Frontiers in Quantitative Finance Volatility and Credit Risk Modeling

About the Editor.

About the Contributors.

PART ONE: Option Pricing and Volatility Modeling.

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

1.1 Introduction.

1.2 No-Arbitrage Conditions.

1.3 Example.

1.4 Conclusion.

CHAPTER 2: On Black-Scholes Implied Volatility at Extreme Strikes (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 (Lorenzo Bergomi).

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 Implied Volatility (Pierre Henry-Labord`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-Diffusion Models (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 American Options.

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 under Linear Coordinate Transforms.

CHAPTER 9: Pricing CDOs with a Smile: The Local Correlation Model (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 Large Pool Assumption.

9.4 Pricing and Hedging with Local Correlation.

CHAPTER 10: Portfolio Credit Risk: Top-Down versus Bottom-Up Approaches (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 Tranche Spreads.

11.6 Conclusion.

Index.