Derivatives productions: the most simple example is an European option in finance

I would refer to the definition of Hull about a derivative:

A derivative can be defined as a financial instrument whose value depends on (or derives from) the values of other. A stock option, for example, is a derivative whose value is dependent on the price of a stock .

One you have an option in finance, it is a contract which allows you to sell or to purchase one or multi-underlying assets for a desired price by a certain date in the future.

There are Call and Put Option. While a Call option gives you the right to buy the underlying assets, a Put gives you the right to sell them.

The European options, you only can exercise your options on its expiration maturity date. The American options can be exercised at any time up to its maturity date. This example illustrates what is an European option.

Today, one IBM stock costs 100$. You guess that in the next 3 months, it can increase to 110$. Therefore, you decide to buy an option which allows you can buy 100 IBM stocks at price 100$ per stock in fixed 3 months later, this option is called a Call European Option. To buy this option today you have to pay 5$ per stocks, totally it costs you 100*5 = 500$. We call the 500$ is the option prime (it is not an option price).

Three months later, thanks Gods, one IBM stock really goes up to 110$. Using your option, you can buy 100 IBM stocks only with 100*100 = 10000$ instead of 100*110 = 11000$. After buying 100 stocks, you can sell all of them to gain the 1000$ difference. To calculate your real profit you have to minus your option prime, so the net income is: 1000 – 500 = 500$. In three months you earn 500$. In practice, you exercise your option whenever your net income is still positive.

However, what will happen if the IBM stocks go down and make your net income be negative. At this moment, you have 2 choices. First one you do not exercise your option then you lose 500$. Second one, you exercise your option, hold your stocks and wait until their price go up. In both cases, you have to lose your option prime.

Beside the European options and the American options, there are also the Asian options, the Russian options, the Parisian options… . Among them, the American option is the most famous and most recent trading option in the world. I have a lots of thing to talk about the American options cause it makes me like crazy. Oh my Gods, my Goddess, I even dream about them, these damn exercise boundaries.