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Delta Hedging Strategies For Options Trading

Hedging is a term used in finance to describe the process of eliminating (or minimizing at best) the risk of a position. Typically, the risk referred to is the directional, or price risk, and the hedge is accomplished by taking the opposite view/position in a similar asset (or same asset traded elsewhere).

Delta hedging is a defensive strategies that is used to reduce the directional exposure of an option or stock position. 
The directional exposure of a position can be gauged by the position delta, which indicates the expected profit or loss of a position when the stock price changes by $1.
Consider the following option positions:

In each of these positions, the position delta may be large or small depending on the trader who has the position. In each of these scenarios, there may come a time when the trader wants to reduce the directional exposure.
For bullish positions (positive delta), directional exposure can be reduced by adding negative delta strategies to the position. 
For bearish positions (negative delta), directional exposure can be reduced by adding positive delta strategies to the position. 
Here is a list of strategies that can accomplish either one of these hedging goals:

Let's go through an example showing the resulting hedging that is needed.
1) Buy 10 call options on ABC with a delta of 0.544. Position delta = 544 (10 * 0.544 * 100)

ContractDeltaPositionPos Delta
Call Option0.54410544
ABC Stock100
Total Delta544
2) You sell 544 shares of ABC (delta 1 of course). Position delta = 0 (544 option delta minus 544 shares of 1 delta)
ContractDeltaPositionPos Delta
Call Option0.5910590
ABC Stock1-544-544
Total Delta46
3) ABC shares increase by 1%. The delta of the call option is now 0.59. Your long 10 calls is now worth 590 deltas. Your short ABC stock is worth - 544 deltas. Net position delta = 46
ContractDeltaPositionPos Delta
Call Option0.54410544
ABC Stock1-544-544
Total Delta0
4) You sell an additional 46 ABC shares. Total deltas of the call position = 590. Total deltas of ABC -590. Total position delta = 0
ContractDeltaPositionPos Delta
Call Option0.5910590
ABC Stock1-590-590
Total Delta0
5) ABC shares trade lower by 0.50%. Call option delta now 0.57 so your position of 10 calls is 570. You are short 590 shares of ABC. Total position delta -20
ContractDeltaPositionPos Delta
Call Option0.5710570
ABC Stock1-590-590
Total Delta-20
6) Now you have a net short delta, which means you will have to buy back 20 shares to square off the delta. Option position delta 570, ABC share delta -570 net = 0
ContractDeltaPositionPos Delta
Call Option0.5710570
ABC Stock1-570-570
Total Delta0
Here are the transactions for the above scenario;
Buy 10 calls @ 4.13
Sell 544 stock @ 100
Sell 46 stock @ 101 (calls at 4.69)
Buy 20 stock @ 100.50 (calls at 4.40)
Note: the option position in this example didn't change after the first trade; the price fluctuations of the underlying stock resulted in the changing delta of the option. As the delta changes, the total position also changes resulting in the need to re-hedge.

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