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How Binary Options Work


This article provides an overview of binary options, commonly known as "digitals" for their on-off payment.  The focus is on real world behavior in moving markets, rather than theoretical or mathematical explanations.

The Components of a Binary Option

Like a standard vanilla American or European style option, binary options are defined in terms of a strike price (payout threshold), a maturity date, and an underlying reference unit, commodity, instrument or security price (the underlying).  Binaries are sold in exchange for an up front premium payment, just like other options.  Both calls and puts are available.

Comparison of a Binary Versus Standard Vanilla Option

Taking price dynamics as a separate subject, the only difference between a binary and standard option is its payout profile.  A binary option pays out a fixed amount, while a standard vanilla option pays out a potentially unlimited variable amount.  Both options can expire worthless "out of the money."  If the underlying instrument moves "in the money", a binary will pay a fixed amount, say $10, while a vanilla option will pay anywhere from $0 to infinity depending on how much the underlying instrument clears the strike price.

Where Binary Options are Used

Binaries are typically bought and sold in the Over the Counter (OTC) markets between sophisticated financial institutions, hedge funds, corporate treasuries, and large trading partners.  They are widely used where the underlying instrument is a commodity, currency, rate, event, or index.  For example:

Binary call and put options are popular in the platinum market, struck on the mid-market price of the metal of a certain quality, quoted by several dealers over a stated time period.  Platinum trades in large varying quantities among major producers and manufacturers, as well as between speculators and dealers.  Prices are determined between disparate parties, with varying frequency, and are not centrally reported or confined to a centralized exchange.  A third party calculation agent is often agreed upon as part of the deal, to guarantee an uninterested price estimate obtained by sampling various dealers on the expiration date.

Binary options are used widely to hedge weather events, such as hurricanes, temperature, rainfall, etc.  Major agricultural and transportation companies can be severely affected by adverse weather conditions.  Weather is highly unpredictable and difficult to measure (e.g. what is a hurricane? How fast do the winds have to be?  How long does it need to last?  Does it need to touch ground or can it remain over water? What must the temperature be?  Where is the exact location of the measurement to take place?).  This makes a binary option a perfect tool for hedging weather events, as it allows the option seller (option writer) to assume a fixed amount of risk tied to the occurrence of a future event whose magnitude is impossible to predict. An uninvolved and highly reliable third party such as a government weather bureau is typically used to determine whether the weather event has occurred. 

Binary options are also traded on inflation figures such as the Consumer Price Index (CPI) or Producer Price Index (PPI) in the U.S.  These figures are reported fairly infrequently based on independent sampling methods, and are often revised after they are released once input values are further verified.  There is no continual stream of prices because inflation is not an actual traded instrument (aside from recent developments in exchange-traded inflation futures).  Without continual input prices, it is very difficult to mark-to-market vanilla American or European options, whose value is highly dependent on dense volatility and price data.  A binary option allows the buyer to obtain inflation protection, while providing the option seller with limited risk in the event that inflation jumps or drops unexpectedly.

Finally, binary options are popular in the foreign currency markets, especially on illiquid and volatile currencies such as the Turkish Lira and Thai Bhat.  Emerging market currencies are often subject to rapid "jump risk" caused by political or economic instability, or simply illiquidity due to the relatively small volume of foreign trade.  Sophisticated currency speculators borrow low-rate developed economy currencies such as USD or EUR and invest in high-rate emerging market currencies, then purchase binary options as protection against currency risk in the high rate leg.  This allows the speculator to earn "carry" while protecting against "jump risk."

Binary Option Pricing Dynamics - Moving From Out of the Money Into the Money

In general, an out of the money binary option will be cheaper to purchase than an equivalent out of the money vanilla option, assuming the same underlying, strike, and time to expiration.  This is because the binary option has a fixed payout in the event it expires in the money.  The vanilla option, on the other hand, can theoretically pay an infinite amount, limited only by the potential underlying price and credit of the option seller.  Out of the money vanilla options typically have greater "time value" than binary options. 

This valuation difference between an out of the money binary and vanilla option has two benefits.  First, it enables the option seller to assume a known limited risk.  Second, from the perspective of the buyer, a binary option can offer significantly greater leverage since the up front premium investment is lower. 

When a binary option moves from being out of the money to in the money, its theoretical value profile is much different than a vanilla option.  The binary option moves up in value very rapidly as it crosses the strike threshold.  For example, with a strike of $50 and a fixed payout of $5, a binary call option will move very quickly from $2.50 to $4.00 or more just as it crosses the $50 strike level.  This is because a move above $50 by any amount (even one-half cent) guarantees a $5 payout.  The resulting profile is a "bulge" or "step".  Conversely, when a binary option moves from in the money to out of the money, its value changes very quickly, dropping towards zero in a steep fall, then leveling off.

Binary vs. Vanilla Call Option:  Sensitivity to Price of Underlying:

In comparison, when a vanilla option moves from being out of the money to in the money, its theoretical value profile changes more gradually.  Its value increases in a curved manner, somewhat like the bottom of a slide for a call or the top of a hill for a put, after which the valuation change becomes more linear.  With the same $50 strike as the binary option, a vanilla call option will move up in value more gradually as the underlying crosses $50, and will continue to move up in a near-linear fashion as the underlying price goes to $60, $70, or above (with Delta approaching 1 as it goes farther in the money).  Likewise, when a vanilla option moves from in the money to out of the money, its value changes more gradually than a similar binary option.

Time Value Dynamics

Time value (the Greek "Theta") profiles are quite different between binary and vanilla options.  The difference primarily lies in how the options behave when they are in the money.

First, let's address the out of the money situation.  Using the same two call options above with $50 strikes and the same underlying and time to expiration, both options will have similar time value changes.  When an option is out of the money, its price is made up solely of time value, which is the estimated probability of being in the money by the expiration date, times the expected payout, across all likely values.  It is easy to understand that an out of the money option will gradually lose all of its value if the underlying instrument never crosses the strike threshold.  Under these circumstances, both binary and vanilla options exhibit a gradual loss of time value with an exponential drop near to expiration.

Now, let's address the in the money situation.  That is, both the binary and vanilla options are in the money after the underlying instrument crossed the strike threshold, and they stay in the money until expiration.  Under these circumstances, the binary option's time value profile is actually the opposite of the vanilla option's.  Vanilla options that are in the money 5-20% usually exhibit residual time value -- in other words, just because the underlying has crossed the $50 strike and is now at $51.00 does not mean the vanilla option will be priced at $1.00 (its intrinsic value).  Rather, the vanilla option will likely be priced at $1.20 ($1.00 intrinsic + $0.20 time value) or above by the market.  There is still a probability that the underlying could move further into the money and this is reflected in the market price.

As time passes, an in the money vanilla option will lose its time value and the market price of the option will fall to its intrinsic value -- in our example $1.00 (underlying price of $51 minus $50 strike).  This occurs gradually at first, then rapidly as expiration nears.

Binary vs. Vanilla Call Option:  Sensitivity to Passage of Time:

The binary option is a completely different beast.  Rather than decreasing to zero as the vanilla option's does, an in the money binary option's value actually increases as expiration approaches.  One month from expiration, the binary option might be valued at $4.  But with 3 days left to expiration, its value may be close to $4.93, assuming it is in the money by the same $1 amount as our vanilla option. 

The reason for this value dynamic is quite logical:  our binary option has a fixed payout of $5, regardless of whether the underlying is at $50.01 or $10,000 when the option expires.  Far away from the expiration date, the binary option's time value is negative, not positive as the vanilla option's is.  Although the binary option may be completely in the money one month away from expiration, there is still a probability that it will move out of the money by the time it expires.  Once the underlying instrument has crossed the strike threshold, the binary option will pay $5 intrinsic value times the probability of remaining in the money until expiration.  It cannot go further into the money like a vanilla option, so it cannot have positive time value.  As expiration nears, the probability of remaining in the money increases, the negative time value goes away, and the option value approaches its full $5 payout (intrinsic value).

Volatility Dynamics

Without getting too deeply into volatility surfaces, smiles, and skews, binary and vanilla options can exhibit different theoretical valuation behavior as volatility changes.

Vanilla options on various underlying assets respond to increases and decreases in the volatility of the underlying in a fairly predictable manner.  Out of the money vanilla options are sensitive to actual or perceived volatility of the underlying instrument.  When the underlying price is near the strike threshold, volatility becomes a larger factor in the vanilla option's theoretical value.  When the underlying price moves deep in the money, the vanilla option's theoretical value becomes somewhat less sensitive to volatility (There are differences in this due to volatility smiles in equities, forex, and interest rate options, but that's a different subject).

Binary vs. Vanilla Call Option:  Sensitivity to Volatility of Underlying:

In comparison, the effect of underlying volatility on the price of a binary option is more exponential, depending on whether the option is deep out of the money, near the money, or deep in the money.  When the underlying instrument is far from the strike price, volatility is only a small component of the binary option's theoretical value.  This is similar to a vanilla option.  However, as the underlying instrument's price nears and crosses the strike threshold, a binary option's value becomes highly sensitive to volatility.  This aligns with the fact that a binary has very high Gamma as it nears and crosses the money threshold -- if underlying volatility increases while it is near the strike price, this essentially "turbocharges" the option's value.  Finally, if the binary option is deep in the money, it becomes less sensitive to underlying volatility just like a vanilla option.

In situations where both the binary and vanilla options are in the money, volatility can have the opposite effect on time value for each.  Since a vanilla option's time value is positive when the option is in the money, an increase in volatility will increase the time value, as there is greater probability that the option will expire further in the money and produce a greater payoff.  In comparison, a binary option's time value is negative when it is in the money.  Therefore, any increase in volatility will increase the probability that the underlying instrument might move out of the money at expiration.  The in the money binary option value will respond by falling, not increasing as the vanilla option value would.

The effects described above can be reversed for decreases in underlying volatility.  


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