Digital Option

A digital option contract pays out a fixed amount on the condition that a certain event happens, while paying 0 otherwise. At expiry the payoff for the Long side is:

$$N\mathbb{I}_{S\geq K}$$

for digital call option, where:

• $\mathbb{I}$ is the indicator function

• N is the digital size i.e. the payout

• S is the underlying price at expiry

• K is the strike price

For a digital put option, the inequality is reversed:

$$N\mathbb{I}_{S< K}$$

Payoff profile of a digital call for $N=100$ and $K=100$

Example

Alice and Bob enter in a Digital Call option contract on SOL/USD. The contract has a digital of 100 USDC, and the strike is set to $30. Alice deposits the option premium of 25 USDC, while Bob deposits 100 USDC as collateral (the max payout).

After 1 week has passed, the profit & loss will depend on the final price of SOL/USD:

• if SOL/USD is at $30 or above, the profit for Alice will be $100 minus the premium paid. So she will claim 100 USDC from the contract (+75 USDC PnL). Bob will only be able to claim the premium earned, 25 USDC

• if SOL/USD is below $30, the option expires worthless. Alice will lose the option premium, while Bob will able to claim 25 USDC + his original collateral of 100 USDC