We show that an American put option with delivery lags  can be decomposed as a European put option and another American-style derivative. The latter is an option for which the investor receives the Greek Theta of the corresponding European option as the running payoff, and decides an optimal stopping time to terminate the contract. Based on the this decomposition , we further show that the associated optimal exercise boundary exists , and is a strictly increasing and smooth curve . We also analyze its asymptotic behavior for both large maturity and small time lag using the free-boundary method .
A make-your-mind-up option is an American derivative with delivery lags . We show that its put option can be decomposed as a European put and a new type of American-style derivative. The latter is an option for which the investor receives the Greek Theta of the corresponding European option as the running payoff, and decides an optimal stopping time to terminate the contract. Based on this decomposition and using free boundary techniques, we show that the associated optimal exercise boundary exists and is a strictly increasing and smooth curve , and analyze the asymptotic behavior of the value function and the optimal exercise boundary for both large maturity and small time lag .
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We show that an American put option
A make-your-mind-up option is an American derivative
A
. We show that its put option
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option and another
and a new type of
R
the this decomposition , we further
this decomposition and using free boundary techniques, we
D
,
R
. We also analyze its asymptotic behavior
, and analyze the asymptotic behavior of the value function and the optimal exercise boundary
D
using the free-boundary method