Digital Options

digital options
Digital Options – Financial Market’s Machine Code

What Are Digital Options?

Digital options are the machine code of financial markets. In the same manner that machine code’s ‘0’s and ‘1’s are at the base of all software programs, all financial instruments can be broken down into their core components of digitals.

Different Digital Options Handles

Digital options have a number of other names such as ‘binary options’, ‘all-or-nothing options’, fixed odds return (FRO) options’, ‘Countdowns’, etc.. Even the most elementary of barrier options, the up-and-in cash-or-nothing and the down-and-in cash or nothing are digitals.

Digital Options, Binary Options (& Trinary Options)

Binary options provide two choices for the settlement value, 0 or 1. Yet this constraint of the ‘binary’ option throws up an immediate issue related to the underlying asset price settling exactly on the strike. What should the settlement price then be? The obvious choice would suggest 0.5. Suddenly binary options have become ‘trinary options’.

Conventional Options Pin-Risk

Digital OptionsOn this site digital options values are constrained to 0 and 1 inclusive. This means that a call or put can settle at 0.5. Why is this important? As a (well-seasoned) conventional options market-maker being ‘pinned’ at expiry was always an unwelcome risk for non-cash settled options, i.e. options where one might have to take delivery of the underlying asset. This would become extremely dangerous at expiry if one had a few thousand ‘pinned’ conversions or reversals on board as one would need to wait to find out how many of the short options had been exercised.

Example: I am long 1,000 100.00 calls, short 1,000 100.00 puts and short 1,000 futures. At any other time than expiry this is a zero risk position as early exercise does not make economic sense.
So how many calls should I exercise, if any? On the few times I was stuck in this predicament I gambled 50% exercise. This would leave with a position that was short 500 futures and short 1,000 puts, or short 500 straddles for zero. Not a great position!
This state of affairs would last until the CCH condescends to tell me how many I had been exercised on. If 500 then I’m flat, if 0 or 1,000 I have a long or short 500 position potentially and one can be sure it will always have gone against you.

Binary Options Pin-Risk

The binary version of this is to settle the calls at 1.00 and puts at 0. Apart from the fact that this is obviously unfair on the binary put holders, the market makers who are long puts and short calls get a similar ‘pin risk’ battering when all they want is to be able to manage a portfolio of options in a limited risk manner. Should the binary options permit settlement of ‘pinned’ options to settle at 0.5 then there is no risk for cash-settled options. But now we have three possible settlement prices, 0, 0.5 and 1.00 (trinary options?).

The ability of digitals to settle within the range of zero to one has three specific advantages:

  1. the aforementioned pin risk is alleviated for options market-makers, and
  2. structures of digital options can now settle at any value between zero and one which now opens up a whole new possibility of strategies, which in turn leads to,
  3. regulators taking a more sympathetic stance to digitals as they are no longer ‘all-or-nothing’ punts.


The following pages offer a rare abundance of digitals.

European Digitals American Digitals Knock-In Digitals Knock-Out Digitals Two-Asset Digitals

European Digitals

‘European’ has no geographical relevance. The term purely means that the option cannot be exercised prior to the option’s expiry.  The most basic of all financial instruments in existence are the digital call and put. Various amalgamations of the call and put lead to a range of instruments that provide the user with a huge increase in choice.

American Digitals

Yet again the ‘American’ terminology has no geographical relevance. A more representative name would be ‘Touch Options’ since as soon as the strike is traded at or through then the position has deemed to be won or lost. Yet again combinations of One-Touch Calls and One-Touch Puts lead to a further range of instruments.

Knock-In Digitals

These instruments require the asset price to touch a barrier for the instrument to morph into, generally, a different instrument. Examples are down-and-in digital call, up-and-in digital put, down-and-in digital put, etc..

They are highly specialised instruments traded over-the-counter (OTC).

Knock-Out Digitals

These can be considered as the opposite to knock-ins as the barrier is now a no-go area where, if hit, the instrument immediately is KO’d and worthless. Examples are down-and-out digital call, up-and-out digital call, up-and-out digital puts, etc..

Knock-outs are also traded OTC but are sometimes marketed to retail customers as ‘Turbos’. Turbos are particularly popular amongst the German trading community.

Two-Asset Digitals

These require the asset prices of two separate assets to adhere to a predefined status at expiry. The trades are usually ‘European’ and only winners and losers are identified at expiry. Examples are spread options, double digital calls, and pyramid options.

The complexity of these options necessitates only being traded on the OTC market. A major feature of the complexity is  that two-asset digitals need to have their correlation analysed. This can be a complicated process in its own right as very often the price will be dependent on the term structure of the correlation coefficient.

Financial Regulation

A site focusing on digital options would be incomplete without a take on regulation. Bland definitions of ‘investment’ and ‘gambling’ do little to define the difference. Indeed, there is a provocative view put forward that investment does not exist, that everything is gambling.

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