Have you ever wondered how the pricing of derivatives works behind the scenes? Pricing derivatives, and specifically binary options, is quite a challenge from the market making perspective. With years of experience as a broker and market maker in the OTC derivatives market, and currently as the head of market making and risk analysis at SpotOption, I would like to provide some insight on how pricing works for binary options. In this document, I will describe two main methodologies that we actively practice, each one with its own advantages and disadvantage.
Methodology 1: Deriving the binary option price from market quotes of vanilla “call” or “put” spread
There are many variations of this well-known formula, the most popular is the classic B&S, for a “call” option:
In general, once you have the standard deviation, the spot rate and interest rate of any long term Vanilla option can be priced for a specific expiry and strike rate. A vanilla option is a simple option that allows the buyer of the option the opportunity (not the obligation) to buy an underlying asset at a predetermined price/strike price for a price or premium. This opportunity will have an expiry at a future and predetermined date. The following chart shows a call option that started with a negative value to the cost of the option, and increases as the underlying asset increases above the strike price:
The Seller of the option is on the other side of this zero sum game, and he receives a premium for the risk that is taken. If the price goes higher than the strike price, he will start to lose money as can be seen on the chart below:
A combination of buying a call option, and selling another call option with a higher strike price is often referred to as a call or bull spread strategy. A combination of buying a put option and selling another put option with a lower strike is often refereed to as a put or bear spread strategy. An example of a call spread strategy looks like the chart below.
The premium for the call spread strategy is lower than a simple call option, however, the profit has maxed at the strike of the call option that has been sold. This strategy can be easily priced for options with maturity date longer than a week as the market volatility is well known. A binary option (unlike the vanilla call option) gives a fixed payout for the call option. In many ways it looks like the call spread strategy where the strike of the call option sold is higher than the strike of the call option bought by a number so small that is close to zero.
So, when pricing a long call binary option, one of the possible methodologies is to buy call option at a strike of X and sell call option of a price of X plus 0.00000001. This methodology is robust where markets are liquid and quotes of options and standard deviations are available. This high liquidity can be found in assets with high volumes and expires longer than a week.
When pricing options for shorter period of times, such as “end of day”, a different methodology can be used.
Methodology 2: Deriving the binary option price from a call or put spread when there are no market quotes
Unlike long term binary options (day, weeks or month), when trying to price an option for a few minutes or hours, there is no well known and agreed standard deviation quoted in the markets. Therefore one should individually calculate the market deviation using the last known ticks. For example, if we wish to price a binary option for 10 minutes we can manually calculate the standard deviation using best practice formulas:
The only question is, what time period should be taken when calculating this standard deviation? My experience has taught me that for single-hour options, the standard deviation should be taken based on up to 3 hours back-log, as long as you stay in the same trading session. That is, if we are trading in the European session, we can create the standard deviation by looking at the last few hours as long as we don’t go before the opening of the main European markets. The advantage of this model is the ability to price the binary option using a standard deviation when there is no quotes in Reuters or Bloomberg terminal for those standard deviations. The disadvantage of this algorithm is that you quote an option based on a theoretical quotes, with no other market quotes to compare to, and if calculated incorrectly, it can lead to losses.
Pricing short term binary options is quite a challenge, but can be done rationally. When pricing a short term binary option, one must calculate the volatility manually through known formulas and parameters optimization (as described in Methodology 2). Pricing long term options, such as those that expire in days, weeks, and months is relatively easier. One simply has to take a well-known formula, such as black and Scholes, and insert the spot market rate, volatility or the volatility surface, as well as the interest rates, and you price the call or put spread. The relevant data can be taken from different data suppliers such as Bloomberg or Reuters, or derived from exchange traded options.
Quotes of binary options, both for long or short term can be seen in exchanges of binary options or through the OTC market, such as the SpotOption Platform.
Back to Blog