What would be the best way to really internalize the interplay of option Greeks? I’m tired of doing long-winded mental calculations to figure out how a change in a factor affects the others.

You could play around with this?

I knew all the greeks and the interplay between them before L2, purely because I used to support an FX options system that we used for booking, pricing, risk etc. Literally zero idea of the specific formulas behind any of it, but I could explain the concepts, and I’ve always found that to be enough. I don’t even really know how I’d start going through mental calculations to figure it out.

Delta is the change in option price in response to the underlying asset price movement, Gamma is the rate of change of the delta in response to the change in underlying, and realistically is the only second order derivative you need to know about. Vega is how volatility affects the options price, Theta is the time decay factor, and Rho is the risk free rate. There’s another one called Lambda which is to do with leverage/gearing, which I had to play around with a few times at work, but I never quite fully understood it, or at least I don’t remember it well enough.

Maybe you could explain what you need to know, why you need to know it etc and some specific questions, it might be easier to give some guidance.

Thanks, that was exactly what I was looking for. The graphs add a lot of depth IMO.

The reason I wanted to get a better understanding of the interplay of the greeks was that I got butchered in an interview back in the day when the interviewer started bombarding me with questions about theta and vega and whatnot.

what were they asking? just for definitions or like long-winded stuff

Rapid-fire style questions like: what happens to a call’s delta if it’s in the money and volatility increases? How is the delta of a long butterfly spread with calls affected as you move closer to expiration? Tell us about how and why the time sensitivity of a long straddle is different from a position of just one option, etc.

Rapid-fire style questions . . .

Were you expected to answer these rapid-fire? I suspect that even people with extensive options trading experience would have to pause a moment to come up with the answers, and if the interviewer knew that you didn’t have extensive options trading experience you should have been allowed to work out the answer.

I believe that the answers are:

(W)hat happens to a call’s delta if it’s in the money and volatility increases?

The delta should decrease, because the time value increases. This is easy to see if you draw a picture.

How is the delta of a long butterfly spread with calls affected as you move closer to expiration?

I’m sure that this depends on where the spot price is vis-à-vis the option strikes for the butterfly.

Tell us about how and why the time sensitivity of a long straddle is different from a position of just one option.

A long straddle has two options so it has higher time value than a position with just one option; its time sensitivity should be greater (if only slightly).

etc.

That’s a toughie.

Just take the first partial derivatives with respect to S,t, r, sigma and the second partial derivative with respect to S to get gamma. Geez, you make it sound difficult!!!