I've noticed that in the literature, whenever European vanilla options are to be priced, the classical approach is to price a European call.
I guess it doesn't matter because we have put-call parity.
However, almost every time I see somebody mention the pricing of American options, the standard approach is to consider an American PUT. We don't have a put-call parity, so considering American Call options seems equally relevant, and yet this doesn't happen.
Is there a reason for this?
EXAMPLE: Shiryev and Peskir's monograph on optimal stopping problems consider pricing American puts and perpetual puts... they don't even mention a call option.