A binary option (digital option) whose underlying is the correlation between two assets or indices: the measurement instrument and the payment instrument. Correlation digital options can be particularly instrumental for hedging specific types of swaps or investments in which events in one market trigger actions in another market. For example, consider the case of an investor who contemplates selling his shares in a given company (XYZ) if the price reaches $40 at the end of the year and investing the proceeds in short-term government bonds for a guaranteed return of 7% at least. In this situation, the measurement asset is the share of the price of company XYZ with a strike price of $40.

The payment asset is the futures price of the short-term interest rate where the gap parameter is 100%- 7% = 93%. Thus, if at maturity the share price is above $40 and interest rates have dropped to 5% so that the interest rate futures price is 100%-5%= 95%, the investor will exercise the option and acquires the bonds at 93% of par. At maturity, the payoff of a European-style correlation digital option is:

Payoff = S_T – G if M ≥ X and 0 otherwise.

where: S is the payment asset, G is the gap, X is the exercise price, and M is the measurement asset.

This option is also known as a correlation binary option.