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Digital Options are also called as 'Binary Options' or 'All or Nothing Options'. They are generally European options with a limited profit and loss to both buyer and seller. If the option is In-the-Money (ITM), the payoff is 1 unit of regardless of the current market price of the underlying. If the option is At-the-Money (ATM) or Out-of-the-Money (OTM), it pays zero or nothing. The payoff is like the binary digits of 1 and 0 and hence their name 'digital options'.

The 1 unit of payment can be either in "cash" or "asset". If the payoff is in cash, the option is called as "Cash or Nothing" digital option or "CON" in short. If the payoff is in the form of an an asset (usually the underlying), the option is called as "Asset or Nothing" digital option or "AON" in short. Just like any other plain vanilla option, there can be both calls or puts on the options. The following table shows the payoff in both puts and calls.

Digital | Calls | Puts | ||
---|---|---|---|---|

ITM | ATM or OTM | ITM | ATM or OTM | |

Cash or Nothing | 1 unit of cash | 0 | 1 unit of cash | 0 |

Asset or Nothing | 1 unit of asset | 0 | 1 unit of asset | 0 |

Long EUR Call on EUR/USD= Right to buy EUR by paying USD

which can also be interpreted as:

Right to sell USD by receiving EUR, which is equal to Long USD Put on EUR/USD.

The payoff in an FX option can be interpreted in the following manner.

Long EUR/USD means Right to buy EUR by paying USD.

This option is In-the-Money (ITM) when USD depreciates (or exchange rate increases) in comparison to EUR.

For example, let's suppose the initial exchange rate (or spot price) is 1.3, and the option, if ITM and exercised, pays 1.5. If the exchange rate becomes 1.4 on expiry date, it means that the value of EUR has increased in comparison to USD. The option is ITM at this point and if exercised, the cash payment would be the difference between 1.5 and 1.3 in terms of USD. That means, a Long EUR/USD digital option's payoff is in terms of the quoting currency, i.e. USD.

If we were to reverse the currency pair i.e. USD/EUR, then the payoff would be reversed too. A 'Cash or Nothing' Long USD/EUR if ITM would have a payoff in the the quoting currency, i.e. EUR.

If a Long EUR/USD FX Asset or Nothing Digital Option is ITM, the buyer will exercise his right to buy EUR and therefore the payoff will be in terms of the base currency, i.e. EUR. If we were to reverse the currency pair i.e. USD/EUR, then the payoff would be revesed too.

The following table shows the payoffs for both CON and AON options.

Currency Pair | Digital | Payoff |
---|---|---|

EURUSD | Cash or Nothing (CON) | 1 unit of USD |

EURUSD | Asset or Nothing (AON) | 1 unit of EUR |

USDEUR | Cash or Nothing (CON) | 1 unit of EUR |

USDEUR | Asset or Nothing (AON) | 1 unit of USD |

Long Call = Right to pay a Fixed Rate and receive Floating Rate

Short Call = Obligation to receive a Fixed Rate and Pay Floating Rate

Long Put = Right to receive a Fixed Rate and pay Floating Rate

Short Put = Obligation to pay Fixed Rate and receive Floating Rate

The strike price of the contract is the fixed rate. For example, a Long Call at 2.5% means that the buyer has the right to pay a fixed rate of 2.5% and receive the prevalent market rate (which is the floating rate) on the expiry of the option. Thus, the option is in-the-money (ITM) for the Call buyer if the floating rate is more than the fixed rate (strike price). For example, if the floating rate is 4% then the Call buyer can exercise his/her option and pay 2.5% fixed and receive 4% floating on the same notional amount thereby making a profit of 1.5% on the option. If the floating rate were to be 2% then the option is out-of-the-money (OTM) and therefore it will not be exercised.

Digital Interest Rate Options modify this payoff but delinking the floating rate (current market interest price) from the payoff, but still uses the floating rate to determine whether the option is ITM or OTM. If the option is ITM, then it will pay a pre-determined interest rate (say for example, 5%) irrespective of the floating rate. For example, if the digital payoff is set to be 5% or nothing and the floating rate at the time of expiry is 4%, then the Call buyer would be paid 2.5% (which is 5% determined minus 2.5% fixed), irrespective of the floating rate.

All interest rate options are settled in cash, and therefore they are only 'Cash or Nothing (CON)' type of options.

An interestig variant of the digital interest rate option is the

Digital Options are the fundamental building blocks for creating structured and other finacial engineering products.

__Updation History__

First updated on 22^{th} May 2021.