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michael9k
Topic Author
Posts: 1
Joined: July 3rd, 2017, 5:01 pm

Short Call Hedge. Options and gamma trading

July 3rd, 2017, 6:58 pm

Let’s say a trader sells a Short Call with strike 100 (for making profit with the premium) at-the-money (for highest extrinsic value there). For hedging until expiration, he buys the underlying share at price 100. If the price goes up, ideally and theoretically, the profit from the share is equal to the loss from the Short Call.
He adjusts his position of the share according to Delta. So in the first place, he buys a position of 0.5 at 100. This means, practically, that immediately above the strike, his shares make less profit than they should for hedging the full options position. However they will compensate by making already some profit below the strike.
Yet this will be true only, if the price starts collecting the profit right from Delta=0 up to Delta=1. If he buys position 0.5 at the strike, and then the price only wanders around above the strike price, even though he is going to increase his position to Delta 1 eventually, the share will never earn the full profit it needs to fully compensate the short call loss (losses from the many small ups and downs not even considered yet).
Would others see it the same way? And what to conclude from that?
  • He could ignore Delta and always hedge with full position size (he is small enough and the market big enough for that). But if the price moves around the strike for long, and he has to fully go long above and fully flat below, his earned premium will be gone soon.
  • Or he just has to bear this cost; it’s covered by the premium anyway. And most likely the price will go a bit underneath the strike anyway, and collect at least a bit of profit there.
  • Or he would need to sell a Call not ATM but OTM, so he can start his hedge from where Delta is near 0. But doesn’t sound good either, as lower extrinsic value there.
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frolloos
Posts: 752
Joined: September 27th, 2007, 5:29 pm
Location: Netherlands

Re: Short Call Hedge. Options and gamma trading

July 3rd, 2017, 7:35 pm

First, the trader doesn't make money from the premium. He makes money from gamma scalping (difference implied vol to realized).

Second, have you read Wilmott's paper on delta hedging profits/losses? It's called Which free lunch would you like today Sir? Google that and I think youbwill be able to find a copy.
 
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outrun
Posts: 4573
Joined: January 1st, 1970, 12:00 am

Re: Short Call Hedge. Options and gamma trading

July 3rd, 2017, 9:59 pm

hedging doesn't add structural P&L (but it reduces risk which is something you might value). There is nothing from stoping you to hedge a option that isn't yours, or not hedge an option you have, or double hedge it. The expected P&L of all those tactics (or any other trading strategy) is zero. The P&L might be positive for some scenarios but it wil have to be negative for other to compensate for that. E.g. not hedging a gamma short postion will be profitable if the market moves sideways, but it will cost you when it start to trend. This is a general balance, and to have an opinion about it is equivalent to saying you can forecasts certain aspects of the future price behaviour better than the market does.