Mathematics of the Bond Market: A Lévy Processes Approach

ISBN-13: 9781107101296 / Angielski / Twarda / 2020 / 398 str.

Michal Barski; Jerzy Zabczyk

Opis

Analyses bond market models with Lévy stochastic factors, suitable for graduates and researchers in probability and mathematical finance.

Spis treści

Introduction; Part I. Bond Market in Discrete Time: 1. Elements of the bond market; 2. Arbitrage-free bond markets; 3. Completeness; Part II. Fundamentals of Stochastic Analysis: 4. Stochastic preliminaries; 5. Lévy processes; 6. Martingale representation and Girsanov's theorems; Part III. Bond Market in Continuous Tme: 7. Fundamentals; 8. Arbitrage-free HJM markets; 9. Arbitrage-free factor forward curves models; 10. Arbitrage-free affine term structure; 11. Completeness; Part IV. Stochastic Equations in the Bond Market: 12. Stochastic equations for forward rates; 13. Analysis of the HJMM equation; 14. Analysis of Morton's equation; 15. Analysis of the Morton–Musiela equation; Appendix A. Martingale representation for jump Lévy processes; Appendix B. Semigroups and generators; Appendix C. General evolution equations; References; Index.