Real Options and American Derivatives: the Double Continuation Region

We thoroughly study the non-standard optimal exercise policy associated with relevant capital investment options and with the prepayment option of widespread collateralized-borrowing contracts like the gold loan. Option exercise is optimally postponed not only when moneyness is insufficient but also when it is excessive. We contribute an important extension of the classical optimal exercise properties for American options. Early exercise of an American call with a negative underlying payout rate can occur if the option is moderately in the money. We fully characterize the existence, the monotonicity, the continuity, the limits and the symptotic behavior at maturity of the double free boundary that separates the exercise region from the double continuation region. We fifind that the fifinite-maturity non-standard policy conspicuously differs from the infifinite-maturity one.