Frontiers in Quantitative Finance: Volatility and Credit Risk Modeling / Edition 1

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Overview

The Petit Déjeuner de la Finance—which Rama Cont hasbeen co-organizing in Paris since 1998—is a well-knownquantitative finance seminar that has progressively become aplatform for the exchange of ideas between the academic andpractitioner communities in quantitative finance. This seminar hasincluded a prestigious list of international speakers who areconsidered major contributors to recent developments inquantitative finance.

Frontiers in Quantitative Finance is a selection of recentpresentations in the Petit Déjeuner de la Finance. Leadingquants and academic researchers cover the most important emergingissues in quantitative finance and focus on portfolio credit riskand volatility modeling.

This comprehensive volume is divided into two parts. The firstpart (Chapters 1–5) deals with advances in option pricing andvolatility modeling in the context of equity and index derivatives.Topics include tests for static arbitrage, asymptotics of impliedvolatility, jump-diffusion models, variance swaps, and cliquetoptions. The second part (Chapters 6–11) covers recentadvances in pricing models for credit derivatives. Topics hereinclude structural vs. hazard rate models, factor models andtop-down models for portfolio credit derivatives, and forwardequations for CDO pricing.

Contributors to this volume include Areski Cousin, Alexandred'Aspremont, Shalom Benaim, Lorenzo Bergomi, Peter Friz, KayGiesecke, Pierre Henry-Labordère, Jean-Paul Laurent, RogerLee, Chris Rogers, Ioana Savescu, Erik Schlögl, LutzSchlögl, Peter Tankov, Julien Turc, Philippe Very, andEkaterina Voltchkova.

For quants, risk managers, consultants, graduate students inquantitative finance, hedge fund managers, and academics, Frontiersin Quantitative Finance is an invaluable guide to thestate-of-the-art knowledge in credit risk and volatilitymodeling.

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Product Details

  • ISBN-13: 9780470292921
  • Publisher: Wiley
  • Publication date: 11/10/2008
  • Series: Wiley Finance Series , #463
  • Edition description: New
  • Edition number: 1
  • Pages: 300
  • Product dimensions: 6.20 (w) x 9.10 (h) x 1.20 (d)

Meet the Author

Rama Cont is Associate Professor at Columbia University and Director of the Columbia Center for Financial Engineering. He is also a founding partner of Finance Concepts, a firm offering training and consulting services in quantitative finance and risk management.

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Table of Contents

Preface.

About the Editor.

About the Contributors.

PART ONE: Option Pricing and VolatilityModeling.

CHAPTER 1: A Moment Approach to Static Arbitrage (Alexandred’Aspremont).

1.1 Introduction.

1.2 No-Arbitrage Conditions.

1.3 Example.

1.4 Conclusion.

CHAPTER 2: On Black-Scholes Implied Volatility at ExtremeStrikes (Shalom Benaim, Peter Friz, and Roger Lee).

2.1 Introduction.

2.2 The Moment Formula.

2.3 Regular Variation and the Tail-Wing Formula.

2.4 Related Results.

2.5 Applications.

2.6 CEV and SABR.

CHAPTER 3: Dynamic Properties of Smile Models (LorenzoBergomi).

3.1 Introduction.

3.2 Some Standard Smile Models.

3.3 A New Class of Models for Smile Dynamics.

3.4 Pricing Examples.

3.5 Conclusion.

CHAPTER 4: A Geometric Approach to the Asymptotics of ImpliedVolatility (Pierre Henry-Labor&dgrave;ere).

4.1 Volatility Asymptotics in Stochastic Volatility Models.

4.2 Heat Kernel Expansion.

4.3 Geometry of Complex Curves and Asymptotic Volatility.

4.4 λ-SABR Model and Hyperbolic Geometry.

4.5 SABR Model with β = 0, 1.

4.6 Conclusions and Future Work.

4.7 Appendix A: Notions in Differential Geometry.

4.8 Appendix B: Laplace Integrals in Many Dimensions.

CHAPTER 5: Pricing, Hedging, and Calibration in Jump-DiffusionModels (Peter Tankov and Ekaterina Voltchkova).

5.1 Overview of Jump-Diffusion Models.

5.2 Pricing European Options via Fourier Transform.

5.3 Integro-differential Equations for Barrier and AmericanOptions.

5.4 Hedging Jump Risk.

5.5 Model Calibration.

PART TWO: Credit Risk.

CHAPTER 6: Modeling Credit Risk (L. C. G. Rogers).

6.1 What Is the Problem?

6.2 Hazard Rate Models.

6.3 Structural Models.

6.4 Some Nice Ideas.

6.5 Conclusion.

CHAPTER 7: An Overview of Factor Modeling for CDO Pricing(Jean-Paul Laurent and Areski Cousin).

7.1 Pricing of Portfolio Credit Derivatives.

7.2 Factor Models for the Pricing of CDO Tranches.

7.3 A Review of Factor Approaches to the Pricing of CDOs.

7.4 Conclusion.

CHAPTER 8: Factor Distributions Implied by Quoted CDO Spreads(Erik Schlögl and Lutz Schlögl).

8.1 Introduction.

8.2 Modeling.

8.3 Examples.

8.4 Conclusion.

8.5 Appendix: Some Useful Results on Hermite Polynomials underLinear Coordinate Transforms.

CHAPTER 9: Pricing CDOs with a Smile: The Local CorrelationModel (Julien Turc and Philippe Very).

9.1 The Local Correlation Model.

9.2 Simplification under the Large Pool Assumption.

9.3 Building the Local Correlation Function without the LargePool Assumption.

9.4 Pricing and Hedging with Local Correlation.

CHAPTER 10: Portfolio Credit Risk: Top-Down versus Bottom-UpApproaches (Kay Giesecke).

10.1 Introduction.

10.2 Portfolio Credit Models.

10.3 Information and Specification.

10.4 Default Distribution.

10.5 Calibration.

10.6 Conclusion.

CHAPTER 11: Forward Equations for Portfolio Credit Derivatives(Rama Cont and Ioana Savescu).

11.1 Portfolio Credit Derivatives.

11.2 Top-Down Models for CDO Pricing.

11.3 Effective Default Intensity.

11.4 A Forward Equation for CDO Pricing.

11.5 Recovering Forward Default Intensities from TrancheSpreads.

11.6 Conclusion.

Index.

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