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Mathematics and Financial Economics
Published in: Mathematics and Financial Economics 4/2013

01-09-2013

Optimal investment with two-factor uncertainty

Authors: Manuel J. Rocha Armada, Paulo J. Pereira, Artur Rodrigues

Published in: Mathematics and Financial Economics | Issue 4/2013

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Abstract

This paper presents a real options model to value the option to invest in a project contingent on two stochastic factors. A general sensitivity analysis is conducted highlighting the importance of the variance and correlation between the two variables. A higher correlation is shown to increase always the values of the trigger, the active project and the option. The impact of uncertainty is more complex and depends on the assumption about which variables adjust and the correlation between the variables and the market.
previous article Dealing with the inventory risk: a solution to the market making problem
next article Utility maximization with a given pricing measure when the utility is not necessarily concave

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Appendix
Available only for authorised users
Footnotes
1
Usually the price-quantity relation is modeled as a demand function with constant parameters. In some real options models, stochastic factors are added to the demand function [2, 4]. Modeling price and quantity as the two stochastic factors, means that we are assuming that there are exogenous factors explaining the behavior of price and quantity, but that does not imply they are independent, since it is assumed that they are (negatively) correlated. In other words, this is equivalent to assume that the relation between price an quantity is not constant over time.
 
2
For a review on the real options theory please refer to [4] and [9].
 
3
For more details, please refer to [1].
 
4
See Appendix A.
 
5
This is an adapted version of their Eq. (13).
 
6
Appendix C.1.2 shows that the sign of the impact of \(\sigma _P\) on the trigger is ambiguous for \(\rho _{Pm}<0,\) whatever the correlation \(\rho \) is.
 
7
A higher trigger value does not mean necessarily delaying investment [8].
 
8
Numerical simulations, not reported here, using parameter values similar to this example, have shown that when the increase in the option value occurs it is of low magnitude.
 
Literature
1.
Adkins, R., Paxson, D.: Renewing assets with uncertain revenues and operating costs. J. Finan. Quant. Anal. 46(3), 785–813 (2011)CrossRef
2.
Caballero, R.J., Pindyck, R.S.: Uncertainty, investment, and industry evolution. Int. Econ. Rev. 37(3), 641–662 (1996)MATHCrossRef
3.
Constantinides, G.: Market risk adjustment in project valuation. J. Finan. 33(2), 603–616 (1978)CrossRef
4.
Dixit, A.K., Pindyck, R.S.: Investment Under Uncertainty. Princeton University Press, Princeton (1994)
5.
McDonald, R., Siegel, D.: Investment and the valuation of firms when there is an option to shut down. Int. Econ. Rev. 26(2), 331–349 (1985)MATHCrossRef
6.
McDonald, R.L., Siegel, D.R.: The value of waiting to invest. Q. J. Econ. 101, 707–728 (1986)
7.
Paxson, D., Pinto, H.: Rivalry under price and quantity uncertainty. Rev. Finan. Econ. 14(3–4), 209–224 (2005)CrossRef
8.
Sarkar, S.: On the investment–uncertainty relationship in a real options model. J. Econ. Dyn. Control 24(2), 219–225 (2000)MATHCrossRef
9.
Trigeorgis, L.: Real Options: Managerial Flexibility and Strategy in Resource Allocation. The MIT Press, Cambridge (1996)
Metadata
Title
Optimal investment with two-factor uncertainty
Authors
Manuel J. Rocha Armada
Paulo J. Pereira
Artur Rodrigues
Publication date
01-09-2013
Publisher
Springer Berlin Heidelberg
Published in
Mathematics and Financial Economics / Issue 4/2013
Print ISSN: 1862-9679
Electronic ISSN: 1862-9660
DOI
https://doi.org/10.1007/s11579-013-0101-1

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