Anyone studying options for long enough begins to wonder about how the Greeks interact. Like, sure, an option’s delta approaches 0 or 1 (depending on its moneyness) as it gets closer to expiration, but what happens to its gamma, as it gets closer to expiration? Does that depend on its delta? Natenburg goes a bit into this with a plethora of graphs in his textbook. The unfortunate thing about books is that they’re all 2D and noninteractive.

I decided to see what I could spin up with Julia and a bit of elbow grease. I grabbed the latest option chain with TD Ameritrade and got to work. (At the time of these graphs, SPY was trading near $419.) Behold, some graphs:

Gamma in response to Time and Delta:

Gamma in response to Time and Delta

Volatility in response to Time and Price (aka Vol Smile) Volatility in response to Time and Price (aka Vol Smile)

If you’d like to play with this, feel free to play around with the repo.