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Nimbus3000
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Re: Listed option IV curve

June 11th, 2017, 7:37 pm

Bid(blue), Ask(red) and Mid(green) are the market curves. The one in black is the curve I get from least square error and the one in magenta is the Levenberg-Marquardt optimization of the results. I've taken these from the Axel Vogt's implementation.
What I meant by not smooth is that some of the options with higher moneyness have lower IV than those with relatively lower moneyness. This isnt the case with liquid index options
 
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Alan
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Re: Listed option IV curve

June 11th, 2017, 7:51 pm

It seems there are various issues here. 

First, two least squares optimizers should give the same result for this problem, IMO.

Second, that parameter result, plugged into the SVI form, should plot as a smooth curve for the IV(K). Neither of your curves look smooth vs K to me. That's what I was asking about on my earlier post re smoothness.

But, since you bring up what you meant by 'smooth', your explanation of that confuses me too. Please give a numerical example from your chart illustrating  "some of the options with higher moneyness have lower IV than those with relatively lower moneyness".

And, again, what are the actual strikes of your market data?
 
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Nimbus3000
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Re: Listed option IV curve

June 12th, 2017, 4:52 am

The one in black is the results I get from excel solver, the one in magenta is LM optimization.
One reason the SVI curve is not smooth can be that I evaluate the curve only at fixed strikes and not at all points. I'll do that as well and post the results.
What I mean as far as the smoothness is concerned is that delta 0.3 options have lower Mid-IV in a few cases than delta 0.25 options. The difference is due to the spreads being wider at some strikes being wider than others. The strikes I've used are from 280 to 340 at a difference of every 5 bucks.
This is my first experience with anything apart from vanilla BS-model so please excuse me if some of my questions seem rather naive. 
 
frolloos
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Re: Listed option IV curve

June 12th, 2017, 10:26 am

It doesn't matter whether SVI is calibrated only to a few fixed strikes. The resulting SVI smile should still be smooth.

Maybe you can attach the discrete mid IVs for your discrete strikes, I can give it a go with SVI.
 
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Nimbus3000
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Re: Listed option IV curve

June 12th, 2017, 12:51 pm

Starting with 280 till 340, with a difference of 5, my IVs are [ 0.3610335  0.33629    0.322188 0.3071335  0.297602   0.301366   0.308532 0.310931   0.325343   0.3342465  0.3472695  0.369975 0.383803 ]
 
frolloos
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Re: Listed option IV curve

June 12th, 2017, 12:56 pm

What tenor?
 
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Nimbus3000
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Re: Listed option IV curve

June 12th, 2017, 1:02 pm

0.027397260274 years to expiry, underlying futures trading at 301.925
The results I get are:
Excel Solver Optimization = [0.360682481, 0.337546389, 0.319759614, 0.307708779, 0.301424743, 0.30055971, 0.304457585, 0.312288467, 0.32318996, 0.336370424, 0.351161344, 0.367029353, 0.383565105]

LM Optimization = [0.359912473, 0.338703805, 0.320991485, 0.308039824, 0.300796921, 0.299503707, 0.30359309, 0.311961629, 0.323375787, 0.33675674, 0.351283567, 0.366381316, 0.3816674]
 
frolloos
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Re: Listed option IV curve

June 12th, 2017, 1:35 pm

My simple no-frequency excel solver gave the result below. Your results seem better, but the issue is that even with yours you fall outside of the b/a spread?

 36.08% 33.78% 31.97% 30.74% 30.10% 30.03% 30.45% 31.26% 32.38% 33.70% 35.16% 36.70% 38.29%

 
 
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Nimbus3000
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Re: Listed option IV curve

June 12th, 2017, 1:41 pm

Yes, I do on more than one strike. 
Any ideas for improvement?
 
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Nimbus3000
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Re: Listed option IV curve

June 12th, 2017, 2:26 pm

Which one is the SVI fit and why isn't it a smooth curve? Also what are the actual strikes of your data? 

If it's a smooth curve and always between the bid-ask IV, I would declare victory.
Unfortunately, its not always within the bid/ask spread
 
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Alan
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Re: Listed option IV curve

June 12th, 2017, 2:38 pm

Some possible issues beyond simply out-of-sync or bad market data:

1. Since this is a single-name stock, what is the exercise style and how are you converting to Euro-style if it is American-style? 

2. Are you using exclusively out-of-the-money options to calculate IV's? (I would, so puts for K < S0, calls for K > S0).

3. Assuming Euro-style or a reasonable conversion to that exercise style, are you then enforcing put-call parity and, if so, how? The CBOE has a method in the "VIX white paper", which will yield an option implied forward price. I would calculate that and compare to the futures price. (BTW, from where are you getting that futures price?) If they are different, try re-running the whole analysis with that option-implied forward price (new IV's, new SVI run, etc).
Last edited by Alan on June 12th, 2017, 2:57 pm, edited 1 time in total.
 
frolloos
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Re: Listed option IV curve

June 12th, 2017, 2:57 pm

Yes, I do on more than one strike. 
Any ideas for improvement?
I'll wait first until you can confirm /answered Alan's points 1 & 2 & 3 above. Also I am assuming that the quotes you gave are snapped at the same time (including the futures/forward level) and that you are only using quotes for which there are (non-stale) bids and offers.


For completeness, can you give the typical b/a spread for this underlying?
 
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Nimbus3000
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Re: Listed option IV curve

June 12th, 2017, 5:33 pm

Some possible issues beyond simply out-of-sync or bad market data:

1. Since this is a single-name stock, what is the exercise style and how are you converting to Euro-style if it is American-style? 

2. Are you using exclusively out-of-the-money options to calculate IV's? (I would, so puts for K < S0, calls for K > S0).

3. Assuming Euro-style or a reasonable conversion to that exercise style, are you then enforcing put-call parity and, if so, how? The CBOE has a method in the "VIX white paper", which will yield an option implied forward price. I would calculate that and compare to the futures price. (BTW, from where are you getting that futures price?) If they are different, try re-running the whole analysis with that option-implied forward price (new IV's, new SVI run, etc).
1. These are european options
2. Yes, I'm using OTMs exclusively
3. Although I havent enforced put call parity conditions, I checked and PCP holds for the prices above if i include transaction costs and spreads
As far as the data is concerned, these data points are in sync and have been taken from a TBT feed
 
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Nimbus3000
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Re: Listed option IV curve

June 12th, 2017, 5:36 pm

Yes, I do on more than one strike. 
Any ideas for improvement?
I'll wait first until you can confirm /answered Alan's points 1 & 2 & 3 above. Also I am assuming that the quotes you gave are snapped at the same time (including the futures/forward level) and that you are only using quotes for which there are (non-stale) bids and offers.


For completeness, can you give the typical b/a spread for this underlying?
Yes Sir, all the options I consider have both bid and ask prices and spreads are sane with respect to the option prices.
For at the money options, the spread is about 0.21 to 0.22 vol points
 
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fomisha
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Re: Listed option IV curve

June 12th, 2017, 5:54 pm

Hello,

Has anyone here worked in fitting a cubic psline to listed option/ exchange traded options of an underlying?
I have a few doubts and was wondering if someone can help me figure out a few details please.

Best.
There are a number of issues with both splines and SVI. Check out Volar vol fitter. It is a high performance, industry tested solution which has pretty much any feature you might need, e.g. a smart temporal filter and an ability to fit W-shaped vol curves (e.g. around earnings in tech names).