Real Options and American Derivatives: The Double Continuation Region

Relevant capital investment options and American derivatives embedded into popular secured loans can be reduced to American option problems with an endogenous negative `interest rate'. We show that such problems can entail a non-standard double continuation region: option exercise is optimally postponed not only when the option is insufficiently in the money but also when it is excessively in the money. We fully characterize the existence, the monotonicity, the continuity, the limits and the asymptotic behavior at maturity of the double free boundary that separates the exercise region from the double continuation region. Our results apply to real options whose project values enjoy robust growth rates while investment costs also markedly escalate. The gold loan is an in-vogue contract of collateralized borrowing whose optimal redeeming strategy constitutes another interesting application of our results.