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MartinGale7
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VIX to Option Pricing Heuristics?

February 21st, 2019, 8:39 pm

I hope that this question isn't to simplistic.

I am (roughly) familiar with the process for how the VIX is calculated. It is taking many ES OOM options prices around 30 days in the future and using this surface to estimate the implied volatility of an OOM options expiring in 30 days.

1) But how far OOM is this estimate? 25/75 delta? For example, if the VIX is 15% today and I look at ES options 30 days in the future, how far out of the money will the implied volatiliy on the smirk be 15%?

2) And, is this OOM above the forward price, or OOM below the forward price? Given the smile isn't symmetric (most likely a smirk), it is likely to be different.

3) Finally, are the any heuristics for taking a VIX value and using it to estimate the implied volatility on a particular ES option (any, or at least a specified 30d OOM)?
 
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Alan
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Re: VIX to Option Pricing Heuristics?

February 21st, 2019, 11:31 pm

Let's suppose there's an actual option chain expiring in 30 days. Then, given the typical shape of the SPX smile, there's going to an an out-of-the-money put with the same implied vol as the VIX level. (The chance of an out-of-the-money call having that implied vol is much lower). Having said that, I'm not sure what identifying that put buys you.

The VIX is very close to the marketed fair strike for a 30-day variance swap. Moreover, that's the basis for its construction (Technically, under a diffusion assumption, although it's robust to corrections to that).  Over time, the VIX tends to average about 3 vol points higher than (annualized) realized volatility. Taken together, I suggest you think of the VIX as the market's best estimate of the (annualized) SPX volatility for the next 30 days + (roughly) 3 vol points of (vol risk) premium. 
 
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MartinGale7
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Re: VIX to Option Pricing Heuristics?

February 22nd, 2019, 4:57 pm

Thank you. That is a useful heuristic. As I check, the VIX is 14.1% and 30d ATM options are at 11.3%. 30d OOM strikes with deltas (-)25% (puts) and (+)25% (calls) are at 14% and 10%. So, for the ATM, that sounds close.

As the VIX moves up and down, do you find that the shape of the 30d smirk tends to remain reasonably constant, just shifted up and down?
 
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Alan
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Re: VIX to Option Pricing Heuristics?

February 22nd, 2019, 7:17 pm

You're welcome. 

Re 'constant shape', I haven't studied shape changes carefully -- esp where the horizontal axis is delta, which I see is your preferred scale. 

Of course, for decades the SPX smirk is indeed a smirk: downward sloping except with a little turn-up at the farthest OTM calls. I do recall noticing a pronounced additional turn-up at that end just prior to the 2003 Iraq War. As option smiles are always forward looking, you'd want to be careful about any major/unusual forward events in the pipeline disrupting any putative shape pattern.   

p.s. I notice the CBOE has a SKEW index that relates to this shape stability question (in particular the chart on pg 4 caught my eye).
 
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MartinGale7
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Re: VIX to Option Pricing Heuristics?

February 24th, 2019, 4:19 pm

Thank you Alan. That is really helpful.
 
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fomisha
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Re: VIX to Option Pricing Heuristics?

March 2nd, 2019, 12:38 am

A good starting point would be VIX white paper and a primer on var swaps.