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Delta Hedging a short call with a long stock

I’m having trouble understanding the following statement

“If the delta of a call option is 0.4, then in order to hedge the sold call option, the option seller needs to purchase 0.4 stocks for every option sold”

I understand the math behind delta. What I don’t understand is, why does someone hedge a sold call? (While the call itself is a hedge)

Is it to be able to close the short call position and exit their obligation in the event that the spot price of the underlying far exceeds the strike price? 

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I think you are assuming shorts are always used to hedge. That is not the case.  Using your example a trader may be selling calls to collect the premiums.  Left uncovered he is exposed to considerable risk of stock appreciation. A long hedge (deltaShares) will hedge his exposure.

In general derivatives are used for both risk management purposes and speculative purposes. Being short on its own does not imply hedge.  

Thanks! It makes sense from a trader’s or hedge provider’s perspective

Hi Seshadri, what the statement meant is by executing that delta hedge you would’ve locked in your exposure regardless of the movement of the underlying stock price. I’m aware that there is no perfect delta hedge as delta is not constant and the hedge needs to be rebalanced over time but for simplicity’s sake let’s just assume delta stays constant.

To address your question of why would anyone hedge a short call, it is because when you short a call, you are exposed to losses if the underlying stock price increases above the strike price at expiry. Hence to mitigate the risk you’d execute a delta hedge. Suppose you’ve sold a call with delta 0.4 to theoretically eliminate your exposure you’d delta hedge by purchasing 0.4 stock. If on the next day the stock price goes up by $1, your stock position is +0.4  and your call position is -0.4 (value of a call increases if the underlying stock price increases, however since you short the call, the opposite would be true for you as it increases the probability that your call could be exercised by the long) hence leaving a neutral position of 0. Conversely if the stock price goes down by $1, your stock position would be -0.4 and your short call would gain a value of +0.4 therefore leaving an unchanged overall position.

Btw calls and puts are not necessarily a hedging instrument, options can be used for speculation be it long or short. 

Shorting a call is like selling an insurance. Not a hedge. Just betting that will not not be executed in amount larger than sum of premiums collected.

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