Perturbation Methods in Credit Derivatives - Strategies for Efficient Risk Management

Stress-test financial models and price credit instruments with confidence and efficiency using the perturbation approach taught in this expert volume
 
Perturbation 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 quants
* Allowing CVA quants to quantify the impact of counterparty risk, including wrong-way correlation risk, more efficiently
* Developing more efficient algorithms for generating stress scenarios for market risk quants
* Obtaining more intuitive analytic pricing formulae which offer a clearer intuition of the important relationships among market parameters, modelling assumptions and trade/portfolio characteristics for traders
 
The methods comprehensively taught in Perturbation Methods in Credit Derivatives also apply to CVA/DVA calculations and contingent credit default swap pricing.

List of contents

Preface xi
 
Acknowledgments xv
 
Acronyms xvi
 
Chapter 1 Why Perturbation Methods? 1
 
1.1 Analytic Pricing of Derivatives 1
 
1.2 In Defence of Perturbation Methods 3
 
Chapter 2 Some Representative Case Studies 8
 
2.1 Quanto CDS Pricing 8
 
2.2 Wrong-Way Interest Rate Risk 9
 
2.3 Contingent CDS Pricing and CVA 10
 
2.4 Analytic Interest Rate Option Pricing 10
 
2.5 Exposure Scenario Generation 11
 
2.6 Model Risk 11
 
2.7 Machine Learning 12
 
2.8 Incorporating Interest Rate Skew and Smile 13
 
Chapter 3 The Mathematical Foundations 14
 
3.1 The Pricing Equation 14
 
3.2 Pricing Kernels 16
 
3.2.1 What Is a Kernel? 16
 
3.2.2 Kernels in Financial Engineering 18
 
3.2.3 Why Use Pricing Kernels? 19
 
3.3 Evolution Operators 20
 
3.3.1 Time-Ordered Exponential 21
 
3.3.2 Magnus Expansion 22
 
3.4 Obtaining the Pricing Kernel 23
 
3.4.1 Duhamel-Dyson Expansion Formula 24
 
3.4.2 Baker-Campbell-Hausdorff Expansion Formula 24
 
3.4.3 Exponential Expansion Formula 25
 
3.4.4 Exponentials of Derivatives 26
 
3.4.5 Example - The Black-Scholes Pricing Kernel 28
 
3.4.6 Example - Mean-Reverting Diffusion 30
 
3.5 Convolutions with Gaussian Pricing Kernels 32
 
3.6 Proofs for Chapter 3 36
 
3.6.1 Proof of Theorem 3.2 36
 
3.6.2 Proof of Lemma 3.1 38
 
Chapter 4 Hull-White Short-Rate Model 40
 
4.1 Background of Hull-White Model 41
 
4.2 The Pricing Kernel 42
 
4.3 Applications 43
 
4.3.1 Zero Coupon Bond Pricing 43
 
4.3.2 LIBOR Pricing 44
 
4.3.3 Caplet Pricing 45
 
4.3.4 European Swaption Pricing 47
 
4.4 Proof of Theorem 4.1 48
 
4.4.1 Preliminary Results 48
 
4.4.2 Turn the Handle! 49
 
Chapter 5 Black-Karasinski Short-Rate Model 52
 
5.1 Background of Black-Karasinski Model 52
 
5.2 The Pricing Kernel 54
 
5.3 Applications 56
 
5.3.1 Zero Coupon Bond Pricing 56
 
5.3.2 Caplet Pricing 58
 
5.3.3 European Swaption Pricing 61
 
5.4 Comparison of Results 62
 
5.5 Proof of Theorem 5.1 65
 
5.5.1 Preliminary Result 65
 
5.5.2 Turn the Handle! 66
 
5.6 Exact Black-Karasinski Pricing Kernel 67
 
Chapter 6 Extension to Multi-Factor Modelling 70
 
6.1 Multi-Factor Pricing Equation 70
 
6.2 Derivation of Pricing Kernel 73
 
6.2.1 Preliminaries 73
 
6.2.2 Full Solution Using Operator Expansion 74
 
6.3 Exact Expression for Hull-White Model 75
 
6.4 Asymptotic Expansion for Black-Karasinski Model 78
 
6.5 Formal Solution for Rates-Credit Hybrid Model 82
 
Chapter 7 Rates-Equity Hybrid Modelling 86
 
7.1 Statement of Problem 86
 
7.2 Previous Work 86
 
7.3 The Pricing Kernel 87
 
7.3.1 Main Result 87
 
7.4 Vanilla Option Pricing 90
 
Chapter 8 Rates-Credit Hybrid Modelling 92
 
8.1 Background 92
 
8.1.1 Black-Karasinski as a Credit Model 92
 
8.1.2 Analytic Pricing of Rates-Credit Hybrid Products 93
 
8.1.3 Mathematical Definition of the Model 94
 
8.1.4 Pricing Credit-Contingent Cash Flows 94
 
8.2 The Pricing Kernel 95
 
8.3 CDS Pricing 101
 
8.3.1 Risky Cash Flow Pricing 101
 
8.3.2 Protection Leg Pricing 103
 
8.3.3 Defaultable LIBOR Pricing 105
 
8.3.4 Defaultable Capped LIBOR Pricing 110
 
8.3.5 Contingent CDS with IR Swap Underl

About the author

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.??

Summary

Stress-test financial models and price credit instruments with confidence and efficiency using the perturbation approach taught in this expert volume

Perturbation 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 quants
* Allowing CVA quants to quantify the impact of counterparty risk, including wrong-way correlation risk, more efficiently
* Developing more efficient algorithms for generating stress scenarios for market risk quants
* Obtaining more intuitive analytic pricing formulae which offer a clearer intuition of the important relationships among market parameters, modelling assumptions and trade/portfolio characteristics for traders

The methods comprehensively taught in Perturbation Methods in Credit Derivatives also apply to CVA/DVA calculations and contingent credit default swap pricing.

Product details

• Authors: C Turfus, Colin Turfus, Colin (Symbian Ltd) Turfus, Turfus Colin
• Publisher: Wiley, John and Sons Ltd
• Languages: English
• Product format: Hardback
• Released: 31.12.2020
• EAN: 9781119609612
• ISBN: 978-1-119-60961-2
• No. of pages: 256
• Series: Wiley Finance; Wiley Finance Editions; The Wiley Finance Series
• Subjects: Social sciences, law, business > Business > Business administration; Finanzwesen, Financial Engineering, Finance & Investments, Finanz- u. Anlagewesen, Finanztechnik, Spezialthemen Finanz- u. Anlagewesen, Finance & Investments Special Topics