Hi, everyone. I am trying to sort out the topic of delta hedging, and there is a problem. In the textbook, there is an example like this: the stock price is 100, and the call option price is 10. imagine an investor who has sold 20 call option contracts--that is, options to buy 2,000 shares. the investor's position could be hedged by buying 0.6*2,000=1,200 shares(the delta is 0.6).If the stock price goes up by 1 (producing a gain of 1200 on the shares purchased), the option price will tend to go up by 0.6 (producing a loss of 1200 on the options written). My problem is that, is the investor in a short call position? And I don't understand why the increase in option price will lead the investor to lose money, rather than gaining money? As we know, the investor will gain more premiun as the option price increases if the investor is in a short call position. Am i right? Or i am in a wrong direction?? The investor follows a long call position? but it says"the investor has sold the contracts"...Thank you!

I think you got that : the value of a call option increases as the value of the underlying increases. Then :- if you have BOUGHT the call (i.e. you are LONG the call), you make money as the value of the underlying increases.- if you have SOLD the option (i.e. you are ... the call) you ... money as the value of the underlying increases.Hopefully you can fill the gaps ?

Thank you. If i am in a short position of a call option, i will lose money if the underlying stock's price is increasing.I've got another question here, if i am in the short position, how much money i lose? Do i need to pay the holder of the option the amount of the difference between strike price and spot stock price, or i need to add some premium?? For example, if the strike is 100, the current stock price is 120, and the price of call option is 10. Does that mean i need to pay (120-100)-10= 10 in this way? If i am correct, why the example in the textbook says that the writter of the option loses the increase in the call price?(0.6 *2000 shares) Which of the two losses is correct??Thanks a lot!

Well you already answered your question in your 1st post ... The loss on the options if the underlying price goes up by 1, is 0.6*2,000 = 1,200.And until the options mature (assuming they're european options) your loss is unrealised, you don't have to pay anything yet, only at expiry.