: Short put options (derivatives) Can anyone solve this question?? "An options trader is short put options on a stock. Explain the directional market risk to this position and how could the trader hedge themselves in the underlying

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Delta is the change in the price of the option for a unit change in the price of the underlying instrument. The trader has shorted 10,000 puts each of which has a delta of -0.50, so the total delta is +5,000 (short puts have a positive delta). To offset this, the trader should short 5,000 shares of the underlying (short stock has a delta of -1.00).

If we assume that delta is fixed (it's not, see below), if the stock drops , the option position loses 10,000*0.5=00 while the short stock position gains ,000 thus offsetting each other.

Note that this hedge will have to be dynamically updated if the stock price keeps falling because delta is dynamic, i.e it does not stay at -0.50. As the stock price keeps falling, delta will increase incrementally, approaching -1.00 if very deep in-the-money or just in-the-money and near expiration. So the trader will have to short additional shares to hedge exposure to the short option position. For example, if the stock price falls to a level where the delta is -0.60, the trader will have to sell an additional 1,000 shares to maintain the hedge.

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For starters, 1 option contract controls 100 shares unless it is an adjusted option.

The directional risk for short puts is a gain in one direction and a loss in the other direction. Google for the specifics.

Calculate the net delta of the option position and then determine how many shares you must buy (or sell) to offset that delta.