In the 3rd bullet point the notes talks about S* and it says that S* is the critical price of the underlying option is at-the-money. I think that the word underlying should be compound instead. Do you agree?
Compound options The short answer is "No, I don't agree", but my more helpful answer is ... You'll exercise the compound option at T1 only if it's in-the-money, ie only if the underlying option is the correct side of K1. So the critical price of the underlying option is K1, which will correspond to a particular price for the underlying asset, which we call S*. This value of S* is then used in the valuation formula for the compound option (given in Hull on page 532, but not needed for ST6). You could use a special symbol to denote the value of the compound option at T1 when the underlying asset is worth S* (and the underlying option is worth K1), but this can't be an input to the compound option valuation formula, since it is the value of the compound option!
