Question on 14.1.2 pricing American option

[mingchenckm]

ASM MFE, P.205, below equation 14.1,
"... exercising the put option corresponds to not exercising the original option at time t1."

I think the original option at time t1 should be the American call option.

McDonald's text, P.455, after point 3,
"In this interpretation, exercising the compound option corresponds to keeping the option on the stock unexercised."

The second option should also be the American call option.

But... I think exercising the put option is not equivalent to exercising the compound option.

Is it a typo? Should it be exercising the CallOnPut option?
Or have I missed something?

Thanks!

[Abraham Weishaus]

Are you just bothered that I said "the put option" instead of "the compound option"? Yes, I meant the compound option to buy a put option.