Real option pricing with mean-reverting investment and project value

In this work, we are concerned with valuing the option to invest in a project when the project value and the investment cost are both mean-reverting. Previous works on stochastic project and investment cost concentrate on geometric Brownian motions (GBMs) for driving the factors. However, when the p...

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Vydáno v:The European journal of finance Ročník 19; číslo 7-8; s. 625 - 644
Hlavní autoři: Jaimungal, Sebastian, de Souza, Max O., Zubelli, Jorge P.
Médium: Journal Article
Jazyk:angličtina
Vydáno: London Routledge 01.09.2013
Taylor & Francis LLC
Témata:
Algorithms
Approximation
C6 (Mathematical Methods and Programming)
Commodities
Derivatives
Development projects
Fourier transforms
Investment
investment under uncertainty
Investments
Mathematical problems
Mathematics
Maturity
mean-reverting
Pricing
real options
Securities prices
stochastic investment
Stochastic models
Studies
Valuation
Value
ISSN:1351-847X, 1466-4364
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Shrnutí:In this work, we are concerned with valuing the option to invest in a project when the project value and the investment cost are both mean-reverting. Previous works on stochastic project and investment cost concentrate on geometric Brownian motions (GBMs) for driving the factors. However, when the project involved is linked to commodities, mean-reverting assumptions are more meaningful. Here, we introduce a model and prove that the optimal exercise strategy is not a function of the ratio of the project value to the investment V/I - contrary to the GBM case. We also demonstrate that the limiting trigger curve as maturity approaches traces out a nonlinear curve in (V, I) space and derive its explicit form. Finally, we numerically investigate the finite-horizon problem, using the Fourier space time-stepping algorithm of Jaimungal and Surkov [2009. Lev´y based cross-commodity models and derivative valuation. SIAM Journal of Financial Mathematics, to appear. http://www.ssrn.com/abstract=972837 ]. Numerically, the optimal exercise policies are found to be approximately linear in V/I; however, contrary to the GBM case they are not described by a curve of the form V*/I*=c(t). The option price behavior as well as the trigger curve behavior nicely generalize earlier one-factor model results.
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ISSN:1351-847X
1466-4364
DOI:10.1080/1351847X.2011.601660