Forums > Pricing & Modelling > P&L of a delta hedged Straddle

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 aschon Total Posts: 164 Joined: Jun 2008
 Posted: 2008-07-04 17:40 "in a bs world you don't need to gamma hedge since continuous delta hedge is enough to remove all the risk relative to stock"Absolut plausible. I should have known.Thanks for your help. In practice, this works, but how about in theory?
 aschon Total Posts: 164 Joined: Jun 2008
 Posted: 2008-07-06 11:12 Just to salve my conscience.The P&L of a straddle differs in the scale factor from that one of a delta hedged option. Right?So you got 1 instead of 1/2 in front of your P&L. In practice, this works, but how about in theory?
 Baltazar Total Posts: 1764 Joined: Jul 2004
 Posted: 2008-07-07 08:43 of course since a straddle is two options, you should compare it with two delta hedged options not with one. Qui fait le malin tombe dans le ravin
 aschon Total Posts: 164 Joined: Jun 2008
 nikol Total Posts: 439 Joined: Jun 2005
 Posted: 2009-08-22 15:29 under BS :   use it in your eq. at the beginning
 aschon Total Posts: 164 Joined: Jun 2008
 Posted: 2009-08-22 17:01 got it..thanks! In practice, this works, but how about in theory?
 snowball Total Posts: 3 Joined: Sep 2009
 Posted: 2009-09-04 08:18 In practice, when you are managing a trading book with multiple positions whether or not you choose to do a straddle vs 2 calls or 2 puts also depends on1) whether or not you want a forward expore as your delta hedge will be in near month future or stocks but a high delta strategy (like 2 calls or puts) will give you a fwd expoure = rates and divs. Which is sometimes good if it offsets your existing fwd positions, but if not then you will have to hedge it away by doing IRS, div swaps, etc so just pay more bid/ask. So in such case you want to do a low delta strategy such as a straddle.2) Not as important but many traders like to buy stradds especially for short term as if the spot moves away from strike sufficiently then due to low time value, they can writeoff the OTM option which not only makes the portfolio cleaner but also introduces a possibility of a later windfall if the option comes back ITM or near ITM.Cheers Its all Greek & Latin to me.
 assoul Total Posts: 1 Joined: Oct 2009
 Posted: 2009-10-12 16:20 Hi, Coming back to this subject (quite old, sorry): I still don't get how being long a straddle and delta hedge it, is equivalent to buy ATM vol. Indeed, even using the relation staten before (\nu = S^2 \sigma t \Gamma), it still doesn't leave us with a PNL paying implied volatility. Can you help please ? Thanks a lot,   Jonathan
 aschon Total Posts: 164 Joined: Jun 2008
 Posted: 2009-10-12 22:47 i think you're right. using the relation between vega and gamma does not give us the right result. i getthe sigma in the denominator depends on whether you are hedging with real oder impl vol. one way to get the desired result is by using a taylor series expansion:(here \Delta V=P&L)please correct me if i'm wrong. In practice, this works, but how about in theory?
 Jurassic Total Posts: 61 Joined: Mar 2018
 Posted: 2018-05-07 12:40 Where are you getting these formulas from?
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