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Advances in Mathematical Finance

  • Book
  • © 2007

Overview

Editors:
  1. Michael C. Fu

    1. Robert H. Smith School of Business Van Munching Hall, University of Maryland, College Park, USA

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  2. Robert A. Jarrow

    1. Johnson Graduate School of Management 451 Sage Hall, Cornell University, Ithaca, USA

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  3. Ju-Yi J. Yen

    1. Department of Mathematics, 1326 Stevenson Center Vanderbilt University, Nashville, USA

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  4. Robert J. Elliott

    1. Haskayne School of Business Scurfield Hall, University of Calgary, Calgary, Canada

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  • Includes contributions from some of the most distinguished researchers and practitioners in the fields of mathematical finance and financial engineering
  • Offers state-of-the-art developments in theory and practice
  • Real-world applications to fixed-income models, credit risk models, CDO pricing, tax rebates, tax arbitrage, and tax equilibrium
  • Ideal for a broad audience of graduate students, researchers, and practitioners in mathematical finance and financial engineering
  • Suitable for readers coming from academia as well as industry

Part of the book series: Applied and Numerical Harmonic Analysis (ANHA)

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Table of contents (16 chapters)

  1. Front Matter

    Pages I-XXVIII
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  2. Variance-Gamma and Related Stochastic Processes

    1. Front Matter

      Pages 1-1
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    2. The Early Years of the Variance-Gamma Process

      • Eugene Seneta
      Pages 3-19

    3. Variance-Gamma and Monte Carlo

      • Michael C. Fu
      Pages 21-34

    4. Some Remarkable Properties of Gamma Processes

      • Marc Yor
      Pages 37-47

    5. A Note About Selberg’s Integrals in Relation with the Beta-Gamma Algebra

      • Marc Yor
      Pages 49-58

    6. Itô Formulas for Fractional Brownian Motion

      • Robert J. Elliott, John van der Hoek
      Pages 59-81

  3. Asset and Option Pricing

    1. Front Matter

      Pages 83-83
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    2. A Tutorial on Zero Volatility and Option Adjusted Spreads

      • Robert Jarrow
      Pages 85-95

    3. Asset Price Bubbles in Complete Markets

      • Robert A. Jarrow, Philip Protter, Kazuhiro Shimbo
      Pages 97-121

    4. Taxation and Transaction Costs in a General Equilibrium Asset Economy

      • Xing Jin, Frank Milne
      Pages 123-146

    5. Calibration of Lévy Term Structure Models

      • Ernst Eberlein, Wolfgang Kluge
      Pages 147-172

    6. Pricing of Swaptions in Affine Term Structures with Stochastic Volatility

      • Michael Heidari, Alil Hirsa, Dilip B. Madan
      Pages 173-193

    7. Forward Evolution Equations for Knock-Out Options

      • Peter Carr, Ali Hirsa
      Pages 195-217

    8. Mean Reversion Versus Random Walk in Oil and Natural Gas Prices

      • Hélyette Geman
      Pages 219-228

  4. Credit Risk and Investments

    1. Front Matter

      Pages 229-229
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    2. Beyond Hazard Rates: A New Framework for Credit-Risk Modelling

      • Dorje C. Brody, Lane P. Hughston, Andrea Macrina
      Pages 231-257

    3. A Generic One-Factor Lévy Model for Pricing Synthetic CDOs

      • Hansjörg Albrecher, Sophie A. Ladoucette, Wim Schoutens
      Pages 259-277

    4. Utility Valuation of Credit Derivatives: Single and Two-Name Cases

      • Ronnie Sircar, Thaleia Zariphopoulou
      Pages 279-301

    5. Investment and Valuation Under Backward and Forward Dynamic Exponential Utilities in a Stochastic Factor Model

      • Marek Musiela, Thaleia Zariphopoulou
      Pages 303-334
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Keywords

About this book

This self-contained volume brings together a collection of chapters by some of the most distinguished researchers and practitioners in the fields of mathematical finance and financial engineering. Presenting state-of-the-art developments in theory and practice, the Festschrift is dedicated to Dilip B. Madan on the occasion of his 60th birthday.

Specific topics covered include:

* Theory and application of the Variance-Gamma process

* Lévy process driven fixed-income and credit-risk models, including CDO pricing

* Numerical PDE and Monte Carlo methods

* Asset pricing and derivatives valuation and hedging

* Itô formulas for fractional Brownian motion

* Martingale characterization of asset price bubbles

* Utility valuation for credit derivatives and portfolio management

Advances in Mathematical Finance is a valuable resource for graduate students, researchers, and practitioners in mathematical finance and financialengineering.

Contributors: H. Albrecher, D. C. Brody, P. Carr, E. Eberlein, R. J. Elliott, M. C. Fu, H. Geman, M. Heidari, A. Hirsa, L. P. Hughston, R. A. Jarrow, X. Jin, W. Kluge, S. A. Ladoucette, A. Macrina, D. B. Madan, F. Milne, M. Musiela, P. Protter, W. Schoutens, E. Seneta, K. Shimbo, R. Sircar, J. van der Hoek, M.Yor, T. Zariphopoulou

Editors and Affiliations

  • Robert H. Smith School of Business Van Munching Hall, University of Maryland, College Park, USA

    Michael C. Fu

  • Johnson Graduate School of Management 451 Sage Hall, Cornell University, Ithaca, USA

    Robert A. Jarrow

  • Department of Mathematics, 1326 Stevenson Center Vanderbilt University, Nashville, USA

    Ju-Yi J. Yen

  • Haskayne School of Business Scurfield Hall, University of Calgary, Calgary, Canada

    Robert J. Elliott

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