Abstract
In this chapter, we discuss alternative ways of computing the options to invest in and divest from an investment project in a CIR economy (Cox et al., Econometrica 53(2):385–408, 1985). Moreover, different methods of determining CIR perpetuities will also be analyzed.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
See [7] for a complete description of the boundary conditions.
- 2.
We must note that since \({\lim }_{t\rightarrow \infty }\frac{\partial P(r,t)} {\partial t} = 0\), the value of a perpetuity is not time dependent.
- 3.
Even though Carmona and León [2] do not present solutions for the option to divest, F 1(r) could also be easily obtained.
- 4.
We have tried other combinations and we have reached the same conclusions.
References
Abramowitz, M., Stegun, I.A.: Handbook of Mathematical Functions. Dover, New York (1972)
Carmona, J., León, A.: Investment option under CIR interest rates. Finance Res. Lett. 4, 242–253 (2007)
Cox, J.C., Ingersoll, J.E., Ross, S.A.: A theory of the term structure of interest rate. Econometrica 53(2), 385–408 (1985)
Delbaen, F.: Consols in the CIR model. Math. Finance 3(2), 125–134 (1993)
Dias, J.C.: Essays in real options models under interest rate uncertainty. PhD Thesis, ISCTE Business School (2006)
Dias, J.C., Shackleton, M.B.: Hysteresis effects under CIR interest rates. Eur. J. Oper. Res. 211, 594–600 (2011)
Feller, W.: Two singular diffusion problems. Ann. Math. 54, 173–182 (1951)
Geman, J.H., Yor, M.: Bessel processes, Asian options, and perpetuities. Math. Finance 3(4), 349–375 (1993)
Acknowledgements
Dias is member of the BRU-UNIDE, and Larguinho and Braumann are members of the Research Center Centro de Investigação em Matemática e Aplicações (CIMA), both centers financed by the Fundação para a Ciência e Tecnologia (FCT). Dias gratefully acknowledges the financial support from the FCTs grant number PTDC/EGE-ECO/099255/2008.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Larguinho, M., Dias, J.C., Braumann, C.A. (2013). A Note on (Dis)Investment Options and Perpetuities Under CIR Interest Rates. In: Oliveira, P., da Graça Temido, M., Henriques, C., Vichi, M. (eds) Recent Developments in Modeling and Applications in Statistics. Studies in Theoretical and Applied Statistics(). Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-32419-2_21
Download citation
DOI: https://doi.org/10.1007/978-3-642-32419-2_21
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-32418-5
Online ISBN: 978-3-642-32419-2
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)