Do Binary Options have Delta and Gamma?
Author: John Kmiecik
Market Taker Mentoring Inc.
No matter what type of vehicle you trade, traders are always looking for an edge to put the odds on their side and binary options are no different. Although binary options do not have listed delta and gamma quotes, there are certain parameters that can help a binary option trader put the odds on his or her side, similar to how an equity option trader uses the option “greeks” to do the same. Let’s start by breaking down what option delta and gamma are, and how equity option traders use these key components.
Option Greeks
The option greeks help explain how and why option prices move. Option delta and option gamma are especially important because they can determine how movements in the underlying can affect an option’s price.
Option delta measures how much the theoretical value of an option will change if the underlying moves up or down by $1. For example, if a call option is priced at 1.50 and has an option delta of 0.60 and the underlying moves higher by $1, the call option should increase in price to 2.10 (1.50 + 0.60).
Option gamma is the rate of change of an option's delta relative to a change in the underlying. In other words, option gamma can determine the degree of delta move. For example, if a call option has an option delta of 0.40 and an option gamma of 0.10 and the underlying moves higher by $1, the new delta would be 0.50 (0.40 + 0.10).
Trader's Definition
It is the traders's definition of delta that draws comparisons to binary options. Many option traders will say that delta is the likelihood of an option expiring in-the-money. Any equity option with a delta of 0.40 can be interpreted by traders to mean that the underlying has a 40-percent chance of expiring in-the-money. One of binary option’s greatest attributes is its simplicity. Binary option pricing can be thought of as the probability the option will expire in (ITM) or out-of-the-money (OTM) at expiration depending on if the option is bought or sold.
A Binary Option Example
At the time of this writing, the CME E-mini S&P 500 Index Futures, the underlying market which the Nadex US 500 binary is based on, was trading around 2099.00. A binary option with a strike price of 2093.50 (meaning the option expires ITM if the Nadex underlying expiration value is even 0.001 above that strike price) expiring the next day could have been bought for 64. The price of 64 is essentially the probability the binary will expire in the money. Risk/reward is clearly defined with binary options, which result in a payout of $100 for every contract. Essentially the buyer puts up $64 a contract and profits $36 (100 – 64) if the underlying market closes above the strike price at expiration. Based on the purchase price, the trader who bought the binary had a 64% chance the option was going to expire in the money, and thus was rewarded with a smaller payout due to percentage being in his favor when the trade was initiated. In essence, the $64 purchase price was close to being like an option that had a 0.64 delta.
Instead of ITM options consider that the binary option will expire out-of-the-money (OTM). Using the same example where the underlying market is trading around 2099.00 but here we are using a higher strike of 2217.50 where the binary price is quoted at 9 expiring the next day. By selling this binary strike level, the trader thinks that the underlying market will not close above 2117.50 at expiration. Obviously the trader has the initial trade edge but puts up $91/contract (100 – 9) for the binary trade. At expiration if this binary remains OTM then the binary will expire worthless (under 2117.50) with the contract settling at 0. At this time the binary seller will receive the $100 settlement expiration payout per contract, netting a $9 profit not including exchange fees.
In this instance, the delta for this strike price could be considered 0.09 because of what the option was sold for. In other words, based on the price, the option had only a 9% chance of expiring ITM which also makes sense from a risk/reward perspective. The trader had a maximum risk of $91 a contract and only a $9 max reward.
Why would any trader consider this scenario? Well the answer is simple, the flip side to a 9% favorable probability is a 91% unfavorable probability so in this instance the binary seller has the odds.
Option Prices Always Changing
If you have ever traded binary or equity options, you know that prices are constantly changing. One of the reasons option prices are changing is due to option gamma for equity options and the perceived gamma in binary options. For both binary and equity options, time erodes the probability for OTM options expiring ITM and time increases the probability of ITM options expiring ITM. Option gamma increases the closer the option gets to expiration. This makes sense because an equity option can have a delta of 1 (ITM) or 0 (OTM) at expiration; nothing in between. The closer the option gets to expiration the more the delta may change because of the delta being either 0 or 1. This is why the gamma grows larger and can affect the delta more as the option heads into expiration.
Perceived Option and Gamma
Although there is no gamma attached to binary options, the prices change just like they would over time with equity options. The best way to understand this principle using binary options is to imagine the underlying that trades sideways as it heads closer to expiration. Going back to our example above where the ITM binary option was purchased with a strike price of 2093.50 expiring the next day, assume the underlying market trades sideways while getting closer and closer to the binary expiration. The binary is already ITM so the binary price will continue to rise, because of the increasing delta or probability of the binary expiring in the money. That probability increases because now there is less time.
For example, the original cost of the 2093.50 strike was 64 with expiration the next day. If the underlying market remains relatively quiet, with only two hours left until expiration, the binary price might increase up to 90. The purchase price and essentially the delta of the option will continue to grow, meaning the payout will continue to shrink due to time. The price will increase on the binary option just like the delta would increase closer to expiration. The closer to expiration, the more gamma plays a role with equity options changing delta. Binary options basically function the same way, albeit the changes are reflected and seen only in the price and not also on an equity option’s chain.
Last Thoughts
The beauty of binary options is that there are so many different expirations, ranging from five minutes up to a week. Keeping delta and gamma in mind, the shorter the time period, the bigger the changes may be to the binary options. For a binary option that is close to expiration, one quick and unexpected move can turn a profitable trade into a loser, and of course it can work favorably as well in a flash. If you have a bias and expect a move before expiration, then the silent “greeks” can potentially give the binary trader a desirable risk/reward ratio.
Consider the perceived or silent delta and gamma of binary options next time you are trading and want to put the odds on your side. it may be the difference in maximum profit and maximum loss sooner than you think!
Futures, options, and swaps trading involve risk and may not be appropriate for all investors.