Squared bessel processes and their applications to the square root interest rate model

Asia-Pacific Financial Markets

Volumn 9, Issue 3-4, 2002, Pages 169-190

  Shirakawa, Hiroshi ^a  

^a Tokyo Institute of Technology ^*  (Japan)

Author keywords

Bessel process; Extended cir model; Option pricing; Time varying dimension

Indexed keywords

EID: 17444410348     PISSN: 13872834     EISSN: None     Source Type: Journal    
DOI: 10.1023/a:1024173313448     Document Type: Article

References (19)

1. Beaglehole, D. and Tenny, M. (1991) General solutions of some interest rate contingent claim pricing equations, J. Fixed Income 1, 69-83.
2. Carmona, P. (1994) Généralisations de la loi de l'arc sinus et entrelacements de processus de Markov, Thèse de Doctorat de l'Université Paris 6.
3. Cox, J. C., Ingersoll, J., and Ross, S. (1985) A theory of the term structure of interest rates, Econometrica 53, 385-4-05.
4. Deelstra, G. (1995) Long-Term Returns in Stochastic Interest Rate Models, Doctoral Dissertation, Free University of Brussels.
5. Delbaen, F. (1993) Consols in the CIR model, Math. Finance 3, 125-134.
6. Feller, W. (1950) Two singular distributions, Ann. Mathematics 24, 173-182.
7. German, H. and Yor, M. (1993) Bessel processes, Asian options, and perpetuities, Math. Finance 3, 349-375.
8. Harrison, J. M. and Pliska, S. R. (1981) Martingales and stochastic integrals in the theory of continuous trading, Stoch. Proces. Appl. 11, 381-4-08.
9. Harrison, J. M. and Pliska, S. R. (1983) A stochastic calculus model of continuous time trading: complete markets, Stoch. Proces. Appl. 13, 313-316.
10. Hull, J. and White, A. (1990) Pricing interest-rate derivative securities, Rev. Financ. Stud. 3, 573-592.
11. Jamshidian, F. (1995) A simple class of square root interest rate models, Sakura Global Capital or Appl. Math. Finance 2, 61-72.
12. Karatzas, I. and Shreve, S. E. (1988) Brownian Motion and Stochastic Calculus, SpringerVerlag.
13. Maghsoodi, Y. (1996) Solution of the extended CIR term structure and bond option valuation, Math. Finance 6, 89-109.
14. Pitman, J. and Yor, M. (1982) A decomposition of Bessel bridges, Zeitschrift für Wahrscheinlichkeitstheorie und verwandte Gebiete 59, 425-457.
15. Rao, C. R. ( 1973) Linear Statistical Inference and Its Applications, John Wiley and Sons, Inc.
16. Revuz, D. and Yor, M. (1991) Continuous Martingales and Brownian Motion, Springer-Verlag, Berlin.
17. Rogers, L. G. C. (1995) Which model for term structure of interest rates should one use, Proc. IMA Workshop on Math. Finance, 93-116.
18. Shiga, T. and Watanabe, S. (1973) Bessel diffusions as a one-parameter family of diffusion processes, Zeitschrift für Wahrscheinlichkeitstheorie und verwandte Gebiete 27, 37-46.
19. Yor, M. (1992) On some exponential functionals of Brownian motion, Adv. Appl. Probab. 24, 509-531.