# Binary Option Pricing

How often do you trade Binary Options? Do you know exactly how an Option is priced?

There are many Binary Option traders that have been trading for a number of years yet still do not know exactly how a Binary Option is priced.

Of course, one does not need to know how itÂ is priced in order to be a successful binary trader. Yet, knowing what impacts on the price of a Binary Option can greatly improve your trading.

Usually the field of Investment Bankers with complicated models, pricing Binary or “digital” options should not be as complicated as it is made out to be. As long as the trader understands the variables that impact on the price they are able to get a sense to the value of the option.

## Recap on Binary Options

We have previously explained Binary Options but you may know by now, a binary option is considered an exotic variant of a traditional European option. An option gives the holder the right but not the obligation to buy or sell the underlying asset at some point in the future.

As such, an option has value if it is in-the-money (above strike) or out-of-money (below strike). Of course, this depends on whether it is a put or call option.

A Binary Option is an option where the holder either gets a Pay-out that is a fixed pay-out or 0 (1 or 0). This is why it is called “Binary” or digital. There are only two possible outcomes.

Of course, the pay-out can be any number but can only either be that number or 0. With most Binary Option brokers, that pay-out is 100 or 0. The cost of this option is usually determined at the beginning and is some percentage of the pay-out.

Of course, there can be a number of other factors that makes the pricing of Binary Options more complicated. Yet, these are usually not required for normal retail options.

## Components of Binary Option Pricing

A Binary Option price, like traditional options, is a component of a number of different variables. These include the **time to expiry**, the **current price**, the expiry level and the **volatility** of the underlying asset.

In option terminology, these are priced using what are called “The Greeks”. Essentially, these are the mathematical terms used to describe the various components. These are then placed into the famous Black Scholes pricing model.

Although the Black Scholes model looks daunting at first, it does not have to be. As long as the trader understands how the various components impact on the price of the option.

### What is Probable?

All of these factors mentioned above impact on what is likely to occur and what is probable. How likely is the option to end in the money at expiry? If it is quite likely then the price would be rather close to 100. However, if it is less likely then the price will reflect this.

For example, assume there is a Binary Option that has a pay-out of 100 if the option expires in the money. Assume that the price of this option is now at 34. This means that if the option ends in the money, the pay-out to the trader will be 66.

Taking a look at the price, one can infer that the chance of the option ending in the money is 34%. This probability is impacted by the components which we will look into now.

### The Current Market Price

The chances that the price of the asset will be above the strike price at expiry is greatly impacted by the current market price. If the current price is above the strike then it is more likely than not that it will be in the money at expiry.

In the above case, the price of the option will usually be above $50. This means there is more than 50% chance that it will be in the money at expiry. Of course, the opposite can be said if the current price is below the strike. The price will most likely be below 50 meaning that it is more likely to expire outside of the money.

Putting this all together, assuming that this is a call option, the further below the strike the price is the cheaper the price of the option. Similarly, the further above the strike the price is, the more expensive the option.

Of course, the opposite can be observed if the option is a put Option. In this case the option is more expensive the higher above the strike the price is.

Looking at an example, assume that you decide to enter a GBP/USD binary option with a strike price of 1.2432 and the current price is at 1.2450. This means that the option price is more likely to be above $50 as there is a more than 50% chance it will expire in the money.

This is of course assuming everything else is held equal including the time to expiry and the volatility in the asset.

### The Time to Expiry

Like traditional options, Binary Options have a time to expiry. This is usually termed **“Theta”** in option Greeks. The time to expiry has a big impact on the price of the option. This is because of the time in which the asset price has to move before expiry.

This is usually termed the **time value** of the option. One can think of it intuitively as well. The longer the Binary Option has until expiry, the more chance there is that the option will move into or out of the money. There is more uncertainty over where the price will end up.

A simpler example can be that of completing an assignment in your college days. The chances of getting an “A” is greatly impacted by the time that you have to complete the assignment. Even if you are not the best writer (asset price) the more time you have to refine your assignment (expiry time) the greater your chance of an “A”.

Taking a look at an example of an actual binary option, assume that we are looking at the above example with GBP/USD. In that case, we saw that the option price was more likely to be above 50 as it was likely to expire in the money.

However, this price may differ substantially based on how far away from the expiry the option was. If the option was 24 hours from expiring, then there is a lot of time for the option to move out of the money in that timeframe.

If, on the other hand, there was only a few hours to go until expiry, there is not that much time for the option to expire out of the money. This therefore means that it is going to be closer to 100 than the option with the longer expiry time.

Interestingly, given the nature of a Binary Options payoff, if the price of the currency is close to the strike and the option is very close to expiry, the option price could swing widely in price. This is also why traders find Binary Options quite profitable.

If the option is currently priced at $50 and is close to expiry that has a jump in the price of the underlying, it has to automatically adjust quite quickly.

### Asset Volatility

In investment banks, option traders are sometimes termed “volatility” traders. This is because volatility usually has such a big impact on the price of the option that the traders are able to take a view on volatility simply by trading options.

Volatility itself can be quite a complex subject. There is **implied volatility, historical volatility as well as volatility on volatility**. However, it is quite simple to understand when one thinks about it terms of uncertainty.

When an asset is quite volatile, there is more uncertainty of where the price of the asset will be at expiry. In financial markets, traders pay to avoid uncertainty. You are usually able to obtain the implied volatility of an asset from its option price.

But how do you use the option’s volatility to trade a Binary Option? You can get a Binary Option at a relatively attractive price when the market is in a low volatility period.

For example, let us assume that an asset which usually moves by 15 points in day has moved only 5 points today. This means it is a rather low volatility day and you can get a Binary Option that is well priced. You can purchase an option that is in the money and it is less likely to move the 15 points placing it out of the market.

You can also use incorporate a volatility arbitrage strategy with numerous other option trading strategies to improve your returns.