Perturbation Methods in Credit Derivatives

Strategies for Efficient Risk Management

Inbunden, Engelska, 2021

Av Colin Turfus, Colin (Symbian Ltd) Turfus

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Stress-test financial models and price credit instruments with confidence and efficiency using the perturbation approach taught in this expert volumePerturbation Methods in Credit Derivatives: Strategies for Efficient Risk Management 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.The book provides innumerable benefits to a wide range of quantitative financial experts attempting to comply with increasingly burdensome regulatory stress-testing requirements, including: Replacing time-consuming Monte Carlo simulations with faster, simpler pricing algorithms for front-office quantsAllowing CVA quants to quantify the impact of counterparty risk, including wrong-way correlation risk, more efficientlyDeveloping more efficient algorithms for generating stress scenarios for market risk quantsObtaining more intuitive analytic pricing formulae which offer a clearer intuition of the important relationships among market parameters, modelling assumptions and trade/portfolio characteristics for tradersThe methods comprehensively taught in Perturbation Methods in Credit Derivatives also apply to CVA/DVA calculations and contingent credit default swap pricing.

Produktinformation

Utgivningsdatum2021-01-28
Mått178 x 246 x 25 mm
Vikt612 g
FormatInbunden
SpråkEngelska
SerieWiley Finance
Antal sidor256
FörlagJohn Wiley & Sons Inc
ISBN9781119609612

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COLIN TURFUS, PHD., works in Global Model Validation and Governance at Deutsche Bank. For the last fifteen years, he has been a financial engineer, mainly analysing model risk for credit derivatives and hybrids. He specialises in the application of perturbation methods to risk management, finding efficient analytic methods for computing prices and risk measures. He also taught courses on C++ and Financial Engineering at City, University of London for seven years. Prior to that, Colin worked as a developer consultant in the mobile phone industry after an extended period in academia, teaching applied mathematics and researching in fluid dynamics and turbulent dispersion.??

Preface xiAcknowledgments xvAcronyms xviChapter 1 Why Perturbation Methods? 11.1 Analytic Pricing of Derivatives 11.2 In Defence of Perturbation Methods 3Chapter 2 Some Representative Case Studies 82.1 Quanto CDS Pricing 82.2 Wrong-Way Interest Rate Risk 92.3 Contingent CDS Pricing and CVA 102.4 Analytic Interest Rate Option Pricing 102.5 Exposure Scenario Generation 112.6 Model Risk 112.7 Machine Learning 122.8 Incorporating Interest Rate Skew and Smile 13Chapter 3 The Mathematical Foundations 143.1 The Pricing Equation 143.2 Pricing Kernels 163.2.1 What Is a Kernel? 163.2.2 Kernels in Financial Engineering 183.2.3 Why Use Pricing Kernels? 193.3 Evolution Operators 203.3.1 Time-Ordered Exponential 213.3.2 Magnus Expansion 223.4 Obtaining the Pricing Kernel 233.4.1 Duhamel–Dyson Expansion Formula 243.4.2 Baker–Campbell–Hausdorff Expansion Formula 243.4.3 Exponential Expansion Formula 253.4.4 Exponentials of Derivatives 263.4.5 Example – The Black–Scholes Pricing Kernel 283.4.6 Example – Mean-Reverting Diffusion 303.5 Convolutions with Gaussian Pricing Kernels 323.6 Proofs for Chapter 3 363.6.1 Proof of Theorem 3.2 363.6.2 Proof of Lemma 3.1 38Chapter 4 Hull–White Short-Rate Model 404.1 Background of Hull–White Model 414.2 The Pricing Kernel 424.3 Applications 434.3.1 Zero Coupon Bond Pricing 434.3.2 LIBOR Pricing 444.3.3 Caplet Pricing 454.3.4 European Swaption Pricing 474.4 Proof of Theorem 4.1 484.4.1 Preliminary Results 484.4.2 Turn the Handle! 49Chapter 5 Black–Karasinski Short-Rate Model 525.1 Background of Black–Karasinski Model 525.2 The Pricing Kernel 545.3 Applications 565.3.1 Zero Coupon Bond Pricing 565.3.2 Caplet Pricing 585.3.3 European Swaption Pricing 615.4 Comparison of Results 625.5 Proof of Theorem 5.1 655.5.1 Preliminary Result 655.5.2 Turn the Handle! 665.6 Exact Black–Karasinski Pricing Kernel 67Chapter 6 Extension to Multi-Factor Modelling 706.1 Multi-Factor Pricing Equation 706.2 Derivation of Pricing Kernel 736.2.1 Preliminaries 736.2.2 Full Solution Using Operator Expansion 746.3 Exact Expression for Hull–White Model 756.4 Asymptotic Expansion for Black–Karasinski Model 786.5 Formal Solution for Rates-Credit Hybrid Model 82Chapter 7 Rates-Equity Hybrid Modelling 867.1 Statement of Problem 867.2 Previous Work 867.3 The Pricing Kernel 877.3.1 Main Result 877.4 Vanilla Option Pricing 90Chapter 8 Rates-Credit Hybrid Modelling 928.1 Background 928.1.1 Black–Karasinski as a Credit Model 928.1.2 Analytic Pricing of Rates-Credit Hybrid Products 938.1.3 Mathematical Definition of the Model 948.1.4 Pricing Credit-Contingent Cash Flows 948.2 The Pricing Kernel 958.3 CDS Pricing 1018.3.1 Risky Cash Flow Pricing 1018.3.2 Protection Leg Pricing 1038.3.3 Defaultable LIBOR Pricing 1058.3.4 Defaultable Capped LIBOR Pricing 1108.3.5 Contingent CDS with IR Swap Underlying 111Chapter 9 Credit-Equity Hybrid Modelling 1169.1 Background 1169.2 Derivation of Credit-Equity Pricing Kernel 1179.2.1 Pricing Equation 1179.2.2 Pricing Kernel 1199.2.3 Asymptotic Expansion 1209.3 Convertible Bonds 1229.4 Contingent CDS on Equity Option 124Chapter 10 Credit-FX Hybrid Modelling 12710.1 Background 12710.2 Credit-FX Pricing Kernel 12810.3 Quanto CDS 12910.3.1 Domestic Currency Fixed Flow 12910.3.2 Foreign Currency Fixed Flow 12910.3.3 Foreign Currency LIBOR Flow 13110.3.4 Foreign Currency Notional Protection 13110.4 Contingent CDS on Cross-Currency Swaps 133Chapter 11 Multi-Currency Modelling 13711.1 Previous Work 13711.2 Statement of Problem 13811.3 The Pricing Kernel 13911.3.1 Main Result 13911.3.2 Derivation of Multi-Currency Pricing Kernel 14211.4 Inflation and FX Options 144Chapter 12 Rates-Credit-FX Hybrid Modelling 14612.1 Previous Work 14612.2 Derivation of Rates-Credit-FX Pricing Kernel 14612.2.1 Pricing Equation 14612.2.2 Pricing Kernel 14812.3 Quanto CDS Revisited 15512.3.1 Domestic Currency Fixed Flow 15512.3.2 Foreign Currency Fixed Flow 15512.3.3 Foreign Currency Notional Protection 15812.4 CCDS on Cross-Currency Swaps Revisited 159Chapter 13 Risk-Free Rates 16313.1 Background 16313.2 Hull–White Kernel Extension 16513.3 Applications 16613.3.1 Compounded Rates Payment 16613.3.2 Caplet Pricing 16613.3.3 European Swaption Pricing 16913.3.4 Average Rate Options 16913.4 Black–Karasinski Kernel Extension 17013.5 Applications 17113.5.1 Compounded Rates Payment 17113.5.2 Caplet Pricing 17213.6 A Note on Term Rates 177Chapter 14 Multi-Curve Framework 17814.1 Background 17814.2 Stochastic Spreads 18014.3 Applications 18214.3.1 LIBOR Pricing 18214.3.2 LIBOR Caplet Pricing 18314.3.3 European Swaption Pricing 186Chapter 15 Scenario Generation 18715.1 Overview 18715.2 Previous Work 18815.3 Pricing Equation 19015.4 Hull–White Rates 19215.4.1 Two-Factor Pricing Kernel 19215.4.2 m-Factor Extension 19415.5 Black–Karasinski Rates 19515.5.1 Two-Factor Pricing Kernel 19515.5.2 Asymptotic Expansion 19515.5.3 m-Factor Extension 19815.5.4 Representative Calculations 19815.6 Joint Rates-Credit Scenarios 201Chapter 16 Model Risk Management Strategies 20316.1 Introduction 20316.2 Model Risk Methodology 20516.2.1 Previous Work 20516.2.2 Proposed Framework 20816.2.3 Calibration to CDS Market 20916.3 Applications 21016.3.1 Interest Rate Swap Extinguisher 21016.3.2 Contingent CDS 21116.4 Conclusions 212Chapter 17 Machine Learning 21317.1 Trends in Quantitative Finance Research 21317.1.1 Some Recent Trends 21317.1.2 The Arrival of Machine Learning 21417.2 From Pricing Models to Market Generators 21517.3 Synergies with Perturbation Methods 21717.3.1 Asymptotics as Control Variates 21717.3.2 Data Representation 218Bibliography 222Index 229