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list1
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volatility trading

July 25th, 2015, 12:28 pm

Volatility in trading is quite a new market development. It comes with instruments trading where volatility word is used. It seems that volatility is too strong word used and in reality we deal with something that relates to volatility but it far from volatility. In other words people talk more than they are doing.Let us take a look at floating leg of a volatility swap. It represents realized volatility times notional principal N. Given GBM model limit of the realized volatility when interval between observations converges to σ. Hence in the limit flouting leg represent σ N. Hence in continuous setting monetized volatility is σ N. Hence value of the strike K which should be exchange for σ is K = σ N and value of the swap is equal to 0. If σ is unknown then realized volatility is a market approximation of the sigma and strike is a current estimate of unknown sigma given that log normal model of asset is perfect. If the lognormal model is an approximation it should be another story. Hence talking about volatility swap we only mean sigma coefficient of the modeldS = m S dt + σ S dwwhich of course does not represents volatility of S
 
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list1
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volatility trading

July 25th, 2015, 1:42 pm

Ok, I am frighten already. let us simplify the problem. You observe S which is a solution ofdS = m S dt + σ S dwIn order to design a volatility swap volatility should have a price.What is the price of a σ on [ 0, 1 ]?
Last edited by list1 on July 24th, 2015, 10:00 pm, edited 1 time in total.
 
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list1
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volatility trading

July 25th, 2015, 3:47 pm

Yes, I meant variance or volatility swap. But your question also suggests that σ has a price depending of what instrument we are going to use.
Last edited by list1 on July 24th, 2015, 10:00 pm, edited 1 time in total.
 
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studenttt
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volatility trading

July 25th, 2015, 4:02 pm

What's the question?
 
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list1
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volatility trading

July 25th, 2015, 6:04 pm

when I talk about how sigma is priced it was assumed thatdS = m S dt + σ S dw When observations on S at dates t_j are given we arrived at an approximation of the price which one assigned to sigma.
 
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list1
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volatility trading

July 25th, 2015, 8:01 pm

outrun, you are right in your comment. My original question bearing in mind your comment is related to :whether or not I can suppose GBM model for stock?if yes, can I assume given GBM that distance 'd' between periodic observations tends to 0?how does one interpret the limit of the realized volatility?I do not talk here about swap. I talk only about realized volatility. My question what is the price of the limit of the realized volatility given GBM model of stock.If we do not have a mathematical model of the stock price what the limit of realized volatility represents itself. This problem is relevant as far as discrete time version is an approximation or estimate of the continuous time limit.
 
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list1
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Joined: July 22nd, 2015, 2:12 pm

volatility trading

July 25th, 2015, 9:46 pm

I use a simple illustrative example related to GBM stock. I do not assume anything about swap family instruments. Using such example one can find out that the limit value of the realized volatility is sigma and given notional be equal to $1 One can conclude that limit value of the realized volatility price is equal to sigma. Then we can see that discrete version sample volatility is a statistical estimate of the sigma. In volatility swap this estimate is exchanged for K. The swap itself does not something new and it is ok with swap. I am somewhat confused with assigning to coefficient sigma the value sigma (when N=$1) and declaration it as price of volatility.
 
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list1
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volatility trading

July 28th, 2015, 9:53 am

And the last point. As as far as σ indS = m S dt + σ S dwis a scaleless parameters one can develop the similar volatility pricing for any observed non financial data which can be approximated by a solution of the SDE.
 
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bearish
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volatility trading

July 28th, 2015, 10:11 am

QuoteOriginally posted by: list1And the last point. As as far as σ indS = m S dt + σ S dwis a scaleless parameters one can develop the similar volatility pricing for any observed non financial data which can be approximated by a solution of the SDE.I'll stay out of the rest of this discussion, but would like to point out that [$] \sigma [$] is not a scaleless parameter. It has units of inverse square root time. A quantity such as [$] \sigma^2 t [$] is scaleless.
 
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MHill
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volatility trading

July 28th, 2015, 12:11 pm

Oddly, this thread makes me think of an article outrun once posted:article