Delta hedge

If we write the options then using a delta hedge we will also buy shares so as to cover ourselves agains the risk. That is the purpose of the delta hedge. So if the share price increases the buyer will exercise the option and we (as the writer will have to pay then and lose money). But at the same time the price of the shares we hold will have increased which 'cancels' out the loss. Have you watched my free lectures on this?

yes, sir I have watched your lectures they are very helpful :). I understand the downside of the options to the writer because there is unlimited downside as share price could just become higher and higher and buying shares can hedge this but There is this example in the study hub in "chap no 13 s13.4.2" where a company holds shares of 10 million and the manager is worried that the share price might fall from 22.56 to 20 dollars and one way they said the manager could hedge this is by selling the call options. The delta was 0.7894 so he would have to sell 12.67 million (10m/0.7894) calls and one cent decrease in share price would result in: suffer a holding loss of $100,000 (0.01 × 10m) on the shares; and make a holding gain of $100,000 (0.01 × 0.7894 × 12.67m) on the short position in call options. now the upside potential to the manager from the call option should only be limited to the premuim recived as if the share price reduces the person who bought the call options will not exersize it but in the above example the gain on the holding is proportional to the delta*change in share price. This i do not understand at all as to how all of the poteintial loss is hedged using this.

Now I understand what you mean. What is happening is that the company is selling options on the stock exchange (they are not writing the options) and then buying back later (i.e. selling short). Therefore they will make a gain of the change in the options price and that will 'cancel' the loss on the shares.