CHAPTER 14 Risk Management with Financial Derivatives 363 Net Profit Profit line from buying a call option X X+ Asset price at expiration (S ) Profit line from writing a call option F I G U R E 14 - Profits from Buying and Writing a Call Option at a price between X and X - ,, the gain would be insufficient to cover the cost of the premium, while at a price above X - , the call will yield a net profit In fact, at a price above X - ,, each $1 rise in the price of the asset will cause the profit of the call option to increase by $1 The payoff function from writing the call option is the mirror image of the payoff function from buying the call and is represented by the dashed line in Figure 14-1 Note that the writer of the call receives the call premium , up front and must stand ready to sell the underlying asset to the buyer of the call at the exercise price X, if the buyer exercises the option to buy In general, the value of a call option C at expiration with asset price S (at that time) and exercise price X is C * max (0, S + X ) In other words, the value of a call option at maturity (also known as the intrinsic value) is the difference between the current asset price and the exercise price, S + X, or zero, whichever is greater If the stock price happens to be greater than the exercise price (S X), the call is said to be in the money, and the owner will exercise it for a net profit of C + , If the asset price happens to be less than the exercise price (S / X), the call is said to be out of the money and will expire worthless A call with S * X is said to be at the money or trading at par As already noted, a second type of option contract is the put option A put option is a contract that gives the owner the right (but not the obligation) to sell an asset (to the option writer) at the specified exercise price within a specific period of time As a put represents an option to sell rather than buy, it is worth buying a put when the price of the underlying asset is PROFIT AND LOSSES ON PUTS