaultable Capped LIBOR Pricing 110\u003c\/p\u003e \u003cp\u003e8.3.5 Contingent CDS with IR Swap Underlying 111\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 9 Credit-Equity Hybrid Modelling 116\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e9.1 Background 116\u003c\/p\u003e \u003cp\u003e9.2 Derivation of Credit-Equity Pricing Kernel 117\u003c\/p\u003e \u003cp\u003e9.2.1 Pricing Equation 117\u003c\/p\u003e \u003cp\u003e9.2.2 Pricing Kernel 119\u003c\/p\u003e \u003cp\u003e9.2.3 Asymptotic Expansion 120\u003c\/p\u003e \u003cp\u003e9.3 Convertible Bonds 122\u003c\/p\u003e \u003cp\u003e9.4 Contingent CDS on Equity Option 124\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 10 Credit-FX Hybrid Modelling 127\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e10.1 Background 127\u003c\/p\u003e \u003cp\u003e10.2 Credit-FX Pricing Kernel 128\u003c\/p\u003e \u003cp\u003e10.3 Quanto CDS 129\u003c\/p\u003e \u003cp\u003e10.3.1 Domestic Currency Fixed Flow 129\u003c\/p\u003e \u003cp\u003e10.3.2 Foreign Currency Fixed Flow 129\u003c\/p\u003e \u003cp\u003e10.3.3 Foreign Currency LIBOR Flow 131\u003c\/p\u003e \u003cp\u003e10.3.4 Foreign Currency Notional Protection 131\u003c\/p\u003e \u003cp\u003e10.4 Contingent CDS on Cross-Currency Swaps 133\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 11 Multi-Currency Modelling 137\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e11.1 Previous Work 137\u003c\/p\u003e \u003cp\u003e11.2 Statement of Problem 138\u003c\/p\u003e \u003cp\u003e11.3 The Pricing Kernel 139\u003c\/p\u003e \u003cp\u003e11.3.1 Main Result 139\u003c\/p\u003e \u003cp\u003e11.3.2 Derivation of Multi-Currency Pricing Kernel 142\u003c\/p\u003e \u003cp\u003e11.4 Inflation and FX Options 144\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 12 Rates-Credit-FX Hybrid Modelling 146\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e12.1 Previous Work 146\u003c\/p\u003e \u003cp\u003e12.2 Derivation of Rates-Credit-FX Pricing Kernel 146\u003c\/p\u003e \u003cp\u003e12.2.1 Pricing Equation 146\u003c\/p\u003e \u003cp\u003e12.2.2 Pricing Kernel 148\u003c\/p\u003e \u003cp\u003e12.3 Quanto CDS Revisited 155\u003c\/p\u003e \u003cp\u003e12.3.1 Domestic Currency Fixed Flow 155\u003c\/p\u003e \u003cp\u003e12.3.2 Foreign Currency Fixed Flow 155\u003c\/p\u003e \u003cp\u003e12.3.3 Foreign Currency Notional Protection 158\u003c\/p\u003e \u003cp\u003e12.4 CCDS on Cross-Currency Swaps Revisited 159\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 13 Risk-Free Rates 163\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e13.1 Background 163\u003c\/p\u003e \u003cp\u003e13.2 Hull–White Kernel Extension 165\u003c\/p\u003e \u003cp\u003e13.3 Applications 166\u003c\/p\u003e \u003cp\u003e13.3.1 Compounded Rates Payment 166\u003c\/p\u003e \u003cp\u003e13.3.2 Caplet Pricing 166\u003c\/p\u003e \u003cp\u003e13.3.3 European Swaption Pricing 169\u003c\/p\u003e \u003cp\u003e13.3.4 Average Rate Options 169\u003c\/p\u003e \u003cp\u003e13.4 Black–Karasinski Kernel Extension 170\u003c\/p\u003e \u003cp\u003e13.5 Applications 171\u003c\/p\u003e \u003cp\u003e13.5.1 Compounded Rates Payment 171\u003c\/p\u003e \u003cp\u003e13.5.2 Caplet Pricing 172\u003c\/p\u003e \u003cp\u003e13.6 A Note on Term Rates 177\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 14 Multi-Curve Framework 178\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e14.1 Background 178\u003c\/p\u003e \u003cp\u003e14.2 Stochastic Spreads 180\u003c\/p\u003e \u003cp\u003e14.3 Applications 182\u003c\/p\u003e \u003cp\u003e14.3.1 LIBOR Pricing 182\u003c\/p\u003e \u003cp\u003e14.3.2 LIBOR Caplet Pricing 183\u003c\/p\u003e \u003cp\u003e14.3.3 European Swaption Pricing 186\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 15 Scenario Generation 187\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e15.1 Overview 187\u003c\/p\u003e \u003cp\u003e15.2 Previous Work 188\u003c\/p\u003e \u003cp\u003e15.3 Pricing Equation 190\u003c\/p\u003e \u003cp\u003e15.4 Hull–White Rates 192\u003c\/p\u003e \u003cp\u003e15.4.1 Two-Factor Pricing Kernel 192\u003c\/p\u003e \u003cp\u003e15.4.2 m-Factor Extension 194\u003c\/p\u003e \u003cp\u003e15.5 Black–Karasinski Rates 195\u003c\/p\u003e \u003cp\u003e15.5.1 Two-Factor Pricing Kernel 195\u003c\/p\u003e \u003cp\u003e15.5.2 Asymptotic Expansion 195\u003c\/p\u003e \u003cp\u003e15.5.3 m-Factor Extension 198\u003c\/p\u003e \u003cp\u003e15.5.4 Representative Calculations 198\u003c\/p\u003e \u003cp\u003e15.6 Joint Rates-Credit Scenarios 201\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 16 Model Risk Management Strategies 203\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e16.1 Introduction 203\u003c\/p\u003e \u003cp\u003e16.2 Model Risk Methodology 205\u003c\/p\u003e \u003cp\u003e16.2.1 Previous Work 205\u003c\/p\u003e \u003cp\u003e16.2.2 Proposed Framework 208\u003c\/p\u003e \u003cp\u003e16.2.3 Calibration to CDS Market 209\u003c\/p\u003e \u003cp\u003e16.3 Applications 210\u003c\/p\u003e \u003cp\u003e16.3.1 Interest Rate Swap Extinguisher 210\u003c\/p\u003e \u003cp\u003e16.3.2 Contingent CDS 211\u003c\/p\u003e \u003cp\u003e16.4 Conclusions 212\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 17 Machine Learning 213\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e17.1 Trends in Quantitative Finance Research 213\u003c\/p\u003e \u003cp\u003e17.1.1 Some Recent Trends 213\u003c\/p\u003e \u003cp\u003e17.1.2 The Arrival of Machine Learning 214\u003c\/p\u003e \u003cp\u003e17.2 From Pricing Models to Market Generators 215\u003c\/p\u003e \u003cp\u003e17.3 Synergies with Perturbation Methods 217\u003c\/p\u003e \u003cp\u003e17.3.1 Asymptotics as Control Variates 217\u003c\/p\u003e \u003cp\u003e17.3.2 Data Representation 218\u003c\/p\u003e \u003cp\u003eBibliography 222\u003c\/p\u003e \u003cp\u003eIndex 229\u003c\/p\u003e\n\u003c\/li\u003e\n\u003c\/ul\u003e","brand":"John Wiley \u0026 Sons Inc","offers":[{"title":"Default Title","offer_id":48866405679447,"sku":"9781119609612","price":57.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781119609612.jpg?v=1722278493","url":"https:\/\/bookcurl.com\/products\/perturbation-methods-in-credit-derivatives-9781119609612","provider":"Book Curl","version":"1.0","type":"link"}