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...

Full description

Saved in:
Bibliographic Details
Published in:The European journal of finance Vol. 19; no. 7-8; pp. 625 - 644
Main Authors: Jaimungal, Sebastian, de Souza, Max O., Zubelli, Jorge P.
Format: Journal Article
Language:English
Published: London Routledge 01.09.2013
Taylor & Francis LLC
Subjects:
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
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ObjectType-Article-2
ObjectType-Feature-1
content type line 23
ISSN:1351-847X
1466-4364
DOI:10.1080/1351847X.2011.601660