I'm completing exercises from
Steve Shreve - Stochastic Calculus for Finance I and I'm stuck on one subtask for which I can't find missing element for 11 stopping times mentioned at the end:
Exercise 4.5. In equation (4.4.5). the maximum is computed over all stopping times in S0. List all t he stopping times in So (there are 26) and from among them, list the stopping times that never exercise when the option is out of the money (there are 11).
But I can find only 10.
Here's intrinsic value tree (for
H goes up, for
T goes down):
0 / 0 / \ 1 1 \ / 3 \ 4
So out-of-the-money is for
So all stopping times where OTM is not exercised are:
HH HT TH TT inf inf inf inf inf inf inf 2 inf inf 2 inf inf 2 inf inf inf 2 2 inf inf 2 inf 2 inf inf 2 2 inf 2 2 2 inf 2 1 1 inf inf 1 1
So 10 in summary and I can't find the 11. stopping time. What did I miss?
Thanks for any guidance!