Is delta independent of vega?

How linear is Theta on the below graph anyway? Doesn't Theta change all the time? How is it Linear with this basic graph?

upload_2022-1-31_21-37-52-png.276976

Are they telling me if I traded KO options vs Tesla options, both their theta decay would still look like this??
 
Graphical "analysis tab" in TOS will allow you to trade from the graph of all your positions displayed on a graphic within the software. It will show you the change in the Delta and Vega and the effect on changes in the underlying price. Great Tool and will give you answer to your question.
 
Yes. For an otm option, change in implied vol will change delta. There is often a correlated relationship between vol and spot movements so you gamma and Vega will need to be managed in concert.

You have three basic risks in an options trade: delta, Vega, gamma/theta. They are often related so you have to manage them all in totality though you can reduce aspects of one.

you can’t have positive theta and flat gamma unless you take on second order risks. This is generally done through some
Kind of skew trade but that will create a massive Vega/delta correlated position. I’ve seen many people make/break their careers on that position.

Does Option IV counteract Delta?

If you look at any IV graph, IV increases with options that are further away from underlying. IV increases options value. However Delta decreases options value too. Thus in the end, Delta wins even though IV increases like crazy, the option is nearly worthless when far away( but has a high IV though)

As the underlying gets closer to strike price, the Delta increases but IV decreases. This is probably the most confusing part to me, does Delta always win? lol. Seems like IV and Delta are always countering each other.
 
Does Option IV counteract Delta?

If you look at any IV graph, IV increases with options that are further away from underlying. IV increases options value. However Delta decreases options value too. Thus in the end, Delta wins even though IV increases like crazy, the option is nearly worthless when far away( but has a high IV though)

As the underlying gets closer to strike price, the Delta increases but IV decreases. This is probably the most confusing part to me, does Delta always win? lol. Seems like IV and Delta are always countering each other.

I don’t know what you mean by wins.
 
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