Solution Of The Extended Cir Term Structure And Bond Option Valuation
AbstractThe extended Cox-Ingersoll-Ross (ECIR) models of interest rates allow for time-dependent parameters in the CIR square-root model. This article presents closed-form pathwise unique solutions of these unsolved stochastic differential equations (s.d.e.s) in terms of functionals of their driving Brownian motion and parameters. It is shown that quadratics in solution of linear s.d.e.s solve the ECIR model if and only if the "dimension" of the model is a positive integer and that this solution can be achieved by construction of a pathwise unique "generalized" Ornstein-Uhlenbeck process from the ECIR Brownian motion. For real valued dimensions an extension of the time-change theorem of Dubins and Schwarz (1965) is presented and applied to show that a lognormal process solves the model through a stochastic time change. Pathwise equivalence to a rescaled time-changed Bessel square process is also established. These novel results are applied to characterize zero-hitting time and to produce transition density and zero-hitting conditions for the ECIR spot rate. the CIR term structure is then extended to ECIR under no arbitrage, and its solutions and the transition density are represented under a new ECIR martingale measure. the findings are employed to derive a closed-form ECIR bond option valuation formula which generalizes that obtained by CIR (1985). Copyright 1996 Blackwell Publishers.
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Volume (Year): 6 (1996)
Issue (Month): 1 ()
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- Christian Gourieroux & Alain Monfort, 2007.
"Quadratic Stochastic Intensity and Prospective Mortality Tables,"
2007-30, Centre de Recherche en Economie et Statistique.
- Gourieroux, C. & Monfort, A., 2008. "Quadratic stochastic intensity and prospective mortality tables," Insurance: Mathematics and Economics, Elsevier, vol. 43(1), pages 174-184, August.
- Angelos Dassios & Jayalaxshmi Nagaradjasarma, 2006. "The square-root process and Asian options," Quantitative Finance, Taylor & Francis Journals, vol. 6(4), pages 337-347.
- Antonio Mannolini & Carlo Mari & Roberto Ren�, 2008. "Pricing caps and floors with the extended CIR model," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 13(4), pages 386-400.
- Griselda Deelstra, 2000. "Long-term returns in stochastic interest rate models: applications," ULB Institutional Repository 2013/7590, ULB -- Universite Libre de Bruxelles.
- Dahl, Mikkel & Moller, Thomas, 2006. "Valuation and hedging of life insurance liabilities with systematic mortality risk," Insurance: Mathematics and Economics, Elsevier, vol. 39(2), pages 193-217, October.
- Guo, Zhi Jun, 2008. "A note on the CIR process and the existence of equivalent martingale measures," Statistics & Probability Letters, Elsevier, vol. 78(5), pages 481-487, April.
- D. Duffie & D. Filipovic & W. Schachermayer, 2002. "Affine Processes and Application in Finance," NBER Technical Working Papers 0281, National Bureau of Economic Research, Inc.
- Erik Schlogl & Lutz Schlogl, 2000.
"A square root interest rate model fitting discrete initial term structure data,"
Applied Mathematical Finance,
Taylor & Francis Journals, vol. 7(3), pages 183-209.
- Erik Schl?gl & L. Schl?gl, 1999. "A Square-Root Interest Rate Model Fitting Discrete Initial Term Structure Data," Research Paper Series 24, Quantitative Finance Research Centre, University of Technology, Sydney.
- Dahl, Mikkel, 2004. "Stochastic mortality in life insurance: market reserves and mortality-linked insurance contracts," Insurance: Mathematics and Economics, Elsevier, vol. 35(1), pages 113-136, August.
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