“One of the practical problems of delta hedging a short position (be it puts or calls) is that you will have to buy shares if they have gone up and sell shares if they have gone down. There is an immediate loss on the rebalancing transaction in either direction.”
If I’m short a put, I will lose if the price of underlying declines so I short shares to produce offsetting gains, but this is done retroactively after my short positions incur a loss after the delta changes. This is what they mean by " immediate loss" correct?
Remember, you are hedged means you shouldnt lose a dime if delta is accurate.
What it means is that you take an immediate loss on the underlying but you have a gain (unrealized) on the option. Your net loss should be zero once the option closes out…
If a dealer has written some call options, let’s say 3000 call options… and then delta on those options is -.60.
The # of shares he has to buy to hedge that is 3000 x (-.60) = 1800 shares. Why 1800? Each stock share has a delta of 1. He is -1800, and if you buy 1800, your are neutral.
Now if the shares go down in value, the delta will change and so will the $ per share. You will lose money on your long stock position but make money on your options. Now you have to rebalance due to the change in delta.
Let’s say the drop in value changes the delta to -.5. So now he is 3000x (-.5) so he has to sell 300 shares. By selling those 300 shares, he will immediately take a loss on the long position. Now he is hedged again. -1500 + 1500 = 0.