The asymptotic expansion approach to the valuation of interest rate contingent claims

Mathematical Finance

Volumn 11, Issue 1, 2001, Pages 117-151

  Kunitomo, Naoto ^a   Takahashi, Akihiko ^b  

^a UNIVERSITY OF TOKYO   (Japan)

^b NONE

Author keywords

Asymptotic expansion; Derivatives; Malliavin Watanabe calculus; Small disturbance asymptotics; Term structure of interest rates

Indexed keywords

EID: 0035589286     PISSN: 09601627     EISSN: None     Source Type: Journal    
DOI: 10.1111/1467-9965.00110     Document Type: Article

References (23)

1. AMIN, K., and J. BODURTHA (1995): Discrete-Time Valuation of American Options with Stochastic Interest Rates, Rev. Financial Stud. 8, 1-22.
2. ANDERSON, T. W. (1977): Asymptotic Expansions of the Distributions of the Estimates in Simultaneous Equations for Alternative Parameter Sequences, Econometrica 45, 509-518.
3. BHATTACHARYA, R. N., and R. RANGA RAO (1976): Normal Approximation and Asymptotic Expansion. New York: John-Wiley.
4. DUFFIE, D. (1992): Dynamic Asset Pricing Theory. Princeton, NJ: Princeton University Press.
5. FUJIKOSHI, Y., K. MORIMUNE, N. KUNITOMO, and M. TANIGUCHI (1982): Asymptotic Expansions of the Distributions of the Estimates of Coefficients in a Simultaneous Equation System, J. Econometrics 18, 191-205.
6. HE, H., and A. TAKAHASHI (2000): A Variable Reduction Technique for Pricing Average-Rate Options, International Review of Finance 1(2), 123-142.
7. HEATH, D., R. JARROW, and A. MORTON (1992): Bond Pricing and the Term Structure of Interest Rates: A New Methodology for Contingent Claims Valuation, Econometrica 60, 77-105.
8. HO, T., and S. LEE (1986): Term Structure Movements and Pricing Interest Rate Contingent Claims, J. Finance 41, 1011-1029.
9. HULL, J. (1993): Options, Futures, and Other Derivative Securities, 2nd ed. Englewood Cliffs, NJ: Prentice-Hall.
10. IKEDA, N., and S. WATANABE (1989): Stochastic Differential Equations and Diffusion Processes, 2nd ed. Tokyo: North-Holland/Kodansha.
11. KIM, Y. J., and N. KUNITOMO (1999): Pricing Options Under Stochastic Interest Rates, Asia Pacific Financial Mkts. 6, 49-70.
12. KUNITOMO, N., K. MORIMUNE, and Y. TSUKUDA (1983): Asymptotic Expansions of the Distributions of Test Statistics for Over-identifying Restrictions in a Simultaneous Equation System, Inter. Econ. Rev. 24, 199-215.
13. KUNITOMO, N., and A. TAKAHASHI (1992): Pricing Average Options, Japan Financial Rev. 14, 1-20 (in Japanese).
14. KUNITOMO, N., and A. TAKAHASHI (1995): The Aysmptotic Expansion Approach to the Valuation of Interest Rate Contingent Claims; Discussion Paper no. 95-F-19, Faculty of Economics, University of Tokyo.
15. KUNITOMO, N., and A. TAKAHASHI (1998): On Validity of the Asymptotic Expansion Approach in Contingent Claim Analysis; Discussion Paper no. 98-F-6, Faculty of Economics, University of Tokyo.
16. KUSUOKA, S., and D. W. STROOCK (1982): Applications of the Malliavin Calculus: Part I, in Stochastic Analysis: Proceedings of Taniguchi International Symposium on Stochastic Analysis, ed. K. Itô. Tokyo: Kinokuniya/North-Holland, 271-306.
17. MORTON, A. J. (1989): Arbitrage and Martingales; unpublished Ph.D. dissertation, Cornell University.
18. TAKAHASHI, A. (1995): Essays on the Valuation Problems of Contingent Claims; unpublished Ph.D. dissertation, Haas School of Business, University of California, Berkeley.
19. TAKAHASHI, A. (1999): An Asymptotic Expansion Approach to Pricing Contingent Claims, Asia-Pacific Financial Mkts. 6, 115-151.
20. WATANABE, S. (1987): Analysis of Wiener Functionals (Malliavin Calculus) and its Applications to Heat Kernels; Ann. Probab. 15, 1-39.
21. YOSHIDA, N. (1992a): Asymptotic Expansion for Statistics Related to Small Diffusions, J. Japan Statis. Soc. 22, 139-159.
22. YOSHIDA, N. (1992b): Asymptotic Expansions of Maximum Likelihood Estimator for Small Diffusion via the Theory of Malliavin-Watanabe, Prob. Theory & Rel. Fields 92, 275-311.
23. YOSHIDA, N. (1997): Asymptotic Expansion for Martingales on Wiener Space and Applications to Statistics, Prob. Theory & Rel. Fields 109, 301-342.