Options Trading Tutorial

Why options price not zero when stock price and strike price are the same?

Ok i get what premium is( i guess ) but my profs gave me an example today that showed, if stock price is 25$ and stike price is 25 also, the exericse value is 0 ( which i get ) and option price is 3 and premium is 3( why i dont get ) and then when stock price is 30 and strike is 25 then exercise value is 5( understandable) and option price is 7.50 and option premium is 2.5 why is that, can someone help pllzz

Public Comments

1. Time value, if an option is not expired it still has value because the underlying stock price can move. The amount traders are speculating the move to be is reflected in the price(premium).
2. The answer is in an understanding of "the greeks"; https://www.redoption.com/options_basics_greeks.php
3. The reason why the option price is higher (with value) even though the exercise value is 0 is because the share price can still move up/down in the future. As long as the time to maturity for the option is still there, the option will still have some value, even if the share price drops way below the strike price. In this situation the option will be called "out-of-money" option, and the premium will be very high. Similarly, when the share price is higher than the strike price, the option price will still be higher than the difference (the exercise value) exactly because of the same reason that there is still time for the share price to move up/down, thus affecting the option price as well. This premium is what you're paying for the possibility of an up move of the share price. The only time when there is no premium whatsoever for the option price, where the option price is the same as the exercise value, is at the day the option expires. Because the option expires, there is no longer any time left for the share price to make a positive/negative move, thus there is no premium needed to be paid. As you get closer to the expiry date, the premium paid for the option (assuming the share price and the strike price remain the same) will decrease to 0.
4. What you are calling the "exercise value" of an option is usually called the "intrinsic value" of the option. An option must sell for more than its intrinsic value to prevent risk-free investments. If the stock was at $25 and I could buy a call option with a $25 strike price for $0.00 I could not lose any money since the value of an option will never be below zero, but I could make money if the price of the stock went up before expiration. Obviously no one would be willing to sell that option for $0.00 since the option seller could not make a profit but could lose money. The option seller must be able to make enough of a profit to justify the risk he is taking, therefore the option seller will always demand more than the intrinsic value of the option. (Remember the only profit an option seller can make comes the amount he received when he sold the option.) Even if an option is out-of-the-money (OTM) the seller will demand some premium in order to justify the risk he is taking. Due to a principle called "put call parity" if an OTM option has some premium associated with it an in-the-money (ITM) option must also have some premium associated with it. True put-call parity requires consideration of interest rates, but the principle can be demonstrated ignoring interest. Using your example where the stock price is $30 and the strike price is $25, a put option with a strike price of $25 has no intrinsic value. However, since no one will sell the option for $0.00 since he could not make a profit, let's assume he is willing to sell the option for $2.5. If the call was priced at its intrinsic value of $5, a person could make a risk free profit by (1) Buying the call option for $5.00 (2) Selling the put option for $2.5 (3) Shorting the stock $30.00 This combination, known as a reverse conversion or reversal, would give the person opening it a credit of $30 + $2.5 - $5 = 27.50 per share at the time he opened it. At expiration, if the stock was over $25 he would exercise the call option to buy the stock for $25.00 per share, giving him a profit of $2.50 per share. If the stock was below $25.00 at expiration he can be confident the holder of the put option would exercise it, selling him the stock for $25 per share, giving him a profit of $2.50 per share. In other words, he ends up with a risk free profit of $2.50 per share regardless of the stock price. He received $27.50 per share to open the position and only paid $25.00 per share to close it. Since a free market will never allow risk free profits, the call option with a strike price of $25 must have a premium over its intrinsic value equal to approximately the premium for a put option with a strike price of $25. That would make the price of the call option $5.00 + $2.50 = $7.50. (As I said earlier, you need to factor in interest rates to get the exact relationship for put call parity, but with current interest rates so low that is not a big factor.) As others have mentioned there are statistical models used to price options which among other things, maintain put-call parity.