Serving the Quantitative Finance Community

 
User avatar
Da0ud
Topic Author
Posts: 1
Joined: October 12th, 2006, 12:29 pm

Long Gamma Hedge and weekly volatility

July 25th, 2011, 3:59 am

Hi all,It is fairly easy to understand that when you are long gamma at let say 30vol (black scholes implied vol on daily return) and if you hedge your delta generated from your gamma every day and the stock moves 2% a day then you make money.Now let?s imagine you are long gamma and you see the stock tends to have a much higher realised vol on weekly returns rather than daily returns. Maybe instead of realising 32vol it realises 37vol. Hence, you want to start delta hedging less frequently.The problem arises on how to delta hedge to follow the weekly return computation of the vol.On daily return it is easy, you hedge your delta every day to start a new day delta neutral.My weekly vol is computed as one fifth of the Monday series, Tuesday series, etc. Hence, how should we hedge the delta implied by the gamma now ?If we arbitrary decide to be delta flat on one day and then hedge our delta in one week time, then it doesn?t follow the way we computed the realised volatility. We could potentially hedge on the least volatile of the 5 series of sub weekly vol...Shall we then hedge one fifth of the delta implied by gamma on first day. Then hedge one fifth of the delta at the end of day 2 (which is the remaining delta at end of day 1 + new extra delta implied by gamma for day 2), etc., until day 5 where we finally hedge all the rest of delta to start a new week delta flat ?I feel like this is not correct either, but the truth should be somewhere in between.I am sure someone must have encountered the same problem and could answer my question. Or maybe shall I be redirected to some paper discussing about the matter ?Thanks very much,Daoud.
Last edited by Da0ud on July 24th, 2011, 10:00 pm, edited 1 time in total.
 
frolloos
Posts: 752
Joined: September 27th, 2007, 5:29 pm
Location: Netherlands

Long Gamma Hedge and weekly volatility

July 27th, 2011, 6:19 pm

if you are going to hedge using a delta that's different than the implied delta (e.g. by keeping your delta constant over a week), and the stock moves a lot, and your dollar gamma is small, the real world drift will be more important than the difference in variance. in other words you should have a strong conviction where the stock is going if you do this.my attempt at answering your question of how much delta to hedge --> depends, are you going to be a delta trader, or a gamma scalper/vol trader? in either case i don't really understand why you would want to do 1/5th delta every day for 5 business days..