Binary options

Cash-or-nothing binary options. The call pays 1 if spot > strike at expiry, otherwise 0; the put is symmetric. Greek functions return both call and put values in a single call.

Contract: Binary.sol

Functions

Conventions

• spot, strike — uint128, 18-decimal fixed-point (1e18 = 1.0).
• timeToExp — uint32, seconds to expiration.
• volatility — uint64, annualized vol as 18-decimal fixed-point (e.g. 50% → 5e17).
• rate — uint64, annualized risk-free rate as 18-decimal fixed-point.
• Unit payout. All results assume a payout of 1. Multiply the result externally for an arbitrary payout Q.
• All functions are internal pure.

Quick example

import "defimath-lib/contracts/derivatives/Binary.sol";

uint256 binCall = DeFiMathBinary.binaryCallPrice(spot, strike, timeToExp, vol, rate);
uint256 binPut  = DeFiMathBinary.binaryPutPrice (spot, strike, timeToExp, vol, rate);

// All binary Greeks return (call, put) tuples.
(int128 dC, int128 dP) = DeFiMathBinary.binaryDelta(spot, strike, timeToExp, vol, rate);

Important notes

• All four Greeks return tuples. Unlike vanilla options (where gamma and vega are equal for call and put under put-call parity), binary call and put have different second-order sensitivities — so all of binaryDelta, binaryGamma, binaryTheta, and binaryVega return (call, put).
• Unit payout — scale externally. To price a digital with payout Q, compute the unit-payout price and multiply by Q on the call site.
• binaryTheta is per day. The result is the price change for a one-day decrease in time to expiration.
• binaryVega is per 1% vol. The result is the price change for a 1-percentage-point change in volatility.
• When to use binary vs. vanilla. Use binaries when the payout is discrete (prediction markets, depeg coverage, threshold hedges). For continuous payoff structures, reach for the Options module.

Limits & errors