Frontiers in Quantitative Finance : Volatility and Credit Risk Modeling

by Cont, Rama

• ISBN13: 9780470292921
• ISBN10: 047029292X
• Edition: Revised
• Format: Hardcover
• Copyright: 2008-11-10
• Publisher: Wiley

Summary

The Petit D'euner de la Finance-which author Rama Cont has been co-organizing in Paris since 1998-is a well-known quantitative finance seminar that has progressively become a platform for the exchange of ideas between the academic and practitioner communities in quantitative finance. Frontiers in Quantitative Finance is a selection of recent presentations in the Petit D'euner de la Finance. In this book, leading quants and academic researchers cover the most important emerging issues in quantitative finance and focus on portfolio credit risk and volatility modeling.

Author Biography

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.

Table of Contents

Preface	p. ix
About the Editor	p. xiii
About the Contributors	p. xv
Option Pricing and Volatility Modeling
A Moment Approach to Static Arbitrage	p. 3
Introduction	p. 3
No-Arbitrage Conditions	p. 7
Example	p. 15
Conclusion	p. 16
On Black-Scholes Implied Volatility at Extreme Strikes	p. 19
Introduction	p. 19
The Moment Formula	p. 20
Regular Variation and the Tail-Wing Formula	p. 24
Related Results	p. 27
Applications	p. 33
CEV and SABR	p. 35
Dynamic Properties of Smile Models	p. 47
Introduction	p. 48
Some Standard Smile Models	p. 50
A New Class of Models for Smile Dynamics	p. 65
Pricing Examples	p. 81
Conclusion	p. 87
A Geometric Approach to the Asymptotics of Implied Volatility	p. 89
Volatility Asymptotics in Stochastic Volatility Models	p. 91
Heat Kernel Expansion	p. 92
Geometry of Complex Curves and Asymptotic Volatility	p. 100
[lambda]-SABR Model and Hyperbolic Geometry	p. 106
SABR Model with [beta] = 0, 1	p. 117
Conclusions and Future Work	p. 122
Appendix A: Notions in Differential Geometry	p. 122
Appendix B: Laplace Integrals in Many Dimensions	p. 125
Pricing, Hedging, and Calibration in Jump-Diffusion Models	p. 129
Overview of Jump-Diffusion Models	p. 131
Pricing European Options via Fourier Transform	p. 137
Integro-differential Equations for Barrier and American Options	p. 140
Hedging Jump Risk	p. 147
Model Calibration	p. 153
Credit Risk
Modeling Credit Risk	p. 163
What Is the Problem?	p. 163
Hazard Rate Models	p. 166
Structural Models	p. 175
Some Nice Ideas	p. 179
Conclusion	p. 181
An Overview of Factor Modeling for CDO Pricing	p. 185
Pricing of Portfolio Credit Derivatives	p. 185
Factor Models for the Pricing of CDO Tranches	p. 189
A Review of Factor Approaches to the Pricing of CDOs	p. 198
Conclusion	p. 212
Factor Distributions Implied by Quoted CDO Spreads	p. 217
Introduction	p. 217
Modeling	p. 220
Examples	p. 224
Conclusion	p. 231
Appendix: Some Useful Results on Hermite Polynomials under Linear Coordinate Transforms	p. 232
Pricing CDOs with a Smile: The Local Correlation Model	p. 235
The Local Correlation Model	p. 236
Simplification under the Large Pool Assumption	p. 240
Building the Local Correlation Function without the Large Pool Assumption	p. 243
Pricing and Hedging with Local Correlation	p. 247
Portfolio Credit Risk: Top-Down versus Bottom-Up Approaches	p. 251
Introduction	p. 251
Portfolio Credit Models	p. 251
Information and Specification	p. 253
Default Distribution	p. 259
Calibration	p. 264
Conclusion	p. 265
Forward Equations for Portfolio Credit Derivatives	p. 269
Portfolio Credit Derivatives	p. 270
Top-Down Models for CDO Pricing	p. 273
Effective Default Intensity	p. 275
A Forward Equation for CDO Pricing	p. 278
Recovering Forward Default Intensities from Tranche Spreads	p. 282
Conclusion	p. 288
Index	p. 295
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