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(binned per thread starter's request) FX Option calculation

  • #1
  • First Post: Jan 4, 2018 1:46am Jan 4, 2018 1:46am
Hello everyone,

How do forex binary option brokers calculate the value of binary options (put and call) ?
Note: FX Binary options are a total SCAM, I am only interested in the calculation.

Thanks
  • #2
  • Edited 10:16am Jan 4, 2018 6:38am | Edited 10:16am
Quoting Mingary
Hello everyone, How do forex binary option brokers calculate the value of binary options (put and call) ? Note: FX Binary options are a total SCAM, I am only interested in the calculation. Thanks
Ha.. there is not much to calculate. It's just a simple 50/50 bet with RR<1. Binary "options" are not real options.

Binary options are based on the assumption that price action is mostly random walk. You have fixed period of time after which the option has to expire "in the money".

For example, lets say you place $100, 60 second call option with 80% payout at 1.2050 and with purchase time 10:00 and expiration time 10:01.
If at 10:01 the market is above 1.2050 then you win $80. If the price is below 1.2050 then you will lose the price of the option - $100.

This means that the expectancy for every bet is fixed and constantly negative. The average loss is always larger than the average gain. While the long term win rate is 50% (You can blame the law of large numbers for this ).

Of course if you are very "smart" and know how to place "high probability" bets then in theory you can beat the house.
In my example above you need consistent 56% win rate to be breakeven. So, to make money you need above 56% win rate.

Some brokers allow the traders to close the option before the expiration time. But you get penalized with smaller payout. In the end the expectancy is the same.
  • #3
  • Jan 4, 2018 7:02am Jan 4, 2018 7:02am
Black Scholes equations value options including binary's
  • #4
  • Jan 4, 2018 10:34am Jan 4, 2018 10:34am
I am entertaining the idea to artificially create an option in mql code to get the implied volatility as an output.
  • #5
  • Jan 4, 2018 11:10am Jan 4, 2018 11:10am
Quoting Mingary
I am entertaining the idea to artificially create an option in mql code to get the implied volatility as an output.
This is not necessary!
Just use ATR and sqrt(t) (https://sixfigureinvesting.com/2014/06/volatility-and-the-square-root-of-time/). Same thing. But much easier to calculate and to scale up and down for any time frame.
In mql4 use these functions:
atr (https://docs.mql4.com/indicators/iatr)
sqrt (https://docs.mql4.com/math/mathsqrt)
  • #6
  • Jan 4, 2018 1:20pm Jan 4, 2018 1:20pm
Quoting alphaomega
{quote} This is not necessary! Just use ATR and sqrt(t) (https://sixfigureinvesting.com/2014/06/volatility-and-the-square-root-of-time/). Same thing. But much easier to calculate and to scale up and down for any time frame. In mql4 use these functions: atr (https://docs.mql4.com/indicators/iatr) sqrt (https://docs.mql4.com/math/mathsqrt)
That is exactly why I wanted to have look ..
I thought it might be similar.
Thanks for your input. You probably saved me a lot of time.
  • #7
  • Edited 4:31pm Jan 4, 2018 4:20pm | Edited 4:31pm
Quoting Mingary
Hello everyone, How do forex binary option brokers calculate the value of binary options (put and call) ? Note: FX Binary options are a total SCAM, I am only interested in the calculation. Thanks
Black-Scholes is most likely used, or some form of it.

Quoting Mingary
I am entertaining the idea to artificially create an option in mql code to get the implied volatility as an output.

I have been trying to do this for months, but unless you have an actual auction marketplace going on, you will always have to plug in historical volatility to get the option price.

Implied volatility is figured by back solving the Black-Scholes model based on what the marketplace prices the option at, not the historical volatility.

Quoting Mingary
{quote} That is exactly why I wanted to have look .. I thought it might be similar. Thanks for your input. You probably saved me a lot of time.
I also don't think ATR is a fair comparison to implied volatility. Mainly because Implied volatility is almost always overstated by the market (people think underlying will move more than they actually do. Also this is in regards to studying implied volatility with stock options, not FX options) while historical volatility is usually understated.

If you study ATR or historical volatility of FX price pairs and stocks, it is almost always understated when it comes to giving probabilities regarding future price movements.

P.S.
When I say overstated, I mean price is within one sigma more than 68% of the time. In the stock options example, price is usually within one sigma 83% of the time instead of 68%. This is because the Standard Deviation given by the IV is overstated.

And when I say understated, I mean price is outside one sigma more than 68%.
  • #8
  • Jan 30, 2018 2:23pm Jan 30, 2018 2:23pm
I'm not sure about the offshore bucket shops, but Nadex and Cantor Exchange binaries are basically the Delta of a call option. With Nadex it switches to pure Theta in the last 5 min. Implied volatility is the hard part with Nadex because it's based on a sliding scale which I haven't nailed down, yet. MQL4 doesn't have a function for Normal Distribution, so you'll either have to write your own or use C library. The one I was using stopped working last year on one of the mt4 updates and I gave up on the project.
  • #9
  • Jan 30, 2018 2:24pm Jan 30, 2018 2:24pm
Quoting alphaomega
{quote} Ha.. there is not much to calculate. It's just a simple 50/50 bet with RR<1. Binary "options" are not real options. Binary options are based on the assumption that price action is mostly random walk. You have fixed period of time after which the option has to expire "in the money". For example, lets say you place $100, 60 second call option with 80% payout at 1.2050 and with purchase time 10:00 and expiration time 10:01. If at 10:01 the market is above 1.2050 then you win $80. If the price is below 1.2050 then you will lose the price of...
Nadex and Cantor work a little different. Similar to the binaries on the CBOE and CBOT. Same $100 up for grabs but you can be on either side to either go for the greater than 1:1 payouts on OTM or higher probability negative r:r on the ITM options.
  • #10
  • Jan 30, 2018 2:38pm Jan 30, 2018 2:38pm
Quoting alphaomega
{quote} This is not necessary! Just use ATR and sqrt(t) (https://sixfigureinvesting.com/2014/06/volatility-and-the-square-root-of-time/). Same thing. But much easier to calculate and to scale up and down for any time frame. In mql4 use these functions: atr (https://docs.mql4.com/indicators/iatr) sqrt (https://docs.mql4.com/math/mathsqrt)
ATR * Sqrt(Time) is wrong. I tried it long time ago. ATR gives out artificialy high values..
The correct way is (MathLog(Close / Close[1]) * Sqrt(Time) )*ZScore
The results are very realistic in showing the possible deviation boundaries.....
  • #11
  • Jan 30, 2018 2:56pm Jan 30, 2018 2:56pm
Quoting GoldTheHun
{quote} ATR * Sqrt(Time) is wrong. I tried it long time ago. ATR gives out artificialy high values.. The correct way is (MathLog(Close / Close[1]) * Sqrt(Time) )*ZScore The results are very realistic in showing the possible deviation boundaries.....
That is interesting you mention ATR giving artificially high values. Can you please explain more? Every time I've measure volatility using any kind of history, the volatility is almost always understated most of the time or gives low values that are understated.

Maybe I misunderstood what you said, but I am very curious to see where you found volatility is usually understated using historic measures.
  • #12
  • Edited 3:46pm Jan 30, 2018 3:24pm | Edited 3:46pm
Quoting Sis.yphus
{quote} That is interesting you mention ATR giving artificially high values. Can you please explain more? Every time I've measure volatility using any kind of history, the volatility is almost always understated most of the time or gives low values that are understated. Maybe I misunderstood what you said, but I am very curious to see where you found volatility is usually understated using historic measures.
Hi Sis.yphus,

Since ATR is mostly based on High and Low relationship between candles, taking the square root of time of the ATR gives out very unrealistic daily range expectations for the next day. I personally think it is a flawed logic. A measure based on deviation should show the potential for the next day's average daily range (ADR).

On the other hand if you try (MathLog(Close / Close[1]) * Sqrt(Time) )*ZScore, the next day ADR seems to be right on the money.
If you use ZScore of 1 in the above calculation, the high and low of the next day stay within the ZScore boundaries approximately %68 of the time. Which is very similar to normal distribution.

As an example let us use 5 minute volatility to estimate next day's volatility.
First you would take the average of MathAbs(MathLog(Close / Close[1])) for the last 288 bars (1 day of 5 minute bars). Let us say this is V5 (Volatility 5 min).
Expected Daily High(next day) = DailyOpen * Exponent(V5 * MathSqrt(288) * Zscore)
Expected Daily Lown (next day) = Daily Open * (2-(Exponent(V5 * MathSqrt(288) * Zscore) ))

I hope it is clear....
  • #13
  • Jan 30, 2018 3:53pm Jan 30, 2018 3:53pm
Quoting GoldTheHun
{quote} Hi Sis.yphus, Since ATR is mostly based on High and Low relationship between candles, taking the square root of time of the ATR gives out very unrealistic daily range expectations for the next day. I personally think it is a flawed logic. A measure based on deviation should show the potential for the next day's average daily range (ADR). On the other hand if you try (MathLog(Close / Close[1]) * Sqrt(Time) )*ZScore, the next day ADR seems to be right on the money. If you use ZScore of 1 in the above calculation, the high and low of the next...
I totally agree the logic is flawed, as is the case with most instances of historical volatility.

Thanks for explaining this.

and I curse you for doing so as well!

Going to play with your calculation tonight to see if I can get the same results.

If so, then I will really curse you because I will probably be playing with that data for a few days

I may PM you for some more clarification on the formula if I think I am missing something.

Just curious, how did you come about that calculation?
  • #14
  • Jan 30, 2018 3:56pm Jan 30, 2018 3:56pm
Quoting Sis.yphus
{quote} I totally agree the logic is flawed, as is the case with most instances of historical volatility. Thanks for explaining this. and I curse you for doing so as well! Going to play with your calculation tonight to see if I can get the same results. If so, then I will really curse you because I will probably be playing with that data for a few days I may PM you for some more clarification on the formula if I think I am missing something. Just curious, how did you come about that calculation?
Anytime Sis, no problem at all..
As to your question, this formula is based on Random Walk theory, so I didn't invent it. I just applied my logic to it, that is all....

Good Luck...
  • #15
  • Jan 30, 2018 10:06pm Jan 30, 2018 10:06pm
Quoting GoldTheHun
{quote} ATR * Sqrt(Time) is wrong. I tried it long time ago. ATR gives out artificialy high values.. The correct way is (MathLog(Close / Close[1]) * Sqrt(Time) )*ZScore The results are very realistic in showing the possible deviation boundaries.....
Thanks for sharing this! I will try your formula.

However IMO the volatility is impossible to predict with high accuracy regardless of the formula. You can use the most sophisticated formula in the world, but the result always deviates from the actual values. You can even use large number of simultaneous real time Monte Carlo simulations with variable inputs, but it's pointless. The market is still unpredictable. There is no way around this.

ATR * Sqrt(Time) works just fine for me. I've done a lot of backtesting with this simple formula and the results completely satisfy my needs (I only need rough estimation as a reference). Also it's quite easy to manipulate the values with external multipliers or multipliers based on some other data.

The whole thing is a bit like comparing apples and oranges in order to decide which one is better. Or we can argue which MA calculation is better and more accurate. SMA or EMA.
  • #16
  • Jan 31, 2018 12:02am Jan 31, 2018 12:02am
Quoting GoldTheHun
{quote} ATR * Sqrt(Time) is wrong. I tried it long time ago. ATR gives out artificialy high values.. The correct way is (MathLog(Close / Close[1]) * Sqrt(Time) )*ZScore The results are very realistic in showing the possible deviation boundaries.....
How is the ZScore calculated ?

Thanks
  • #17
  • Jan 31, 2018 12:29am Jan 31, 2018 12:29am
Quoting Mingary
{quote} How is the ZScore calculated ? Thanks
The z-score (z) for a data
item x measures the distance (in standard deviations StdDev) and direction
of the item from its mean (U):
z = (x-StdDev) / U
A value of zero indicates that the data item x is equal to the mean U, while
positive or negative values show that the data item is above (x>U) or below
(x Values of +2 and -2 show that the data item is two standard deviations
above or below the chosen mean, respectively, and over 95.5% of all data
items are contained within these two horizontal references (see Figure 1).
We substitute x with the closing price C, the mean U with simple moving
average ( SMA (https://www.tradingview.com/scripts/simplemovingaverage/) ) of n periods (n), and StdDev with the standard deviation of
closing prices for n periods, the above formula becomes:
Z_score = (C - SMA (https://www.tradingview.com/scripts/simplemovingaverage/) (n)) / StdDev(C,n)

https://www.tradingview.com/script/TX4QupA2-Z-Score-Strategy/

One more thing to add to my long list of programming projects.
  • #18
  • Jan 31, 2018 12:46am Jan 31, 2018 12:46am
May i ask why is binary options deemed a scam? I have just deposited at a broker and was going to share my experience along with my trades for everyone to see, but after what you have stated, i have thought about it twice.
  • #19
  • Jan 31, 2018 1:11am Jan 31, 2018 1:11am
Quoting Harp
May i ask why is binary options deemed a scam? I have just deposited at a broker and was going to share my experience along with my trades for everyone to see, but after what you have stated, i have thought about it twice.
What is the payout when you win, what is the payout when you lose ?
  • #20
  • Jan 31, 2018 1:39am Jan 31, 2018 1:39am
Quoting alphaomega
{quote} Thanks for sharing this! I will try your formula. However IMO the volatility is impossible to predict with high accuracy regardless of the formula. You can use the most sophisticated formula in the world, but the result always deviates from the actual values. You can even use large number of simultaneous real time Monte Carlo simulations with variable inputs, but it's pointless. The market is still unpredictable. There is no way around this. ATR * Sqrt(Time) works just fine for me. I've done a lot of backtesting with this simple formula...
Hi Alpha, I respect your view. But ATR * Sqrt(Time) has no valid grounds.. It might work for you, but you have to fit some multiplier to it in order for it to work.
Ex: ATR * Sqrt(Time) * Multiplier
The value of this multiplier has to found by some kind of optimization.

However in the other method the multiplier is the ZScore (1, 1.96, 2.58) just to name a few significant ones. It is a proven statistical method.

Of course one can always argue that the trading price returns are not based on normal distribution, which is true...

Good Luck...
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