Binary option ideas and intuitions

In the world of Trading there is a large panel of options in which the Binary Option is one the easiest to understand. To understand the initial idea of Binary Option you can imagine a simple bet between two friends during the football World Cup finale. The two friends called A and B put $50 each in a box, if England wins against France A wins if not B wins. At the beginning of the match both football team have 50% chance of winning the game. Imagine the following scenario:

  1. At the beginning of the match both A and B have  50% chance to win
  2. At half time there are no goal so both A and B have again 50% chance to win
  3. After 5 minutes of the second half time England scores making Player A probability to win the bet moving from 50% to approximatively 70%
  4. After another 5 minutes England scores a second goal making Player A probability to win the bet moving from 70% to approximatively 90%
  5. 10 minutes before the end of the match the French scores a goal making Player A probability to win the bet moving from 90%  back to approximatively 70%
  6. At the end of the match the score don’t change and Player A won the box ($100)


The below chart shows the probability chance to win the bet with respect to the score.

Player A probability of winning

Notice that the probability for Player A to win the Bet is approximatively equivalent of the value of the Bet itself. We will see later that the probability for a Player to win a Bet is key to evaluate Binary Options.

This above bet example is the same that a binary option, why?

  • There is a premium to pay to bet (the $50 in the box)
  • The bet profit and loss are know from the beginning (loss =  $50 and profit = $100)
  • The bet exists until the match finishes  (there is a clear and precise expiration date)
  • The probability to win the Bet varies with respect to the score

Buying a Binary Option is the same concept of the above bet because:

  • You pay a premium to play
  • Profit and loss are known from the beginning
  • The option has a expiration time (Precise time in the future)
  • The probability to win the bet varies with respect to the underlying stock or currency or Commodity or …

A Binary Option is a bet. Traders use those options to bet on the rise or decline of a stock or currencies or commodity or FOREX, those investment vehicle are called the underlying of the option (the underlying of our football bet example would be the football finale). The below chart shows an example of a binary price move in parallel with its underlying price. For matter of simplicity I took the similar characteristics than the football game:

  1. Trader (player) A bets that the blue line will be above $100 at the end of the bet
  2. The Bet is $50 (the red line represents the option (bet) value and it starts at $50)
  3. The gain will be $100

Binary option price vs its underlying price, a winner case.
As we can see the option price in red is equivalent of the value of the bet and it changes with respect to the underlying but also with respect to time.

The below chart shows a scenario of an underlying decline and Trader A losing its bet. As we can see the option value falls quickly to zero at the end of the game as its probability to win decrease quickly.

Binary option vs its underlying price, a loser case.

Some Mathematicians developed a mathematical formulae that allow Traders to know the option price at any point in time. This equation need several parameters to give a solution the main one being:

  1. The underlying price
  2. The time left until the end of the bet (the expiration time)
  3. The bet itself called the strike (in our above example the strike is a bet that the underlying is above $100 so the strike is 100)
  4. The volatility of the underlying (measure the speed of move of the underlying)
  5. Interest rate

Both point 4 and 5 will be explained in more details later.

Like a car dealer that knows the value of each second hand cars he sells a Trader can also know the value of the options he holds at any given point in time. As we saw above the option value varies with respect to time and the Trader A that bought the option at $50 can sell the option (at $60 for example) to another trader to take its profit. Everyday thousand of Binary option are traded on financial market or over the counter.