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Khoshtip
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Variance Swap Practical/Dynamic Hedging

November 26th, 2008, 7:37 am

Thanks rmeenaks!Really nice and extensive documetn. However, with regards to the dynamic hedge they have a couple of "generic" sentences ... I guess they dont wanna give away hard earned knowledge ;-) Corridor variance swapsI know that for pricing one easy way is to take strike range from lower barrieir to upper barrier. But there must be some adjustment made for the barrier both in pricing and in hedging.Any one know to get rid of the barrier risk in the corridor?Cheers,K
 
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seppar
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Variance Swap Practical/Dynamic Hedging

November 26th, 2008, 2:02 pm

QuoteOriginally posted by: probablyWhen pricing using an SV model, you will get a big difference for 1m-2m options whether you price on variance (== quadratic variation) or actually log-square returns. Here is some more on basics (dividends, rv vs qv etc)behaved.Nice presentation! You are right - since the variance of the estimator for the realized variance decreases linearly with the number of samples, you cannot ignore this term for short term options on the realized variance. I was looking for one of references you quote - Jordinson et al: “Realise Variance”, 2006 (in preparation) - but could not find it. Do you have an up-to-date link to this paper?
 
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probably
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Variance Swap Practical/Dynamic Hedging

November 26th, 2008, 4:33 pm

Try this one which covers variance swaps from pg.15 onwards. (Dr. Jordinson never finished the paper I was quoting..)
Last edited by probably on November 25th, 2008, 11:00 pm, edited 1 time in total.
 
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hichmoul
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Variance Swap Practical/Dynamic Hedging

November 26th, 2009, 1:43 pm

Hello,This is a simpler more theoretical question than the posts before:I am referring here to the Demeterfi-Derman-Kamal-Zou paper. In a classical ideal B-S-M world,in terms of trades, if I were to go :- enter a long a 3month variance swap struck at (20%)^2, with variance continuously sampled, from this moment, to hedge it completely, I would need to- short a continuum of calls/puts with 1/strike^2 weights with strike from 0 to +InfAND continuously delta hedge this option stripAND separately, go a static long 1/S* futures (adjust for the notional amount)1. Is this right?2. The Delta wrt to spot/future of the hedging position ( strip delta-hedged + static long 1/S* ) is NOT 0 (it should be if the pos is to replicate the varswap)3. Is the option strip's delta actually the same as the 1/S* future position, and so I just need to do the delta hedging for the strip?4. If I am long the varswap and short the strip and ..., whatever realized variance turns out to be, I would have 0 P/L (of course in the ideal B-S world) ?regards,
 
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probably
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Variance Swap Practical/Dynamic Hedging

November 26th, 2009, 10:33 pm

a) Demterfi et al do not use a classical BS world - it works in any setting where the stockprice has no jumps (SV can have jumps)b) your hedge is nearly right except a factor of 2 (and you assume that r=d=0)2 dlog S(t) = - 2/S(t) dS(t) + 1/S(t)2^ dS(t)^2ie\int_0^T 1/S(t)2^ dS(t)^2 = 2 { log S(T) - log S(0) + \int_0^T 1/S(t) dS(t) }c) the option strips' delta is the same only in BS
 
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hichmoul
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Variance Swap Practical/Dynamic Hedging

November 27th, 2009, 8:53 am

a) I understand.b) under BS then, you are saying I don't need to do BOTH the initial delta hedge for the option strip (which would take initial instantaneous delta to 0)AND take the long 2/S* futures position.Only the initial delta hedge of the strip, and then continuously delta hedge is enough (of course all this from the theoretical point of view)thanks
Last edited by hichmoul on November 26th, 2009, 11:00 pm, edited 1 time in total.
 
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yetanotherquant
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Variance Swap Practical/Dynamic Hedging

May 21st, 2010, 5:49 pm

umm, I'm a bit lost now. I *think* what probably said is that one needs to continuously delta hedge the option strip *and* go long a const $2 delta position (with delta = 2/S). Otherwise I don't see how the cash position generated by the continuous delta hedging of the option strip can be offset (again, exactly only in the infinite option case) by the cash position generated by continuosly rebalancing $2 delta position, no?Then what about the claimed "static hedge" of variance swaps.. is this only going to give the *terminal* p&l to be the same as the dynamic delta hedging scheme?Thanks for clarifying.