 # Max Put/Call Loss/Gain for writer & owner.

Can someone please elaborate below chart? Am not able to figure out why max loss for Writer(For Put) will be “strike price - premium”? Max loss for call writer is unlimited? loss and gain for the call writer/owner: Writer Owner Maximum Loss unlimited premium Maximum Gain premium unlimited maximum loss and gain for the put writer/owner: Writer Owner Maximum Loss strike price - premium limited to premium Maximum Gain limited to premium strike price - premium thanks.

You seem to be confused with both the vocabulary and the way options work; so let me try to clarify it for you. Basically, there are four positions, long call, short call, long put and short put. 1. Long call That’s the position of the buyer/holder/owner of a call option. Let’s take an easy example, and assume that the strike price is 10, and that the premium (i.e., the cost of buying the option) is 1. You buy the call option for 1. At expriation (let’s assume we only deal with European options), assume that the stock price is below the strike price (let’s say it is 5). Would you prefer to pay the stock price (5) or the strike price (10) to buy the stock? The stock price, so your call option is out of the money (OTM), the payoff is 0, and you make a loss of 1 because of the premium you paid upfront. Alternatively, assume that the stock price is above the strike price (let’s say it is 15). Would you prefer to pay the stock price (15) or the strike price (10) to buy the stock? The strike price, so your call option is in the money (ITM), the payoff is 5 (you can buy the stock for 10 and immediately sell it for 15), and you make a gain of 4 because of the premium. In general terms: The value of the option is CT=Max(0,ST-X), here CT=Max(0,5-10)=0 in the first case and CT=Max(0,15-10)=5 in the second case; The profit is Max(0,ST-X)-premium, here Max(0,5-10)-1=-1 in the first case and Max(0,15-10)-1=4 in the second case. 2. Short call That’s the position of the seller/writer of the call option. The beauty about options is that they are symetrical: what one sides wins is exactly equal to what the other sides loses. As the long is the one who makes the decision about what they want to do (i.e., exercise or not), once you know what happens to the long, you know what happens to the short. In my previous example, when the stock price is below the strike price, the owner of the call option does not exercise, the value for him is 0 and his profit is -1. So for the writer of the call option, the value is 0 and the profit is +1. On the other hand, when the stock price is above the strike price, the owner of the call option exercises, the value for him is 5 and his profit is 4. So for the writer of the call option, the value is -5 and the profit is -4. Now, if the stock price increases substantially, the owner of the call option will make a big profit, and the writer, a big loss. The profit for the owner of a call option is unlimited, so is the loss for the writer of a call option. 3. Long put That’s the position of the buyer/holder/owner of a put option. Let’s take an easy example, and assume that the strike price is 10, and that the premium (i.e., the cost of buying the option) is 1. You buy the put option for 1. At expriation, assume that the stock price is below the strike price (let’s say it is 5). Would you prefer to receive the stock price (5) or the strike price (10) to sell the stock? The strike price, so your put option is ITM, the payoff is 5, and you make a gain of 1 because of the premium you paid upfront. Alternatively, assume that the stock price is above the strike price (let’s say it is 15). Would you prefer to receive the stock price (15) or the strike price (10) to sell the stock? The stock price, so your put option is OTM, the payoff is 0, and you make a loss of 1 because of the premium. In general terms: The value of the option is CT=Max(0,X-ST), here CT=Max(0,10-5)=5 in the first case and CT=Max(0,10-15)=0 in the second case; The profit is Max(0,X-ST)-premium, here Max(0,10-5)-1=4 in the first case and Max(0,10-15)-1=-1 in the second case. 4. Short put That’s the position of the seller/writer of the put option. Once again, what one sides wins is exactly equal to what the other sides loses. In my previous example, when the stock price is below the strike price, the owner of the put option exercises, the value for him is 5 and his profit is 4. So for the writer of the put option, the value is -5 and the profit is -4. On the other hand, when the stock price is above the strike price, the owner of the put option does not exercise, the value for him is 0 and his profit is -1. So for the writer of the put option, the value is 0 and the profit is 1. Hope it helps.

FrenchRiviera is right on. If you are confused why the maximum Gain/Loss on any sort of Put option is limited, while the maximum G/L on any sort of Call option is unlimited, consider the nature of stock prices. They can theoretically go as high as infinity but can never drop below zero. So using frenchriviera’s example, The maximum value of a put option to the holder is when the stock price falls to zero. The option will be worth (Strike price = 10) - (Exercise Price = 0) = \$10 And the profit is (Option Value = 10) - (Premium Paid for Option = \$1) = 9 Total profit is 9. You cannot earn more than that, so the profit is limited. Flip that around and the maximum loss for the Short Put Writer's is -9 On the other hand, the max value for a long call option is when the stock price reaches infinity. At that point, the value to the Call holder will be (Exercise price = infinity) - (Strike price = \$10) = unlimited value and Profit is (Option value = unlimited) - (Premium = \$1) = still unlimited (infinity minus \$11 still equals infinity) So the maximum gain for the Long call holder is unlimited Again the value to the Short Call Writer is the just the opposite, negative infinity (ouch!) Hope that helps, MDD

Excellent ! FrenchRiviera & chasinggoats explanation was too good. thanks a lot.

now relate the above to the graphs for the Put and the Call for the Long and short sides. Much easier to remember the graphs – CP