Finance at fields / editors, Matheus R. Grasselli, Lane P. Hughston.

Includes bibliographical references and index.

Preface: Reflections on the Crisis and a Glimpse at the Future of Mathematical Finance Matheus R. Grasselli and Lane P. Hughston; CONTENTS; 1. Heat Kernel Interest Rate Models with Time-Inhomogeneous Markov Processes Jiro Akahori and Andrea Macrina; 1. Introduction; 2. Heat Kernels for Supermartingales; 3. Pricing with Time-Inhomogeneous Markov Information; 4. Explicit Pricing Kernel Models; 5. Fixed-Income Derivatives with Brownian Bridge Information; Acknowledgments; References; 2. Stress Testing the Resilience of Financial Networks Hamed Amini, Rama Cont and Andreea Minca; 1. Introduction.

2. Network Models of Banking Systems2.1. Asymptotic analysis of default cascades in large networks; 2.2. Size of default cascade; 3. Stress Testing; 3.1. Stress testing resilience to macroeconomic shocks; 3.2. An example of infinite network; 3.3. A finite scale-free network; 4. Discussion; Acknowledgments; References; 3. Managing Corporate Liquidity: Strategies and Pricing Implications Attakrit Asvanunt, Mark Broadie and Suresh Sundaresan; 1. Introduction; 1.1. Overview of major results; 1.2. Review of the literature; 2. The Model; 2.1. Basic setup; 2.2. Equity dilution; 2.3. Cash balance.

2.4. Loan commitment3. Welfare and Pricing Under Costly Equity Dilution; 3.1. Exogenous bankruptcy boundary; 3.1.1. Equity value; 3.1.2. Debt value; 3.2. Endogenous bankruptcy boundary; 3.3. Impacts of costly equity dilution; 3.3.1. Security values; 3.3.2. Debt capacity and optimal capital structure; 4. Cash Balances to Manage Illiquidity; 4.1. Optimal level of cash; 4.2. Impacts of cash balance; 5. Loan Commitment; 5.1. Optimal draw down and repayment decisions; 5.2. Impacts of loan commitment; 6. Conclusion; Appendix A; Appendix B; Appendix C; Appendix D; Appendix E; Appendix F.

AcknowledgmentReferences; 4. Valuation and Hedging of CDS Counterparty Exposure in a Markov Copula Model T.R. Bielecki, S. Crepey, M. Jeanblanc and B. Zargari; 1. Introduction; 1.1. Outline of the paper; 2. Cash Flows and Pricing in a General Set-Up; 3. Model; 4. Pricing; 5. Hedging of Counterparty Exposure; 5.1. Dynamics of cumulative CVA; 5.1.1. Markovian case; 5.2. Hedging of CVA; 5.2.1. Rolling CDS; 5.2.2. Mean-variance hedging; 6. Model Implementation; 6.1. Marginals; 6.2. Joint defaults; 6.3. Calibration; 7. A Variant of the Model with Extended CIR Intensities; 7.1. Implementation.

8. Numerical Results8.1. Calibration to market data; 8.2. CVA stylized features; 8.3. Case of a low-risk reference entity; 8.4. Spread options implied volatilities; 8.5. The analysis of the contribution of the joint default; 9. Conclusions; Appendix A; Acknowledgments; References; 5. Information-Based Asset Pricing Dorje C. Brody, Lane P. Hughston and Andrea Macrina; 1. Introduction; 2. The Modelling Framework; 3. Modelling the Cash Flows; 4. Modelling the Information Flow; 5. Asset Price Dynamics in the Case of a Single Cash Flow; 6. European-Style Call Options.

This outstanding collection of articles includes papers presented at the Fields Institute, Toronto, as part of the Thematic Program in Quantitative Finance that took place in the first six months of the year 2010. The scope of the volume in very broad, including papers on foundational issues in mathematical finance, papers on computational finance, and papers on derivatives and risk management. Many of the articles contain path-breaking insights that are relevant to the developing new order of post-crisis financial risk management.

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