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Khoshtip
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“Heston Vega” vs. BS-Vega

March 6th, 2008, 8:00 am

I am wondering if anybody knows a good article/way to calculate the vega when one uses the Heston pricing model.In BS model can calculate the vega by just adding a small constant value to the volatility surface calculate the new prices and divide the price difference to the constant.In Heston this gets much trickier. I would like to somehow manipulate the Heston parameters in such a way that the surface increases with the same amount everywhere (Since this seems to be an utopian desire I would be content with the any good approximation) .A solution would be to go the other way around. Add a constant value to the volatility surface and do a calibration in order to get the new parameters. But this is quite time consuming and not very efficient. Regards,
 
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tontonkum
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“Heston Vega” vs. BS-Vega

March 6th, 2008, 8:13 am

QuoteOriginally posted by: KhoshtipI am wondering if anybody knows a good article/way to calculate the vega when one uses the Heston pricing model.In BS model can calculate the vega by just adding a small constant value to the volatility surface calculate the new prices and divide the price difference to the constant.In Heston this gets much trickier. I would like to somehow manipulate the Heston parameters in such a way that the surface increases with the same amount everywhere (Since this seems to be an utopian desire I would be content with the any good approximation) .A solution would be to go the other way around. Add a constant value to the volatility surface and do a calibration in order to get the new parameters. But this is quite time consuming and not very efficient. Regards,I think the solution is to go the other way round, as you say, if you want a Heston vega that can be compared to the BS one. Otherwise, you might try to bump the initial and/or final vol.
 
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tontonkum
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“Heston Vega” vs. BS-Vega

March 6th, 2008, 8:20 am

Furtehrmore, if youset the entry point of your bumped calibration at the value of your result point of your original calibration, it should not be that long.
 
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Christophe1
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“Heston Vega” vs. BS-Vega

March 6th, 2008, 9:04 am

I think that a bumped calibration is quick if you use the methodof of tontonkum.In your first message you say a re-calibration is not efficient.You want to say that you obtain a fool value for your vega or an other thing ?
 
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probably
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“Heston Vega” vs. BS-Vega

March 9th, 2008, 3:34 pm

What do you mean by "the vega" ?To clarify my question: once you computed the "vega" you want how do you intend to hedge it?
 
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Paul
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“Heston Vega” vs. BS-Vega

March 10th, 2008, 10:27 am

probably is right, there are many interpretations of 'vega' here. So first we need to know what you will do with it, then we figure out which vega you mean, and finally we see how to calculate it!P
 
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horacioaliaga
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“Heston Vega” vs. BS-Vega

April 6th, 2008, 3:01 am

what about bumping the IVs of the instruments used for calibration?
 
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PaperCut
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“Heston Vega” vs. BS-Vega

April 6th, 2008, 4:53 pm

horacio's right. Vega in the ordinary sense is the sensitivity to a parallel shift in BS vols. So you need to bump the a priori BS surface, re calibrate, the measure valuations, then difference them.Otherwise, by measuring sensitivities to Heston parameters, you have gone down a road of "parameter hedging," which is not truly "explanatory" and can screw up.
 
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Alan
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“Heston Vega” vs. BS-Vega

April 7th, 2008, 1:55 pm

QuoteOriginally posted by: PaperCuthoracio's right. Vega in the ordinary sense is the sensitivity to a parallel shift in BS vols. So you need to bump the a priori BS surface, re calibrate, the measure valuations, then difference them.Won't this just generate the same -formula- for the BS vega, except the volatility in it is the BS implied vol.?Or, what am I missing?
 
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probably
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“Heston Vega” vs. BS-Vega

April 7th, 2008, 2:41 pm

(sorry clciked the submit button twice)
Last edited by probably on April 6th, 2008, 10:00 pm, edited 1 time in total.
 
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probably
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“Heston Vega” vs. BS-Vega

April 7th, 2008, 2:42 pm

Yes it would plus heavy numerical problems because a fit to the original surface has no reason to be close to the fit of a bumped one.(BTW It gets a bit better if you bump not the implied itself but the implied vol of the options given the calibrated Heston parameters. That's more stable and faster, usually 6 iterations.)However, back to my original question:What are you going to do with that? Are you going to hedge that "vega" with, say, the ATM options? I think your "vega" should reflect the intended aim (ie hedging method)
 
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PaperCut
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“Heston Vega” vs. BS-Vega

April 7th, 2008, 11:35 pm

QuoteOriginally posted by: AlanQuoteOriginally posted by: PaperCuthoracio's right. Vega in the ordinary sense is the sensitivity to a parallel shift in BS vols. So you need to bump the a priori BS surface, re calibrate, the measure valuations, then difference them.Won't this just generate the same -formula- for the BS vega, except the volatility in it is the BS implied vol.?Or, what am I missing?Yes, I think you are right, I guess I was assuming that the structure in question was somehow not Black Scholes friendly, but there was still a requirement for a "vega" hedge.
 
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torquant
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“Heston Vega” vs. BS-Vega

April 9th, 2008, 12:01 am

Heston model has a drawback that it is not one-to-one model, i.e. its calibration to the market vols is not unique in a local extremum of least squares sense. The conventional approach of bumping the implied vols and recalibrating the model may put you into a different well of the optimization cost function. The usual workaround as with other models susceptible to calibration noise is to consider local first order approximation in the parameter space -- that is translate the implied vol risk into Heston parameters risk. The linear inverse of this transformation should be applied to sensitivities to the Heston parameters.
 
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probably
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“Heston Vega” vs. BS-Vega

April 9th, 2008, 4:00 am

Did you ever try that in practise?
 
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Alan
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“Heston Vega” vs. BS-Vega

April 9th, 2008, 1:57 pm

QuoteOriginally posted by: torquantHeston model has a drawback that it is not one-to-one model, i.e. its calibration to the market vols is not unique in a local extremum of least squares sense. The conventional approach of bumping the implied vols and recalibrating the model may put you into a different well of the optimization cost function. The usual workaround as with other models susceptible to calibration noise is to consider local first order approximation in the parameter space -- that is translate the implied vol risk into Heston parameters risk. The linear inverse of this transformation should be applied to sensitivities to the Heston parameters.I repeat my earlier comment -- why isn't this prescription the world's longest way to generate the vega from the Black-Scholes formula? Do I have to write an equation?