You are an options portfolio mananger. You need to maintain a delta neutral position at all times. You have just traded (unhedged) with an corporate customer who has sold 51 put option contracts of PBS shares to you. Each contract is based on 1000 shares, and has a delta of 30 % How many additional shares in PBS do you need to trade into the open market to remain delta neutral? (If you need to buy shares, please enter a positive integer, or a negative integer if you need to sell)
Question
You are an options portfolio mananger. You need to maintain a delta neutral position at all times. You have just traded (unhedged) with an corporate customer who has sold 51 put option contracts of PBS shares to you. Each contract is based on 1000 shares, and has a delta of 30 % How many additional shares in PBS do you need to trade into the open market to remain delta neutral? (If you need to buy shares, please enter a positive integer, or a negative integer if you need to sell)
Solution
To maintain a delta neutral position, you need to offset the delta of the options you've bought.
Here's how you can calculate it:
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First, calculate the total delta of the options. The delta of each option is 30%, or 0.3. Since each contract is for 1000 shares, the delta for each contract is 0.3 * 1000 = 300.
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Multiply this by the number of contracts to get the total delta. In this case, you have 51 contracts, so the total delta is 300 * 51 = 15300.
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To maintain a delta neutral position, you need to offset this by trading shares in the open market. Since buying shares increases your delta and selling shares decreases your delta, you need to sell shares to offset the positive delta from the options.
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Therefore, you need to sell 15300 shares in PBS to remain delta neutral.
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