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You would be over hedged in your call position if it was delta neutral before the stock cratered. Since you are long delta on the call, you would have shorted stock to make the original position delta neutral. When the stock fell, your long call delta would have fallen, and you would buy to cover some of your short stock hedge. However, being long the ...


You are long a vanilla option, so long gamma (positive gamma). If the stock price decreases, so does the delta of your option. Since you short-sold the stock to hedge, you now have short-sold too much since delta has decreased. As a consequence, you must buy back some stock.


Construct the delta-neutral position in the question: buy the 0.5 and sell two of the delta 0.25. Then consider the position's payout as a function of the underlying just before expiry. Its maximum then lies close to the strike of the delta 0.25 where the position's delta then will be zero. Now, as time to expiry increases (we go backward in time!) the ...

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