Fluctuations in option prices can be explained by intrinsic value and extrinsic value, which is also known as time value. An option's premium is the combination of its intrinsic value and time value. Intrinsic value is the in-the-money amount of an options contract, which, for a call option, is the amount above the strike price that the stock is trading. Time value represents the added value an investor has to pay for an option above the intrinsic value. This is the extrinsic value or time value. So, the price of the option in our example can be thought of as the following:


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For example: A trader in October 2016 agrees to deliver 10 tons of steel for INR 30,000 per ton in January 2017 which is currently trading at INR 29,000 per ton.  In this case, trade is assured because he got a buyer at an acceptable price and a buyer because knowing the cost of steel in advance reduces uncertainty in planning. In this case, if the actual price in January 2017 is INR 35,000 per ton, the buyer would be benefitted by INR 5,000 (INR 35000-INR 30,000). On the other hand, if the price of steel becomes INR 26,000 per ton then the trader would be benefitted by INR 4,000 (INR 30,000- INR 26000)
American options can be exercised at any time between the date of purchase and the expiration date. European options are different from American options in that they can only be exercised at the end of their lives on their expiration date. The distinction between American and European options has nothing to do with geography, only with early exercise. Many options on stock indexes are of the European type. Because the right to exercise early has some value, an American option typically carries a higher premium than an otherwise identical European option. This is because the early exercise feature is desirable and commands a premium.
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Volatility: If an options market is highly volatile (i.e. if its daily price range is large), the premium will be higher, because the option has the potential to make more profit for the buyer. Conversely, if an options market is not volatile (i.e. if its daily price range is small), the premium will be lower. An options market's volatility is calculated using its long-term price range, its recent price range, and its expected price range before its expiration date, using various volatility pricing models.

If there’s a company you’ve had your eye on and you believe the stock price is going to rise, a “call” option gives you the right to purchase shares at a specified price at a later date. If your prediction pans out you get to buy the stock for less than it’s selling for on the open market. If it doesn’t, your financial losses are limited to the price of the contract.
Volatility also increases the price of an option. This is because uncertainty pushes the odds of an outcome higher. If the volatility of the underlying asset increases, larger price swings increase the possibilities of substantial moves both up and down. Greater price swings will increase the chances of an event occurring. 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.
There is a concert of Coldplay happening in an auditorium in Mumbai next week. Mr X is a very big fan of Coldplay and he went to ticket counter but unfortunately, all the tickets have been sold out. He was very disappointed. Only seven days left for the concert but he is trying all possible ways including black market where prices were more than the actual cost of a ticket. Luckily his friend is the son of an influential politician of the city and his friend has given a letter from that politician to organizers recommending one ticket to Mr.X at actual price. He is happy now. So still 6 days are left for the concert. However, in the black market, tickets are available at a higher price than the actual price.
Call writers and put writers (sellers), however, are obligated to buy or sell if the option expires in-the-money (more on that below). This means that a seller may be required to make good on a promise to buy or sell. It also implies that option sellers have exposure to more, and in some cases, unlimited, risks. This means writers can lose much more than the price of the options premium.
However, options are not the same thing as stocks because they do not represent ownership in a company. And, although futures use contracts just like options do, options are considered lower risk due to the fact that you can withdraw (or walk away from) an options contract at any point. The price of the option (its premium) is thus a percentage of the underlying asset or security. 
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