Serving the Quantitative Finance Community

• 1
• 2

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

### My 5 cents on the smile

QuoteOriginally posted by: list1QuoteOriginally 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.I don't know where or how to start explaining. I really think it is a language issue, don't take that the wrong way. If I, with my childish PDE and probability skills can get at least a basic understanding of option pricing, you should definitely be able as well. So if I were you, try to find a good book on option pricing in your mother language.
Last edited by frolloos on June 30th, 2016, 10:00 pm, edited 1 time in total.

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

### My 5 cents on the smile

frolloos if I do not mistake implied volatility is one that comes up from calculation sigma in based on historical data of the option prices. In other words we are in BS world ( t , S ) are variables and ( T , K ) are fixed parameters. LV concept takes BS price and consider ( t , S ) as fixed parameters and ( T , K ) are variables in [ t , +$\infty$ ) and K > 0. LV construction states that C ( t , S ; T , K ) when ( t , S ) as fixed parameters and ( T , K ) are variables is defined by a random process K( T ) with diffusion coefficients known as local volatility surface. In such setting I could not interpret the original question. Though as you noted I might confuse something here.

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

### My 5 cents on the smile

I havn't heard of the GVV framework. I recognise your problem, but I simply avoided it by looking at expiration >= 14 days. So I won't be of much help when looking at that short expiration dates, unfortunately.

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

### My 5 cents on the smile

QuoteOriginally posted by: volatilityManI havn't heard of the GVV framework. I recognise your problem, but I simply avoided it by looking at expiration >= 14 days. So I won't be of much help when looking at that short expiration dates, unfortunately.No worries. GVV = gamma-vomma-vanna framework by Arslan et al (from Deutsche), and Giryavets also contributed to this framework. But their working papers are not publicly available.
Last edited by frolloos on June 30th, 2016, 10:00 pm, edited 1 time in total.

PrinceQnt
Posts: 9
Joined: October 27th, 2020, 11:36 pm

### Re: My 5 cents on the smile

Not much value beyond 5 delta for most observed chains in liquid products. There are often sequences of "flat priced" 0-.05 bid-ask options in clusters out that far. The issue becomes very significant with low volatility, wide strike, and low priced underlyings. Market makers effectively work ridiculous prices, which are sometimes flat 15 cents..."out-there". It is easy to know a good price to work for those options, but a fair price is a very different story.