Brokers who offer Put Spread vehicle also for CashAccts

You are quibbling over the definition of leverage.
To keep it simple If a stock fully paid for moves up ten percent percent and the fully paid for option moves up 50% a person would not be wrong to say the leverage is 4 to 1. However there is time decay for the option because it has an expiration date. Therefore the leverage factor changes over time. As the option is for an out of the money strike price approaches expiration it will decline to zero on the last day.
As the option is fully paid for the broker is not loaning you money. the broker is not extending leverage to the customer. The leverage comes from the option itself.

 

This is wrong thinking, b/c imagine this: if you trade options only, then the price of the underlying stock does not interest you, ie. you know only the option premium as basis for your PnL calculations... Q.E.D.

 

Would that PnL graph look any different were it an American-style option?

 

The general rule is changes in the price of the stock causes change in the price of the option.

 

No. The PnL is the same for both American as well European style options.
The only difference btw. them is the exercise possibility:
American style option: an option that may be exercised on any trading day on or before expiration.
European style option: an option that may only be exercised on expiry.

The practical meaning of exercise with American style is this: if you short-sold a Call option then the counterparty (ie. the buyer of the option) can demand anytime that he/she wants "delivery" of the underlying stock Usually of course only when his/her position is much in the profit zone.
For a Put seller such an exercise means: he/she has to buy the underlying stock of the counterparty immediately using the agreed-upon price (ie. the strike price).
With European style this choice of anytime is not possible.

And: these two above are often described as vanilla options.
There are some more of such option styles, like Asian, Bermudan, Barrier, Binary, Exotic, ...
But these are non-standard, and not used in the regular US market of listed stocks & options.

 

Not always... Multiple factors play a role, incl. IV...

 

No. Premium paid are not the same.

 

Prove your claim.

 

Here's a demonstration of the above said using a Call option with Strike=10:

USpot=10.00 DTE=365 IV=50 --> Premium=1.9741

on the next day USpot rises and IV falls:

USpot=10.25 DTE=364 IV=45 --> Premium=1.9277

Ie. stock rose but premium fell! This was caused by the IV falling to 45 from 50, as well now having 1 day less DTE.

Of course one can easily find also parameters where premium stays the same, eventhough stock price has changed

 

Good riddance!