Modeling term structure dynamics: An infinite dimensional approach

International Journal of Theoretical and Applied Finance

Volumn 8, Issue 3, 2005, Pages 357-380

  Cont, Rama ^a  

^a CENTRE DE MATHÉMATIQUES APPLIQUÉES   (France)

Author keywords

Forward rates; Hilbert space; Multifactor models; Random field; Stochastic PDE; Term structure of interest rates

Indexed keywords

EID: 18644364888     PISSN: 02190249     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0219024905003049     Document Type: Article

References (33)

1. R. A. Adams, Sobolev Spaces (Academic Press, New York, 1975).
2. Y. Ait-Sahalia, Telling from discrete data whether the underlying continuous-time model is a diffusion, Journal of Finance 57 (1977) 2075-2112.
3. G. Ballocchi, M. M. Dacorogna, C. M. Hopman, U. A. Muller and R. B. Olsen, The intraday multivariate structure of the Eurofutures markets, Journal of Empirical Finance 6 (1999) 479-513.
4. T. Björk, G. Di Masi, Y. Kabanov and W. Runggaldier, Towards a general theory of bond markets, Finance and Stochastics 1(2) (1997) 141-174.
5. J. P. Bouchaud, R. Cont, N. El Karoui, M. Potters and N. Sagna, Phenomenology of the interest rate curve, Applied Mathematical Finance 6 (1999) 209-231.
6. J. P. Bouchaud, R. Cont, N. El Karoui, M. Potters and N. Sagna, Strings attached, RISK (July 1998).
7. M. J. Brennan and E. J. Schwartz, A continuous-time approach to the pricing of bonds, Journal of Banking and Finance 3 (1979) 133-155.
8. R. Cont, A structural model for term structure dynamics, working paper (2003).
9. G. Da Prato and J. Zabczyk, Stochastic Equations in Infinite Dimensions (Cambridge University Press, 1992).
10. R. Douady, Yield curve smoothing and residual variance of fixed income positions, working paper (1997).
11. D. Duffie and R. Kan, Multifactor models of the term structure, in Mathematical Models in Finance, eds., Howison, Kelly and Wilmott (Chapman & Hall, London, 1995).
12. P. Dybvig, J. Ingersoll and S. Ross, Long forward and zero-coupon rates can never fall, Journal of Business 69 (1996) 1-26.
13. N. El Karoui, A. Frachot and H. Geman, A note on the behavior of long zero coupon rates in a no arbitrage framework, Review of Derivatives Research 1(4) (1998) 351-369.
14. D. Filipovic, Consistency Problems for Heath-Jarrow-Morton Models, Lecture Notes in Mathematics Vol. 1760 (Springer, Berlin, 2000).
15. R. Goldstein, The term structure of interest rates as a random field, Review of Financial Studies 13(2) (2000) 365-384.
16. B. Goldys and M. Musiela, Infinite dimensional diffusion, Kolmogorov equations and interest rate models, in Option Pricing, Interest Rates and Risk Management, eds., E. Jouini and S. Pliska (Cambridge University Press, 2001).
17. D. Heath, R. A. Jarrow and A. Morton, Bond pricing and the term structure of interest rates: A new methodology for contingent claims valuation, Econometrica 60 (1992) 77-105.
18. K. Ito, Stochastic Differential Equations in Infinite Dimensions (SIAM, Providence, 1984).
19. D. P. Kennedy, The term structure of interest rates as a Gaussian random field, Mathematical Finance 4 (1994) 247-258.
20. R. Litterman and J. Scheinkman, Common factors affecting bond returns, Journal of Fixed Income 1 (1991) 49-53.
21. J. Moraleda, On the pricing of interest rate options, Ph.D. thesis, Tinbergen Institute Research Series, Vol. 155 (1997).
22. M. Musiela, Stochastic PDEs related to term structure models, preprint (1993).
23. H. Pages, Interbank interest rates, in Mathematical Finance: Theory and Practice, Series in Contemporary Applied Mathematics, eds., R. Cont and J. Yong (Higher Education Press, Beijing, 2000), pp. 317-352.
24. E. Pardoux, Stochastic partial differential equations: A review, Bulletin des Sciences Mathématiques 117(1) (1993) 29-47.
25. N. Pearson and A. Zhou, A non-parametric analysis of the forward rate volatilities, in The New Interest Rate Models, ed., L. Hughston (Risk Books, London, 2001).
26. S. Pliska, Introduction to Mathematical Finance (Blackwell Publishers, 1997).
27. R. Rebonato, Interest Rate Option Models (Wiley, Chichester, 1997).
28. P. Santa Clara and D. Sornette, The dynamics of the forward interest rate curve with stochastic string shocks, Review of Financial Studies 14(1) (2000), 149-185.
29. D. Schaefer and E. Schwartz, A two factor model for the term structure: An approximate analytical solution, Journal of Financial and Quantitative Analysis 19 (1984) 413-424.
30. E. Schlögl and D. Sommer, Factor models and the shape of the term structure, Journal of Financial Engineering 7(1) (1998) 79-88.
31. O. Vasicek, An equilibrium characterization of the term structure, Journal of Finance 5 (1977) 177-188.
32. J. B. Walsh, An introduction to stochastic partial differential equations, in Ecole d'Ete de Probabilité de Saint-Flour, Session XIV, Lecture Notes in Mathematics 1180 (Springer, Berlin, 1986).
33. M. Yor, Existence et unicité de diffusions à valeurs dans un espace de Hilbert, Annales de l'Institut Henri Poincaré 10 (1974) 55-88.