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Binary Options

## Introduction

A Binary Option is an option with a fixed, pre-determined payoff if the underlying instrument or index is at or above the strike at expiration. The value of the payoff is not affected by the size of the difference between the underlying and the strike price, and can be in the form of a cash payment or delivery of the underlying. The options described here are path independent, which means that the payout profile depends only on the value of the underlying asset on the expiration date of the option. For a call, the payout is received if the underlying asset price is greater than the strike price, and for a put, the payout is received if the strike is greater than the underlying asset price.

## Technical Details

The simplest Binary (also known as Digital) options are cash-or-nothing and asset-or-nothing options. In a cash-or-nothing option, a predetermined amount is paid if the asset is, at option expiry, above (call) or below (put) some strike level, independent of the path taken. An asset-or-nothing option is similar to a cash-or-nothing option except that the holder of the option is entitled to either the full asset value - at option expiry - or nothing.

A simple generalization of the asset-or-nothing option is a digital-gap-option. A digital gap option has a payout profile equal to the asset value, less the gap value, depending on whether the asset finishes above or below the strike price. It is clear that a digital gap option is simply the difference between an asset-or-nothing and a cash-or-nothing digital option with the cash amount set to the gap value.

## Analysis Supported

FINCAD Binary options functions can be used for the following:

• Calculate the fair value and delta for a path independent digital (or binary) gap option. The payout at expiry, if the option is in-the-money, is equal to the asset value, less the gap value.
• Calculate the fair value and risk statistics for a path independent digital (or binary) all-or-nothing option. The payout at expiry, if the option is in-the-money, requires the delivery of either a specified cash amount or the underlying asset.

To evaluate an FINCAD product that can value Binary Options, contact a FINCAD Representative

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