# Binary Option Behavior as Expiration Approaches-Free Binary Options

With regular put/call options, as expiration approaches, the time value goes down. This is known as time decay. With binary options,as expiration approaches, you will start to notice a very interesting phenomenon. This phenomenon occurs due to the binary nature of these options. It also presents some interesting opportunities and should be addressed, as it is a key attribute of binary options.

UNDERSTANDING DELTA:In order to illustrate this phenomenon, you must understand the concept of delta. Delta is simply the amount that the price of the option changes for every dollar that the price of the underlying changes. For example, with a deep‐in‐the‐money option, the delta will be 1 to 1 since for every dollar that the underlying grows, the option will also grow by \$1.If you have a deeply out‐of‐the‐money option, the option will have a lower delta.

This is due to the fact that as the underlying grows by \$1,the option does not become signifi cantly more likely to be in‐the‐money.Therefore, the \$1 growth in the underlying will have only a minimal impact on the price of the option.As you will shortly see, the delta will behave signifi cantly differently with vanilla put/call options than with binary options.With traditional put/call options, the principle is simple:

The closer you get to being “in‐the‐money,” the higher the delta. Also, the closer you get to expiration, the lower the delta becomes for each strike price.Now let’s look at what happens with binary options around expiration time:Let’s assume that you purchased a “> 1250” at‐the‐money option when the underlying was trading at 1250. Based on the option chain above, you would have purchased that call for \$51.6 per contract.

As expiration approaches, if the S&P 500 futures close above 1250,your collateral investment of \$51.6 will turn into \$100. However, if the S&P 500 futures close at 1249.99 or below, your initial investment of \$51.6 will turn to \$0.Exhibit 9.3 demonstrates the price behavior of a binary option at expiration. If at expiration the underlying is above the 1250 strike price, the initial investment of \$51.6 is in‐the‐money and worth \$100.

If at expiration the underlying is below the 1250 strike price, the initial investment of \$51.6 is out‐of‐the‐money and worth \$0.As you can see, this is a huge difference. A one‐cent move in the price of the underlying right before expiration represents a difference of \$100 in the price of the option at expiration.

If there is still a lot of time before expiration, then a \$1 move around the “at‐the‐money” price point of the underlying is fairly insignificant since there is still plenty of time for it to make a move in one direction or another and still roughly a 50 percent chance that it will end up above or below the at‐the‐money price.However, as expiration approaches, the underlying has less time to move in one direction or another.

For this very reason, the premiums of the options with strike prices around market price will have huge deltas, as every dollar move can potentially make the difference between a \$0 value at expiration and a \$100 value at expiration.So now let’s look at the option chain again and make some assumptions about where the options premiums are likely to end up as expiration approaches, based on these principles.