
Options contracts are essentially the price probabilities of future events. The more likely something is to occur, the more expensive an option would be that profits from that event. This is the key to understanding the relative value of options.
Let’s take as a generic example a call option on International Business Machines Corp. (IBM) with a strike price of $200; IBM is currently trading at $175 and expires in 3 months. Remember, the call option gives you the right, but not the obligation, to purchase shares of IBM at $200 at any point in the next 3 months. If the price of IBM rises above $200, then you “win.” It doesn’t matter that we don’t know the price of this option for the moment – what we can say for sure, though, is that the same option that expires not in 3 months but in 1 month will cost less because the chances of anything occurring within a shorter interval is smaller. Likewise, the same option that expires in a year will cost more. This is also why options experience time decay: the same option will be worth less tomorrow than today if the price of the stock doesn’t move.
Returning to our 3month expiration, another factor that will increase the likelihood that you’ll “win” is if the price of IBM stock rises closer to $200 – the closer the price of the stock to the strike, the more likely the event will happen. Thus, as the price of the underlying asset rises, the price of the call option premium will also rise. Alternatively, as the price goes down – and the gap between the strike price and the underlying asset prices widens – the option will cost less. Along a similar line, if the price of IBM stock stays at $175, the call with a $190 strike price will be worth more than the $200 strike call – since, again, the chances of the $190 event happening is greater than $200.
There is one other factor that can increase the odds that the event we want to happen will occur – if the volatility of the underlying asset increases. Something that has greater price swings – both up and down – will increase the chances of an event happening. Therefore, the greater the volatility, the greater the price of the option. Options trading and volatility are intrinsically linked to each other in this way.
With this in mind, let’s consider a hypothetical example. Let's say that on May 1, the stock price of Cory's Tequila Co. (CTQ) is $67 and the premium (cost) is $3.15 for a July 70 Call, which indicates that the expiration is the third Friday of July and the strike price is $70. The total price of the contract is $3.15 x 100 = $315. In reality, you'd also have to take commissions into account, but we'll ignore them for this example. On most U.S. exchanges, a stock option contract is the option to buy or sell 100 shares; that's why you must multiply the contract by 100 to get the total price. The strike price of $70 means that the stock price must rise above $70 before the call option is worth anything; furthermore, because the contract is $3.15 per share, the breakeven price would be $73.15.
Three weeks later the stock price is $78. The options contract has increased along with the stock price and is now worth $8.25 x 100 = $825. Subtract what you paid for the contract, and your profit is ($8.25  $3.15) x 100 = $510. You almost doubled our money in just three weeks! You could sell your options, which is called "closing your position," and take your profits – unless, of course, you think the stock price will continue to rise. For the sake of this example, let's say we let it ride.
By the expiration date, the price of CTQ drops down to $62. Because this is less than our $70 strike price and there is no time left, the option contract is worthless. We are now down by the original premium cost of $315.
To recap, here is what happened to our option investment:
Date  May 1  May 21  Expiry Date 
Stock Price  $67  $78  $62 
Option Price  $3.15  $8.25  worthless 
Contract Value  $315  $825  $0 
Paper Gain/Loss  $0  $510  $315 
So far we've talked about options as the right to buy or sell (exercise) the underlying good. This is true, but in reality, a majority of options are not actually exercised. In our example, you could make money by exercising at $70 and then selling the stock back in the market at $78 for a profit of $8 a share. You could also keep the stock, knowing you were able to buy it at a discount to the present value. However, the majority of the time holders choose to take their profits by trading out (closing out) their position. This means that holders sell their options in the market, and writers buy their positions back to close. According to the CBOE, only about 10% of options are exercised, 60% are traded (closed) out, and 30% expire worthless.
At this point it is worth explaining more about the pricing of options. In our example the premium (price) of the option went from $3.15 to $8.25. These fluctuations can be explained by intrinsic value and extrinsic value, also known as time value. An option's premium is the combination of its intrinsic value and its time value. Intrinsic value is the amount inthemoney, which, for a call option, means that the price of the stock equals the strike price. Time value represents the possibility of the option increasing in value. Refer back to the beginning of this section of the turorial: the more likely an event is to occur, the more expensive the option. This is the extrinsic, or time value. So, the price of the option in our example can be thought of as the following:
Premium =  Intrinsic Value +  Time Value 
$8.25 =  $8 +  $0.25 
In real life options almost always trade at some level above their intrinsic value, because the probability of an event occurring is never absolutely zero, even if it is highly unlikely. If you are wondering, we just picked the numbers for this example out of the air to demonstrate how options work.
A brief word on options pricing. As we’ve seen, the relative price of an option has to do with the chances that an event will happen. But in order to put an absolute price on an option, a pricing model must be used. The most wellknown model is the BlackScholesMerton model, which was derived in the 1970’s, and for which the Nobel prize in economics was awarded. Since then other models have emerged such as binomial and trinomial tree models, which are also commonly used.
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