I understand the concept of delta hedging. If you own the stock and are delta hedged (short call option) the value of your long position is precisely offset by the loss of value of the short option position.
But what about this example:
you own 100 stock, you sell 1 call contract (thus on 100 stock). Are you them underhedged? A change of +1 in the underlying will nog longer match the loss in value of of the option contract right?(assuming delta is not 1)
i dont get this because in this example you know the value of the portfolio at expiration date which is 100 times the exercise price right (assuming the call option ends up in the money)? But looking at delta hedging this doesnt make any sense… Where is my thinking going wrong?
I’m not 100% sure I get your question but here is my answer.
your call option my be for 100 shares but the delta of this wont necessarily be equal to a hundred. For example, if your call is at the money with 1 month to expiry, your delta may only be 50. So the change in value of your call options won’t replicate the change in value of your stock position. You would need to sell 2 call contracts (200 shares) in this case to be delta hedged. As time goes by your delta on your calls will change so you will need to adjust the position to maintain your delta hedge.
Thanks, but i already sorted it out in my head.
If you are delta hedged your total portfolio value will no longer move (changes in the Stock will be precisely offset by changes in the hedged position)
If you just hedge a 100 long stock position (e.g. with 1 put option contract) you have bought like an insurance that the total portfolio value will not drop below a certain amount, but the total portfolio value can stil vary between the minimum amount (exercise price in this example) and basically infinity.
That’s not true.
If you are delta hedged your portfolio value won’t move for a single point in time. But the price of stock and the option prices move at different rates, ie delta which is always changing. Therefore you need to re-evaluate your position frequently
Which is why it’s better to hedge with far in-the-money or far out-of-the-money options: gamma is close to zero, so delta changes very little; perhaps little enough that you don’t need to change your hedge position unless the price changes a ton.