Mathematics of Derivative Securities

A collection of premier papers on financial mathematics. Broad coverage.

Michael A. H. Dempster (Edited by), Stanley R. Pliska (Edited by)

9780521584241, Cambridge University Press

Hardback, published 13 October 1997

600 pages, 60 b/w illus. 40 tables
23.6 x 15.9 x 4.3 cm, 1.085 kg

'Merton, in his Foreword, characterizes the contents as 'representative of the high quality and mathematical sophistication of research in the field.' … I have no reason to differ with this evaluation.' Peter Bloomfield, JASA

During 1995 the Isaac Newton Institute for the Mathematical Sciences at Cambridge University hosted a six month research program on financial mathematics. During this period more than 300 scholars and financial practitioners attended to conduct research and to attend more than 150 research seminars. Many of the presented papers were on the subject of financial derivatives. The very best were selected to appear in this volume. They range from abstract financial theory to practical issues pertaining to the pricing and hedging of interest rate derivatives and exotic options in the market place. Hence this book will be of interest to both academic scholars and financial engineers.

Foreword R. C. Merton
Part I. Introduction: 1. Editors' introduction
2. Stochastic calculus and Markov methods L. C. G. Rogers
3. The risk premium in trading equilibria which support Black-Scholes option pricing S. D. Hodges and M. J. P. Selby
4. On the numeraire portfolio P. Artzner
Part II. Option Pricing and Hedging: 5. Convergence of Snell envelopes and critical prices in the American Put N. J. Cutland, P. E. Kopp, W. Willinger and M. C. Wyman
6. Some combination of Asian, Parisian and Barrier options M. Yor, M. Chesnay, H. Geman and M. Jeanblanc-Piqué
7. Co-movement term structure and the valuation of crack energy spread options A. Mbanefo
8. Pricing and hedging with Smiles B. Dupire
9. Filtering derivative security valuations from market prices R. J. Elliott, C. H. Lahaie and D. B. Madan
10. Option pricing in the presence of extreme fluctuations J.-P. Bouchard, D. Sornette and M. Potters
11. Hedging long maturity commodity commitments with short-dated futures contracts M. J. Brennan and N. I. Crew
12. Nonlinear financial markets: hedging and portfolio optimization J. Cvitanic
13. Semimartingales and asset pricing under constraints M. Frittelli
14. Option pricing in incomplete markets M. H. A. Davis
15. Option pricing and hedging in discrete time with transaction costs F. Mercurio and T. C. F. Vorst
Part III. Term Structure and Interest Rate Derivatives: 16. Bond and bond option pricing based on the current term structure P. H. Dybvig
17. Dynamic models for yield curve evolution B. Flesaker and L. P. Hughston
18. General interest rate models and the universality of HJM M. W. Baxter
19. Swap derivatives in a Gaussian HJM framework A. Brace and M. Musiela
20. Modelling bonds and derivatives with default risk D. Lando
21. Term structure modelling under alternative official regimes S. H. Babbs and N. J. Webber
22. Interest rate distributions, yield curve modelling and monetary policy L. El-Jahel, H. Lindberg and W. Perraudin
Part IV. Numerical Methods: 23. Numerical option pricing using conditioned diffusions S. K. Gandhi and P. J. Hunt
24. Numerical valuation of cross-currency swaps and swaptions M. A. H. Dempster and J. P. Hutton
25. Numerical methods for stochastic control problems in finance H. J. Kushner
26. Simulation methods for option pricing J. P. Lehoczky
27. New methodologies for valuing derivatives S. H. Paskov.

Subject Areas: Probability & statistics [PBT], Finance [KFF]