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I've recently gotten into binary options trading. I've tried multiple brokers like deriv, IQ options,Pocket options etc. What I want to know is how these brokers give the return value for a winning bet. what variables are they considering?

I thought about it for a bit and I think there are only three main aspects that they can consider:

Market: Trends, volatility, news ...

Broker's inner data: Their reserves, marketing...

User behavior: Succes rate of users, their reaction to return rate, average bets...

Since the rates these brokers offer are fairly similar I think the algorithm they are using is not complex so I doubt the consider all of this data. what are the main variables these brokers consider?

Thanks in advance.

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  • Are these brokers taking the opposite side of your bet or just facilitating bets between clients? If it's the latter, then it's just supply/demand - meaning what are the counterparties willing to pay if the bat pays off?
    – D Stanley
    Jan 17, 2023 at 21:23
  • @DStanley no they take opposite side of clients bet, and they have the same return rates for all clients at any given time.
    – Anthraxff
    Jan 17, 2023 at 21:31

4 Answers 4

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Binary options are also called digitals. In the flat vol Black-Scholes (BS) world using the usual BS notation, the fair price of the cash or nothing option is:

e^(โˆ’rt)*N(d2) which is the discounted probability of the option expiring in the money.

In reality, market makers price a digital as a tight call spread to capture skewness. For example, setting strikes at ๐พยฑ = ๐พ ยฑ1/2๐‘‘๐พ, in the limit of ๐‘‘๐พ โ†’ 0, the payoff approaches that of a digital. The reason is that a tight call spread, by using two vanilla options, effectively accounts for the volatility smile skew. I doubt your brokers do that themselves but rather have a direct link to actual market makers via professional trading systems like 360T or Bloomberg FXGO and the like.

Theoretically, an infinitesimally small spread will price a digital exactly. However, the required notional becomes increasingly large. Therefore, there is a trade-off between being partially unhedged and liquidity considerations. Why? A digital call is replicated by buying a call at the lower strike and selling a call at the upper strike. Think for example of EURUSD (CCY1CCY2 to make it generic), with notional in EUR and payment in USD. A call spread will pay max(0, ๐‘†_t โˆ’ ๐พ_{๐‘™๐‘œ๐‘ค๐‘’๐‘Ÿ}) โˆ’ min(0, ๐‘†_๐‘ก โˆ’ ๐พ_{๐‘ข๐‘๐‘๐‘’๐‘Ÿ}).

Specifically, the call spread is implemented as ๐ท๐‘–๐‘”๐‘–๐‘ก๐‘Ž๐‘™ = ๐ต๐‘†(๐พ +1/2๐‘‘๐พ, ๐‘ฃ๐‘œ๐‘™(๐พ +1/2๐‘‘๐พ)) โˆ’ ๐ต๐‘†(๐พ -1/2๐‘‘๐พ, ๐‘ฃ๐‘œ๐‘™(๐พ -1/2๐‘‘๐พ)) with ๐‘‘๐พ = 1% for example, i.e. 1/2๐‘‘๐พ = 0.005. This notation shows that each strike has its own associated IVOL.

Below the lower strike, both options are OTM and expire worthless. The payoff is net zero above the upper strike. The area in between is not fully hedged and max profit equals the spread (๐‘†_๐‘ก โˆ’ ๐พ_{๐‘™๐‘œ๐‘ค๐‘’๐‘Ÿ}) โˆ’ (๐‘†_๐‘ก โˆ’ ๐พ_{๐‘ข๐‘๐‘๐‘’๐‘Ÿ}) = ๐พ_{๐‘ข๐‘๐‘๐‘’๐‘Ÿ} โˆ’ ๐พ_{๐‘™๐‘œ๐‘ค๐‘’๐‘Ÿ}. As long as CCY1 notional corresponds to the desired payoff in CCY2, any desired CCY2 payoff can be achieved by scaling the notional by 1/๐‘‘๐พ. Therefore, the smaller the spread, the larger the notional.

If the underlying expires (๐‘†_๐‘’) in a small region ๐พ < ๐‘†_๐‘’ < ๐พ + ๐œ– where ๐œ– < ๐‘‘๐พ/2 then a seller of the digital has to pay out more than the hedge nets. If on the other hand, you set the strikes as ๐พ_โˆ’ = ๐พ-๐‘‘๐พ/2 and ๐พ, then you make money regardless of where the underlying expires. This is called an over-hedge as illustrated in the figure below.

enter image description here

An over-hedge will cost more than the centred hedge on the barrier strike, because its payoff is strictly higher. That is a detail that is omitted in the figure above (the payoff diagrams would shift slightly, reflecting different costs for the premium).

Market makers frequently make the spread expiry and vol dependent. That is something you will typically not find at vendors like Bloomberg (their internal pricer, not what market makers show on FXGO) where spreads are simply kept constant for all digitals (like the 1% illustrated above).

Theoretically, there exists another way of computing the value of a digital by using BS and adjust it numerically. Digital = BS_{dig} + cp โˆ— BS_{vega} โˆ— (dvol / dK) where BS_{dig} = N(d2), cp is a call or put flag and dvol / dK is done numerically.

However, the preferred way of pricing digitals is via call spreads.

On a side remark, do not invest in something that you do not understand. If you cannot explain the investment opportunity in a few words and in an understandable way, you may need to reconsider the potential investment.

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Binary options can be priced with the same types of probabilistic methods that non-binary options are priced with - the difference is simply the payoff function. The math to price a binary option using "binomial tree" methods is the exact same method as binomial models for american options. So most likely they are all priced similarly because they all use the same models. If they varied significantly, you could probably come up with some sort of arbitrage between these brokers and listed, non-binary options.

The inputs to these models are not based on marketing, revenue, "intuition" or anything other then available market data for non-binary options - specifically, the implied volatility of these options. That implied volatility is then used in the binary option models that use the same probabilistic methods.

To minimize their risk, the brokers are most likely taking offsetting bets with other counterparties, or managing their exposure through listed options or other derivatives. I highly doubt they have any significant exposure to any one company/crypto/fx/whatever.

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When it comes down to it, binary options are gambling under another name. When you place a bet on which football team will win a match, you're not investing in a football team, you're betting against a bookmaker.

The same goes for binary options. You're betting against the broker. Like any bookmaker, they won't have the time to intensely study everything they offer an option on. Instead they will set the odds so that they win most of the time. So long as most customers lose money in the long term, they are happy.

And most customers do lose money in the long term.

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  • yeah, this is how I imagined it would be, but since there is competition among these brokers, by what logic they can give the highest possible return rate to stay above competition?
    – Anthraxff
    Jan 17, 2023 at 21:54
  • @aSimpleTrader if you want to beat the competition, study what the competition are offering. But it may be more profitable to offer worse odds, but advertise more.
    – Simon B
    Jan 17, 2023 at 22:19
  • This is also true of all stocks, currencies and derivatives, so I'm not sure it adds a whole lot to say it's true of binary options in particular. Yes, binary options do seem to give the broker more opportunities to take your money because they are apparently not regulated for fairness. Jan 18, 2023 at 11:22
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The two options pricing models I'm familiar with are the binomial pricing model and the Black-Scholes model (or Black-Scholes-Merton). Both of these set a lot of assumptions, e.g. the return profile for the underlying in Black-Scholes is a normal distribution and independent of the previous period's return, and volatility is assumed to be constant throughout the period.

If those companies use the above pricing models or even an expanded version of the above, you're right that there are many variables they aren't accounting for. They'll dedicate resources to determine the best values for the variables they do use, balanced with the cost of adding more resources to be "more right". After all, as Simon said, they don't need to be right every time, they just need to be right enough to make a consistent profit.

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