Question

1. Explain to your boss why you would or would not change your hedging position to keep the delta exposure neutral as the option moves from being In-The-Money to being At-The-Money. What trades, if any, would you make?

Answer 1

Delta hedging is an options strategy that aims to reduce or hedge, the risk associated with price movements in the underlying asset. In the given situation option is moving from the in the money to at the money it means delta of this underlying assets is changing rapidly in this scenario ideally we have to reduce the option position in the same ratio in which delta is changing. We can understand this with below example:

Assume that you have a stock position that you believe will increase in price in the long term. You are worried, however, that prices could decline in the short term, so you decide to set up a delta neutral position. Assume that you own 200 shares of Company X, which is trading at $100 per share. Since the underlying stock's delta is 1, your current position has a delta of positive 200 (the delta multiplied by the number of shares).

To obtain delta neutral position, you need to enter into a position that has a total delta of -200 (overall). Assume then you find in-the-money put options of Company X that are trading with a delta of -0.5. You could purchase 400 of these put options, which would have a total delta of (400 x -0.5), or -200.

With this combined position of 200 Company X shares and 400 long in-the-money put options on Company X, your overall position is delta neutral.

Suppose this hedged put options of Company X that are moving from in the money to at the money and its delta changed to -1.0 and in order to hedge the position you want a total delta of -200 (overall). In this situation we have to option either we have to reduce our position in the option from 400 to 200 to keep the delta neutral. Position will reduce in the same ration in which option delta changed as -0.5 to -1.0 i.e. half of the old one. Hence we have changed our position in the same ration from by half from 400 to 200.

I will explain my boss with the above given example option is moving from the in the money to at the money it means ideally we have to reduce the option position in the same ratio in which delta of underlying option is changing.

If you will ask me what I will do in this scenario I will purchase the in the money put option of the underlying assets after checking the delta of put and underlying assets, in the same quantity which can cover hedge my overall position of my assets. If that put options move from in the money to at the money, then I will reduce the exposure in put option in the same ratio in which it delta has been changed with underlying assets. Detailed example are given above for more clarity on it.