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frolloos
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Location: Netherlands

### My 5 cents on the smile

How much of the smile for OTM calls is determined by options not selling for less than say 5 cents?

Alan
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Joined: December 19th, 2001, 4:01 am
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### My 5 cents on the smile

I think one should never report an implied vol for a market smile unless the otm option bid > 0.Otherwise, agree, you get a totally artificial increasing smile due to put quotes at (no-bid, 0.05) for arbitrary decreasing strikes.But, with the bid>0 rule, the otm smile for, say, SPX is quite prominent and clearly increasing as the strikes decrease.
Last edited by Alan on June 28th, 2016, 10:00 pm, edited 1 time in total.

Posts: 23951
Joined: September 20th, 2002, 8:30 pm

### My 5 cents on the smile

This thread discussed the issue in some depth.
Last edited by Traden4Alpha on June 28th, 2016, 10:00 pm, edited 1 time in total.

frolloos
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Joined: September 27th, 2007, 5:29 pm
Location: Netherlands

### My 5 cents on the smile

Thank you both.The bid > 0 rule makes sense. But in my case, that is the extrapolation method I use, using only bid > 0 market quotes can lead to my call strikes IV extrapolation decreasing rapidly to absurd values of say 5% for equities for really far OTM strikes. I am more comfortable with my put strikes extrapolation.I will read the larryrichard thread. The links he posted thiugh dont't seem to work anymore. Not sure if one of you still have his paper.
Last edited by frolloos on June 28th, 2016, 10:00 pm, edited 1 time in total.

Alan
Posts: 10617
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### My 5 cents on the smile

QuoteOriginally posted by: frolloosThank you both.The bid > 0 rule makes sense. But in my case, that is the extrapolation method I use, using only bid > 0 market quotes can lead to my call strikes IV extrapolation decreasing rapidly to absurd values of say 5% for equities for really far OTM strikes. I am more comfortable with my put strikes extrapolation.I will read the larryrichard thread. The links he posted thiugh dont't seem to work anymore. Not sure if one of you still have his paper.IV extrapolation is a separate problem. When I first started using Gatheral's SVI method, I encountered your problem. My solution was to work out the analytic formula for $\sigma_{svi,min}$ and then constrain the fit routine to never letthe min value fall below a user-supplied judgment. For example, you might think 8% was the lowest reasonable value. If you are using some other method, a similar trick should work if the fitted smile has a minimum at a finite strike, which it probably should have.p.s. My recollection is that that thread was a waste of time -- after my post, of course!
Last edited by Alan on June 28th, 2016, 10:00 pm, edited 1 time in total.

volatilityMan
Posts: 114
Joined: January 16th, 2015, 6:06 pm

### My 5 cents on the smile

Which models/inter/extrapolation methods are you using?I dealt with SVI, stochastic volatility models and jump diffusion models for modelling the entire IV surface. Likewise, I only used bid > 0 and price > 0.05. Alternatively, I only looked at log-moneyness in the range [-0.35;0.35] dealing with OTM put and call options. Everything outside this range was more or less noise, IMO.

frolloos
Topic Author
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Joined: September 27th, 2007, 5:29 pm
Location: Netherlands

### My 5 cents on the smile

I am using / testing the GVV framework. Using a user-defined minimum as Alan suggested will work. Alternatively I was thinking maybe work backwards: start with the longer maturities for which there are quotes, and then use some sort of algorithm to get the shorter tenor OTM call strike IVs.

volatilityMan
Posts: 114
Joined: January 16th, 2015, 6:06 pm

### My 5 cents on the smile

And what is the lower bound on expiration? 7 days, 14?

list1
Posts: 1696
Joined: July 22nd, 2015, 2:12 pm

### My 5 cents on the smile

QuoteOriginally posted by: frolloosHow much of the smile for OTM calls is determined by options not selling for less than say 5 cents?I probably do not understand the question but the question does not fully clear for me. The essence of the local volatility concept is that: call option price C is a function of time and stock price ( t , S ) . Loc Vol considers call option price as a function of strike and maturity ( T , K ). Out of the money at t means that S < K, ie C = max ( S ( t ) - K , 0 ) = 0. What does it mean "not selling for less than say 5 cents" ?

volatilityMan
Posts: 114
Joined: January 16th, 2015, 6:06 pm

### My 5 cents on the smile

QuoteOriginally posted by: list1QuoteOriginally posted by: frolloosHow much of the smile for OTM calls is determined by options not selling for less than say 5 cents?What does it mean "not selling for less than say 5 cents" ?If you consider the bid/ask spread on options, you'll se a buyer and seller side. For (especially) short maturities and far OTM (both put and call) the bid side is 0. Hence absolutely no liquidity. It is very difficult to model an IV smile or surface in this case.You can, when looking for longer expiration. However, if you want to stay consistent with a compact set (strike and maturity) the problems start to arise.

list1
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Joined: July 22nd, 2015, 2:12 pm

### My 5 cents on the smile

Thanks vM for comment. and how does local volatility is implied in bid-ask format pricing of the option?

frolloos
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Location: Netherlands

### My 5 cents on the smile

QuoteOriginally posted by: volatilityManAnd what is the lower bound on expiration? 7 days, 14?5 business days, so 1 week, is lower bound. Looking at weekly options.

list1
Posts: 1696
Joined: July 22nd, 2015, 2:12 pm

### My 5 cents on the smile

One thought that might come with LV concept. Local vol deals with the same option price as it presented by BSE. In a simple version LV presents volatility of a theoretical not the real underlying of the option in ( T, K ) coordinate space and nothing more than that. Thus if one receives an adjustment to BS option price then it is formally incorrect even when LV establishes statistically more reliable estimate. Such adjustment is an argument that BS option price does not close to the market premium for specified period. The same conclusion holds for any other pricing adjustments like calibration. Practical closeness to real data does not a formal argument in favour of the adjustment is formally correct.

frolloos
Topic Author
Posts: 1621
Joined: September 27th, 2007, 5:29 pm
Location: Netherlands

### My 5 cents on the smile

QuoteOriginally posted by: list1One thought that might come with LV concept. Local vol deals with the same option price as it presented by BSE. In a simple version LV presents volatility of a theoretical not the real underlying of the option in ( T, K ) coordinate space and nothing more than that. Thus if one receives an adjustment to BS option price then it is formally incorrect even when LV establishes statistically more reliable estimate. Such adjustment is an argument that BS option price does not close to the market premium for specified period. The same conclusion holds for any other pricing adjustments like calibration. Practical closeness to real data does not a formal argument in favour of the adjustment is formally correct.You are confusing, not for the first time, the concepts of local vol and implied vol. The reason for that is possibly the common notation, $\sigma(K,T)$ for local vol, which is also used for implied vol. But they really are different (although related) things.

list1
Posts: 1696
Joined: July 22nd, 2015, 2:12 pm

### My 5 cents on the smile

QuoteOriginally posted by: frolloosQuoteOriginally posted by: list1One thought that might come with LV concept. Local vol deals with the same option price as it presented by BSE. In a simple version LV presents volatility of a theoretical not the real underlying of the option in ( T, K ) coordinate space and nothing more than that. Thus if one receives an adjustment to BS option price then it is formally incorrect even when LV establishes statistically more reliable estimate. Such adjustment is an argument that BS option price does not close to the market premium for specified period. The same conclusion holds for any other pricing adjustments like calibration. Practical closeness to real data does not a formal argument in favour of the adjustment is formally correct.You are confusing, not for the first time, the concepts of local vol and implied vol. The reason for that is possibly the common notation, $\sigma(K,T)$ for local vol, which is also used for implied vol. But they really are different (although related) things.frolloos, I could confused, not for the first time but it seems that implied volatility is calculated for the fixed T, K and therefore it uses the option data for the dates $t_k$ , k = 0, 1, 2, ... which show that we are in ( t , S )- coordinate space and not in ( t , K ) which correspond to loc vol dynamics.
Last edited by list1 on June 29th, 2016, 10:00 pm, edited 1 time in total.