The Components of Binary Option Pricing.
By this point you should understand what a binary option is and the benefits of its capped risk-reward. Now let's look at what goes into a binary option's price and how it changes with the movement of the underlying market.
The pricing of binary options is straightforward. If you have traded options before, you may know about advanced topics like the Black-Scholes pricing model or the delta and gamma. If you know that stuff, great. But you don't need to learn it to trade binary options.
What Buyers and Sellers Think is Probable.
Binary options are priced between zero and 100. That price reflects what the buyers and sellers in the market collectively believe is the probability of the binary option expiring above the strike price (in the money).
To get a rough but useful idea of the probability, just find the mid-point between the contract's bid and offer price, the prices that sellers and buyers are paying, respectively.
For example, if the binary contract EUR/USD > 1.1200 is trading at a bid of 30 and an offer of 34, you take the mid-point between the two, which is 32. That means the market is saying there is about a 32% probability of the EUR/USD rate being above 1.1200 at expiration. The seller, therefore, has a 68% probability at that moment of being correct.
How does the market form this view? A few components go into shaping the price. They are the underlying market and its relationship to the strike price, the time remaining, and the market volatility.
Price and the Underlying Market.
If the underlying market is higher than the strike price, the binary option price will typically be above $50. A binary option is based on the condition that the market will be above the strike price at expiration. So if the underlying market price already is above the strike price before expiration, the probability is that the binary will finish above it. The higher price reflects that expectation. The odds are in the buyer's favor at that time.
Conversely, if the underlying market price is lower than the strike, the probability is lower that the binary will expire in the money. That makes the price go lower as well. The odds at that moment are in the seller's favor, not the buyer's.
In other words, if you are a buyer:
The further below the strike price the underlying market is, the lower the price of the binary, down to the lower limit of zero. The further above the strike price the underlying market goes, the higher the price of the binary option, until the binary approaches its maximum of $100.
If you're a seller, the reverse is true.
For example, if a market has an average daily range of 17 points, and the underlying market is currently over the strike price by 15 points, the binary price will be higher than a contract that is only 1 point over the strike. At expiration, however, it doesn't matter since the binary option's price can only be zero or $100.
Factoring in Time.
All binary contracts have an expiration time at which they will be worth either zero or 100. The more time is left in the contract, the greater the chance that either outcome could happen. If you want to drive 1000 miles and you have 3 days to do it, the probability is pretty high that you'll succeed. If you have 5 hours, the probability is low.
Let’s go back to the example of a market with an average daily range of 17 points. If this market is 8 points above the strike price, but there is a full day before expiration, the probability will be over 50, but still near the middle of the 0-100 price range. That's because it still has a full day in which it could lose those 8 points. If the same contract had only 15 minutes left until expiration, the binary price would be closer to 100 since it has only 15 minutes left in which it could lose those 8 points and become unprofitable.
If a binary option has little time left until expiration and the underlying market is trading right around the strike price, the binary option's price can make some extreme moves. That's because only one tick of movement means the difference between a zero outcome and a $100 outcome. With only minutes or seconds left, an option worth $80 could drop to $20 on only a few ticks of movement in the underlying market. Or a $20 option could go to $80. This is one way binary options can give you more profitable results than trading the underlying market.
Watch the Nadex 5-minute binary options in forex to see this happen again and again. We designed those 5-minute options for traders who like fast results, with the protection of defined risk.
Volatility: Anything Can Happen.
You could take several college courses in market volatility and learn about standard deviation and implied vs. historical vs. relative volatility, but to trade on Nadex, you just need to know what volatility looks like in the movement of the price.
Volatile markets make bigger moves. If a market has an average daily range of 17 points, during a period of high volatility its range may expand to 25 to 30 points or more.
When markets are less volatile, these ranges tend to contract. A market that typically moves 17 points in a day might only move 6 or 8 points.
The more volatility there is in the underlying market, the closer the price will be to the middle of the zero to 100 range .
One day, you may see a binary priced with a bid/offer of 76/80 with 8 hours remaining and then the next day see the same binary with the same time remaining priced at only 62 bid / 66 offer. Because the market is more volatile on the second day, sellers are more averse to risk, bringing the prices closer to the middle of the range.
Volatility is a factor in the binary option's price. You can also use it as a factor in your trading strategy. If a market which typically moves 17 points in a day has only moved 8 points in low volatility market, then a binary option with a strike price 15 points below the market price has a higher probability of staying in the money until expiration. In such a slow-moving market, it is less likely to move 15 points that day, unless the situation changes. Of course, it always can, but the probability is greater than usual that it will stay above the strike price. You can look at the chart to see the volatility and use that information to decide whether to take the trade. Low volatility is not hard to spot—it's when the price is meandering sideways and not moving up or down very much.
The three factors that shape the price of a binary option The way that the binary option price reflects the probability of a profitable outcome How time, volatility, and the price of the underlying market work together to affect the price of the binary option.
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Trading on Nadex involves financial risk and may not be appropriate for all investors. The information presented here is for information and educational purposes only and should not be considered an offer or solicitation to buy or sell any financial instrument on Nadex or elsewhere. Any trading decisions that you make are solely your responsibility. Nadex instruments include forex, stock indexes, commodity futures, and economic events.

Pricing a binary option

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Binary Option Pricing.
Are you a regular Binary Option trader? How profitable is your trading? These are questions which no doubt go to the core of any dedicated trader.
What we at the trading club have noticed is that traders who are trading options these days are not necessarily using strategies that take advantage of Binary Option Pricing . More particularly, they do not take a view on the various components of this price.
Why simply trade the trend on the EUR/GBP when you can take advantage of underlying movements in the volatility, time to expiry and strike to shape your strategy?
Of course, Binary Options pricing can be quite a complicated procedure. Indeed, most online resources will point people to explanations which involve advanced derivative mathematics like the black Scholes model. These are mainly used by OTC traders at global investment banks.
This, however, should not deter you . If you can understand the main components of a Binary Options price, then you are best positioned to make a profit from the movements in these variables.
Short Overview of Binary Options.
As many will now know, a binary is a unique type of option that has only two payoffs. These are either 0 or 100 on most platforms. Of course, the pay-out can technically be a number other than 100 but we are keeping it at this level for simplicity sake.
The trader enters the option and will get the pay-out if the option expires in the money and will lose the entire initial investment if it expires out of the money. Whether the current price is above or below the strike at expiry and how it impacts “money-ness” is a function of whether the option was a call or put option.
You can read more about what Binary Options are if you would like to understand these concepts more concretely before continuing.
Components of a Binary Option Price.
What is important to note about Binary Options is that they are merely a variant of traditional American options with a Binary Payoff. As such, they are impacted by the same components and inputs as traditional American options.
If you are vaguely familiar with Option pricing then you will know that it is normally determined by a function called the Black Scholes model. As complicated as it may look, one merely needs to understand that the function has a number of inputs. The main inputs of this function are no doubt the current price , the volatility in the underlying price and the in the time to expiry.
Hence, if either of these inputs changes, it will most likely have an impact on Binary Option pricing. As such, this is the opportunity for the astute trader to make extensive returns and improve their performance.
How Likely is a Win?
A great deal of binary option pricing and trading comes down to probability theory . How likely is it that the option will expire in the money and hence pay-out? This probability will impact on the price someone is willing to pay for a Binary Option in the market. The more certain the traders are that the option will end in money, the closer there are willing to pay to the 100 pay-out number.
All of the components that we have mentioned above will impact on the probability that the option will end in the money at expiry.
Using an actual example, assume that there is a Binary Option which has a pay-out of 100 with an expiry in the money. The current price of the option is at 30. If the option expires in the money, the pay-out will be 70. This implies that the chance of the option expiring in the money is only 30%.
Current Price (S)
This is probably one of the factors that most greatly impacts binary option pricing. This is because where the current price is will determine whether the option has expired in-the-money and whether the trader has won.
Therefore, it also impacts on the probability of an expiry in-the-money if there is still time till expiry. For example, taking a look at a CALL option. If the current price is above the strike then the price of the option is likely to be above 50 to reflect the increased probability that it will expire in-the-money.
Similarly, on the flip side if the price of the underlying is considerably below the strike, there is a reduced probability that it will expire in the money and hence a lower option price to reflect this.
If we wanted to take a look at an example that involved actual option pricing, let’s say that you wanted to enter a GPB/JPY binary CALL option with expiry in 2 hours. The strike price of the option (K) is at 140.50 and the current GBP/JPY level is at 142. This implies that the option is more likely than not to expire in the money and hence it will demand a price above 50.
This does assume that the other two components that we will mention below are held constant.
Volatility (σ)
In traditional option pricing, volatility (σ) drives the price as well. In fact, in big Investment banks, the option traders are termed the “volatility traders” and these traders only take views on the movement of the volatility and not necessarily the price.
Indeed, volatility is quite a complex discipline to understand. There are different classifications such as implied volatility, realised volatility, and volatility on volatility. However, for the average Binary Options trader, all you have to understand is that the volatility is a measure of how quickly and regularly the underlying asset moves in price.
For the trader, this is an important component. It means that the option may quickly swing into the money before expiry even if it is currently below the strike price. Similarly, it could also impact on the price of an option that is in-the-money. This is because there is also a chance that it could move out of the money and lose.
If you were a trader who wanted to trade the asset’s volatility, how would you go about it? You could make a relative value trade on the volatility implied by the option price and that which is currently prevailing in the market.
For example, let us assume that there is an asset which usually moves about 18 points in a day. However, currently the market is relatively quiet and its maximum movement over the past few hours was only 8 points. This means that if the option is in the money, you can enter the Binary Option at a relative bargain as it is unlikely to swing out-of-the money and result in a losing trade.
Time to Expiry ( T-t )
We are all aware of the old adage that “time is money”. In option land, that also holds true and in many cases time to expiry (T-t) is termed the “time value” of the option.
Coming back to probability calculation that the trader makes, the time to expiry adds uncertainty to the calculation . This is indeed true for many other things in life. The more time that we have the more certain we are of reaching an end goal. This could be completing assignment or reaching a destination on a trip.
When someone is pricing a binary option, the time the option has to expire will impact on their mental calculation of whether they will win the trade. For example, if the binary option is currently out of the money and is 30 seconds to expiry, you can be fairly certain that it will expire and you will lose the trade.
However, if there was still 12 hours to go to expiry then there is still enough time for the option to move into the money before expiry.
How might the Binary Option trader enter a trade based on the time to expire? Given the unique nature of a Binary Option payoff, a chance for large payoffs is possible when the option is near expiry. For example, if the price of the option is quite near the strike price and near expiry, there is the chance of a large swing in the price as it approaches the “all or nothing” payoff.
Taking a look at the above example of the GBP/JPY, if the strike is at 140.50 and the current price is equal to the strike, there is an almost 50% chance that it will either payoff 0 or 100 in a very short period of time. Hence, a trader who strategically enters the option near expiry can make a rather impressive return on the trade.
A Comprehensive Approach.
Of course, the astute trader will not merely look at only one component and trade solely based on that. Each of these factors have an impact on binary option pricing to varying degrees dependent on the underlying asset. One can think of them as three legs to a chair. Each as is important as the other and a trader needs to make a careful analysis of the relative impact of each on the option price.
Moreover, the really successful trader will combine use these factors in a comprehensive trading strategy. This should include a strategy that includes technical analysis with binary option signals and fundamental analysis of Economic conditions.
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While Binary Trading Club is dedicated to bringing you the very best in ratings and recommendations for binary & forex brokers and service providers, it is important to note that Forex, Binary Options, CFDs and Spread Betting are highly speculative in nature and involve substantial risk. Investors should be fully aware of the risks involved and solely accept any and all negative consequences associated with such trading. Online trading may not be suitable for all investors, so only invest money you can afford to lose and seek professional financial advice before undertaking any such investments.

Pricing a binary option

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How does volatility affect the price of binary options?
In theory, how should volatility affect the price of a binary option? A typical out the money option has more extrinsic value and therefore volatility plays a much more noticeable factor. Now let's say you have a binary option priced at .30 as people do not believe it will be worth 1.00 at expiration. How much does volatility affect this price?
Volatility can be high in the market, inflating the price of all options contracts, but would binary options behave differently? I haven't looked into how they are affected in practice yet, just looking to see if they would be different in theory.
Also, the CBOE's binaries are only available on volatility indexes, so it gets a bit redundant trying to determine how much the "value" of volatility affects the price of binary options on volatility.
The price of a binary option, ignoring interest rates, is basically the same as the CDF $\phi(S)$ (or $1-\phi(S)$ ) of the terminal probability distribution. Generally that terminal distribution will be lognormal from the Black-Scholes model, or close to it. Option price is.
$$C = e^ \int_K^\infty \psi(S_T) dS_T$$
Volatility widens the distribution and, under the Black-Scholes model, shifts its mode a bit. Generally speaking, increased volatility will.
Increase the density in the "payoff region" for out-of-the-money options, thereby increasing their theoretical value. Assuming your option was worth 0.30 due to probabilities and not high risk-free rates $ r $, more volatility will increase its value.
Increase the density in the "no-payoff region" for in-the-money options, thereby decreasing their theoretical value. An option now worth 0.70 will lose value, as the probability of ending outside the payoff region is increased.
As volatility $\sigma$ approaches $ \infty $, all option prices converge toward 0 for calls and 1 for puts. In Black-Scholes land, even though the term $ \frac > \to 0$ and the probability distribution is spreading out all the way to infinity on the positive as well as negative side of the exponential of its distribution, it concentrates lognormally on values less than any finite strike.
Therefore, out-of-the-money calls will take on a maximum value at some volatility that concentrates as much probability as possible below the strike before concentrating the distribution too close to zero.
Edit : A huge thank-you to Veeken to pointing out that it is out-of-the-money calls, rather than puts, which take on a maximum theoretical value.
all of the volatility effects on a binary option struck at 105 with a one dollar payoff are approximately the same as the volatility effects on the following portfolio of options:
short 100 of the 104.99 calls / long 200 of the 105 calls / short 100 of the 105.01 calls.
I have a mathematical proof with no graphs or pictures. Suppose $r=0$, what we want is to see what happens if volatility changes in $E^Q[1_ ]$.
The latter quantity is $Q(S_T>K)=Q(\log S_T > \log K)$.
Under Q, we know that $S_T=S_0 \exp\left(-\frac12 \sigma^2T + \sigma W_T\right)$, so $\log S_T$ is distributed as $ N(\log S_0 -\frac12\sigma^2T, \sigma^2 T)$.
So we can write $Q\left(\sigma \sqrt N + \log(S_0) -\frac12 \sigma^2T > \log K\right)$ which equals $ Q\left(N>\frac >+\frac12 \sigma^2T> \right). $
Since $f(y)=Q(N>y)$ decreases in $y$, it is enough to study $y=y(\sigma)=\frac >+\frac12 \sigma^2T> $.
If $K>S_0$ (out of the money option), then if $\sigma \to 0$, $y(\sigma)\to +\infty$ and the same happens if $\sigma \to +\infty$. Hence there is a minimum for $\sigma=\sqrt >>$. We deduce (by continuity) that $f(y(0))=0$, $f(y(+\infty))=0$, and we have a maximum for $\sigma=\sqrt >>$.
If instead $K<S_0$ (in the money option), $\sigma \to 0$ gives $-\infty$, $\sigma\to \infty$ still gives $\infty$ and the function $y(\sigma)$ is strictly increasing. So $f(y(0))=1$, $f(y(+\infty))=0$ and $f$ is strictly decreasing.
Finally, for an at the money option $S_0=K$, we have $f(y)=Q\left(N > \frac12 \sigma \sqrt T\right)$, so $f(0)=\frac 12$, and $f$ strictly decreases to the value $0$.