Modeling IV

M

morganpbrown

Latest in the taking one for the (uneducated) team series.

It seems that if you can model the "vol surface" for any option, you are ahead of the game. Maybe it's not so much about finding minima of the vol surface, so much as finding areas of steepest gradient?

Anyway, today I manually tabulated IV for SPY puts, for a variety of expirations and deltas.

upload_2021-9-22_14-9-33.png


For every delta, the IV curve seems to be roughly parabolic, with an exponential "smile" near 0 DTE. I guess this is vol smirk or something.

upload_2021-9-22_14-10-7.png


The translucent curves are my fit. To make the fit, I assumed a functional form of IV = A*exp(B*DTE) + C*(DTE-DTE0) + D*delta + E. In plain speak, an exponential plus a parabola centered at DTE0, with a linear dependence on delta.

Then I used Excel's non-linear solver to estimate the parameters. Here are the parameters (purple column), the prediction error for each tabulated IV (yellow), and the sum of the errors (lonely purple)

upload_2021-9-22_14-20-9.png



A few questions:
1) Are people putting any thought into this problem?
2) If yes, then I'm sure they have much smarter solutions(?)
3) I'm analyzing IV versus DTE and delta (better than strike?). Where else is the "action"?
 
Short answers:
1) Yes, a lot of thought
2) Yes, there are a ton of papers out there. As a primer, check the SABR model
3) IV in delta and time space is the correct way to approach things opposed to IV in strikes and DTE (depending on what you want to do, of course)

Long answer:
You're opening a can of worms here, as you are getting into the deep end of vol - trading. The tricky part is constructing a position that is robust over time and underlying price as deltas change with time and vol.

You'll end up with an options portfolio that consists of dozens of strikes and maturities and you have to be able to constantly adjust and balance it out.
Think about a risk reversal:

You are selling a 25 delta put, buy a 25 delta call both 60 days out and hedge to delta neutral with spot. Now spot rallies and suddenly you own a 40 delta call and a 10 delta put, which has a completely different dynamic.
On top of that 20 days have passed and vol dropped a bit. You are not delta neutral anymore but short delta into a rising market...not good.

So if you have a retail account with ToS or IB, you better drop that idea because commissions will eat you alive.

On the other hand, there is a lot of edge to be gained when looking at the vol surface. You can express your directional views with positions that have tremenduous risk/reward if done correctly.

Hint 1: look at the gamma/theta profile of the individual options. The lower DTE and IV, the higher gamma and the less theta you have to pay. Buy these and sell options with high IV, low gamma and higher theta. Balance out the greeks you are after to your liking which will give you a lot of bang for your buck. Positive gamma, positive theta and short vol is usually better than just slapping on an Iron Condor for "income" that explodes in your face once the market gets going. You will end up with a lot of calendars, though.

Hint 2: Chart your results in a different way: IV on the y-axis and delta on the x-axis. DTE in different lines. You can see the opportunities better:
upload_2021-9-22_22-53-6.png
upload_2021-9-22_22-53-6.png
 
MrMuppet said:
Short answers:
You're opening a can of worms here, as you are getting into the deep end of vol - trading.
More...

Thanks man. Yeah, I suspected that I was probably partially down a rabbit hole. An interesting one, for sure!

MrMuppet said:
Hint 1: look at the gamma/theta profile of the individual options. The lower DTE and IV, the higher gamma and the less theta you have to pay. Buy these and sell options with high IV, low gamma and higher theta. Balance out the greeks you are after to your liking which will give you a lot of bang for your buck. Positive gamma, positive theta and short vol is usually better than just slapping on an Iron Condor for "income" that explodes in your face once the market gets going. You will end up with a lot of calendars, though.

Hint 2: Chart your results in a different way: IV on the y-axis and delta on the x-axis. DTE in different lines. You can see the opportunities better:
View attachment 268312View attachment 268312
More...

Some homework...thanks for it!

I had the delta vs IV chart, but it looked boring. ;-)

upload_2021-9-22_16-49-57.png


Though at second glance, the curves crossing certainly deserves more investigation!

A question about your graph - is the left side of the x- axis puts? and the right side calls?
 
Don't think too, overly, technically and linearly. Remember, the market is a game...between people, and emotions. Forces. Everyday, it's part art ...part science.

You can't approach the market...with a scientists mindset, mind frame. It's similar to listening to music or watching a movie, you experience and observe a great deal of a range of emotions.

You can either choose to be a real world trader, or an academic trader. And last time I looked, academics don't make that much, or experience that much.

This video clip sums up the market everyday, the two forces colliding,
 
Last edited:
You must log in or register to reply here.
Back
Top