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mtsm
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CEV and SABR for beta outside of [0,1]

March 13th, 2012, 12:51 pm

Hi guys,can you help me with a superficial account what happens to the CEV and SABR models when you plugin values for beta that lie outside of [0, 1], both positive and negative values?Has this been studied? Any references?I always thought that in SABR it is assumed that beta is in [0, 1).What about CEV?Thanks,mtsm
 
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spv205
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CEV and SABR for beta outside of [0,1]

March 13th, 2012, 2:06 pm

 
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list
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CEV and SABR for beta outside of [0,1]

March 13th, 2012, 2:30 pm

There is no sense to study a nonlinear model for security price as far as regardless how good data match to the model such model contradicts sense of the stock price. For example, two stocks would not present the same rate of return as 1 and it will be good to ask an author what the sense of the stock price notion he used in the paper. Though a nonlinear model makes sense for interest rates.
 
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SierpinskyJanitor
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CEV and SABR for beta outside of [0,1]

March 13th, 2012, 4:29 pm

QuoteThere is no sense to study a nonlinear model for security price as far as regardless how good data match to the model such model contradicts sense of the stock price. For example, two stocks would not present the same rate of return as 1 and it will be good to ask an author what the sense of the stock price notion he used in the paper. Though a nonlinear model makes sense for interest rates.How can someone condense so much nonsense in 3 sentences? Do you know the difference between model callibration and implementation? Also, under which assumptions does a nonlinear model makes sense for IR? Are you talking about forward-rates, spot-rates, swaption prices, caps, yield-curves, WTF are you talking about? And please don´t tell us you already have an "article" about it....
 
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Cuchulainn
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CEV and SABR for beta outside of [0,1]

March 13th, 2012, 4:42 pm

discussion
Step over the gap, not into it. Watch the space between platform and train.
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Alan
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CEV and SABR for beta outside of [0,1]

March 13th, 2012, 4:53 pm

yeah.Plus, I dsicuss dS = S^p dW (p > 1) in Ch 9 of my stoch. vol. book. It is a classic example of a strictly local martingale.
 
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list
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CEV and SABR for beta outside of [0,1]

March 13th, 2012, 5:46 pm

if we buy 1 stock for say 10 dollars and over a period the stock price is 20 dollars that means that buying say 5 stocks for the 50 dollars over the same period their price would be 100 dollars regardless whether our background is 3class or PhD. If we use a model which does not imply this is not calibration it rather misunderstanding of the notion price in finance. This is the same as to assume for say calibration that cos x = 3.5.
 
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Alan
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CEV and SABR for beta outside of [0,1]

March 13th, 2012, 5:59 pm

QuoteOriginally posted by: listit rather misunderstanding of the notion price in financeexactly!
 
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spv205
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CEV and SABR for beta outside of [0,1]

March 13th, 2012, 6:01 pm

list - so what?The model is for a stock price, not your portfolio value (or anything else) 1* (StockPriceToday-StockPriceYesterday)=105* (StockPriceToday-StockPriceYesterday)=50 this has no dependency on model for how stock price changes
 
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TinMan
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CEV and SABR for beta outside of [0,1]

March 13th, 2012, 8:03 pm

Yep. It's another world beater.
 
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daveangel
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CEV and SABR for beta outside of [0,1]

March 13th, 2012, 8:18 pm

QuoteOriginally posted by: spv205list - so what?The model is for a stock price, not your portfolio value (or anything else) 1* (StockPriceToday-StockPriceYesterday)=105* (StockPriceToday-StockPriceYesterday)=50 this has no dependency on model for how stock price changeswhy is that every time i buy a lot of stock i lose a lot of money ?
knowledge comes, wisdom lingers
 
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SierpinskyJanitor
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CEV and SABR for beta outside of [0,1]

March 13th, 2012, 8:23 pm

dunno, but we can be sure our articu-list has already theorised about it somewhere.... aren't there any ignobel prizes in finance?
 
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Paul
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CEV and SABR for beta outside of [0,1]

March 13th, 2012, 8:50 pm

I'm (mostly) with list on this one. From a modelling perspective, just about the only clue we have in finance is that stocks should be lognormal in nature for the reason list gives. If you want to fiddle around with something so as to calibrate then it makes more sense to have a fancy model for vol. (*Not that there's any sense whatsoever in calibration.) People's obsession with closed forms and calibration has led them to throw out the one useful piece of modelling information.Interest rates can do almost anything, in terms of an sde model, there are no clues there for functional forms.And BTW, SABR is, of course, based on asymptotics for low vol of vol and so should not be used for stocks anyway, that is simply people's misunderstanding of what asymptotics is all about. (*But if you insist on calibrating then you can choose whatever model you like, you might as well fit a polynomial to prices, makes as much sense.)P
 
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list
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CEV and SABR for beta outside of [0,1]

March 13th, 2012, 9:36 pm

QuoteOriginally posted by: spv205list - so what?The model is for a stock price, not your portfolio value (or anything else) 1* (StockPriceToday-StockPriceYesterday)=105* (StockPriceToday-StockPriceYesterday)=50 this has no dependency on model for how stock price changesFormally this statement can be written in the form : S ( t ; 0 , x ) = G ( * , S ( * ) ) where G is a linear homogeneous functional on [ 0 , t ].IlustrationS ( t ) = x + int _0^t m ( u ) S ( u ) du + int_0^t h ( u ) S ( u ) dw(u)if we divide both sides of the eq on x we see that each dollar invested in such stock has the same return and volatility as S. If we multiply both sides of the eq on N we see that N stocks have the same return as 1 for each scenario. It is true because S ( t ) / x and N S ( t ) governed by the same equation. If volatility or drift are nonlinear this property does not hold and our common sense does not correspond to model. So we can talk about the solution of the SEV equation that is a random function that in some case we wish to call price. We need to present clear the environment and the reason why one can call the random process price while it initially could not call it price. Calibration it to a certain degree is an adjustment of the "real world" to the model though in other fields people are trying to reach the opposite goal. Actually my point is close to Paul's remark.
Last edited by list on March 13th, 2012, 11:00 pm, edited 1 time in total.
 
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spv205
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CEV and SABR for beta outside of [0,1]

March 13th, 2012, 10:33 pm

If I buy a single tulip for £1 or £1,000,000 do you think the price dynamics have to be the same to adhere to your "common sense"?do you think buying 1 tulip for £1, should be the same as buying 1 millionth of a £1,000,000 tulip?as for SABR it is a small time expansion, not small vol-of-vol
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