chatgpt told me to come here, for help about leverage

[mjxue]

So I can't really explain my question well enough to find it on google, and ChatGPT doesn't really help, told me that people on quantnet would know. I'm a very naive person in the world of finance, know nothing about it, and I just don't get something that probably will be really trivial to answer for you guys.

Okay, so lets say I have a call option ATM premium 10 dollars, underlying 100 dollars. And I have a put option ATM strike 10 dollars, underlying 100 dollars.
I think american options price puts above calls because exercising early is more advantageous for puts than calls, so let's look at european, where they should be equal besides the rho factor which can be kind of ignored in this context

If my underlying stock explodes! say it goes to 200 dollars underlying. My call option goes ITM and I'm very happy! But my leverage also changes, right, in that I now "control" a lot more money with my option.

So if a new ATM option were minted at the 200 dollar mark, it'll be more expensive than the 100 dollar one, because you control more money. So if we want to keep the 10x leverage, or about that, the premium might be around 20 dollars, assuming the greeks like time decay and IV are the same.

Okay. So, now, looking at puts. Say the stock tanks a ton to 20 bucks. I go ITM and I'm very happy! But my leverage changes too, in that now I control a lot less value with my option. So if a new ATM option were minted at 20 bucks, it definitely wouldn't be the same ATM premium as the 100 dollar one. It would be much less, maybe 2 dollars to reflect that leverage.

So.. I lose money through puts if they go ITM? And I make money through calls if they go ITM?
But that obviously makes no sense at all. You don't "make" more or "lose" more, because if you go ITM that's just the price minus strike + premium. It's very simple, and it's always been like that. So a portion of the price change is that change in leverage, like a hidden overlay that increases or decreases but doesn't really matter in the long term?


If I bought an OTM put and the price went up, does that mean anything either?

european model, delta and gamma are symmetrical around puts and calls. leverage has no price action, then?

but being able to control more stock is good, right? Doesn't that mean something?

I just don't get where this ghost lives, if that makes sense. Where does leverage hide? Is leverage even a thing?

Thanks if you could get through this, I'm just a very confused individual.

 

[code breaker]

Leverage is a thing, but it isn't exactly A thing you own or lose, ITS A MEASUREMENT based on the potential gains relative to your cost.
Also there's different types of options: ATM, ITM, OTM I'll assume that you know those.

Here's an example:
Say we have a call options and the stock does go up.
You bought an ATM call at $100 strike, and stock rise up to $200 and a new ATM call would have a strike of $200 and it's premium would be $20, in this case your right it will be expensive because it controls more dollar value.

Then what happens to your ATM call at $100 strike?
Here's what happens:
intrinsic value: $200 - $100 = $100
your call value is $100 now, if you gain from it you get $90 because ur premium is $10.

So where did the leverage go?
You controlled $100 of a stock for $10, thats like 10-1 leverage.
Your option is now mostly intrinsic value , it's behaving more like a stock. The leverage decreased but you are already profiting cause u made 900% return ($90 profit / $10 premium)

TLDR:
Leverage is the ratio of the value you control to the price you paid. It always decreases as you go deep in the money(ITM).

• For a Call: Leverage decreases as the stock price rises far above your strike.
• For a Put: Leverage decreases as the stock price falls far below your strike.