European digital options are conceptually one of the simplest exotic products; at maturity the option either pays out a fixed cash amount or nothing, depending on whether spot is above or below a specified digital level. However, the risk management of these options, particularly at expiry, can be challenging due to the binary nature of the payout (either receive all the cash or none) over a one-pip spot difference.
A European digital call option pays out cash on the delivery date if spot at maturity is at or above the digital level, as shown in Exhibit 21.1. While a European digital put option pays out cash on the delivery date if spot at maturity is below the digital level.
As a technical aside, the European digital call here is defined as paying out at the digital level while the European digital put does not. This is not necessarily the case but it is important that European digital put + European digital call = guaranteed payout at maturity. Put another way, transacting both the digital put and digital call with all other details the same should not result in both contracts paying out. In practice these issues are dealt with via the confirmation documents agreed when trading the contract.
European digital options prices are quoted as a percent of the payout amount, with prices ...