OJAppS  Vol.3 No.1 B1 , April 2013
Models of the Short Interest Rate in Discrete Processes
Abstract: The modeling of the term structure of interest rates is one of primary topics for researches in financial economics. Here we consider models of the short interest rate in discrete processes. Our methodology of analysis follows the framework of discrete stochastic calculus.
Cite this paper: N. Ishimura, B. Javkhlan, M. Nakamura and Z. Wei, "Models of the Short Interest Rate in Discrete Processes," Open Journal of Applied Sciences, Vol. 3 No. 1, 2013, pp. 12-14. doi: 10.4236/ojapps.2013.31B1003.

[1]   O. Vasiçek,“An Equilibrium Characterization of the Term Structure,” Journal of Financial Economics, Vol. 5, No. 2, 1977, pp. 177-188. doi:10.1016/0304-405X(77)90016-2

[2]   T. Björk, “Arbitrage Theory in Continuous Time,” 2nd edition., Oxford University Press, Oxford, 2004. doi:10.1093/0199271267.001.0001

[3]   J. Cox, J. Ingersoll and S. Ross, “A Theory of the Te Structure of Interest Rate,” Econometrica, Vol. 53, No. 2, 1985, pp. 385-408. doi: 10.2307/1911242

[4]   D. Heath, R. Jarrow and A. Morton, “Bond Pricing and the Term Structure of Interest Rates,” Eco-nometrica, Vol. 60, No. 1, 1992, pp. 77-106. doi:10.2307/2951677

[5]   T. Ho and S. Lee, “Term Structure Movements and Pricing Interest Rate Contingent Claims,” The Journal of Finance, Vol. 41, No. 5, 1986, pp. 1011-1029. doi:10.1111/j.1540-6261.1986.tb02528.x

[6]   J. Hull and A. White, “Pricing Interest-rate-derivative Securities,” Review Financial Studies, Vol. 3, No. 4, 1990, pp. 573-592. doi:10.1093/rfs/3.4.573

[7]   A. Pelsser, “Efficient Methods for Valuing Interest Rate Derivatives,” Springer, London, 2000. doi:10.1007/978-1-4471-3888-4

[8]   T. Fujita, “Introduction to the Stochastic Analysis for Financial Derivatives (Finance No Kakuritsu-Kaiseki Nyumon),” Kodan-shya, Tokyo, Japanese. 2002

[9]   T. Fujita, N. Ishimura and N. Kawai, “Discrete Stochastic Calculus and Its Applications: An Expository Note,” Advances in Mathematics Economics, Vol. 16, 2012, pp. 119-131. doi:10.1007/978-4-431-54114-1_6

[10]   T. Fujita and Y. Kawanishi, “A Proof of ItÔ’s Formula Using a Discrete ItÔ’s Formula,” Stud. Scienti. Math. Hungarica, Vol. 45, 2008, pp. 125-134.

[11]   A. V. Mel’nikov, “Financial Markets,” American Mathematical Society, Providence, 1999.