Binary options pricing and Greeks

DeFiMath now supports binary (cash-or-nothing) options end-to-end, with both call and put pricing plus the full Greek set. All functions assume a unit payout of 1 — scale the result for any payout size.

New functions:

• binaryCallPrice — Black-Scholes price of a binary call (pays 1 if spot > strike at expiry, else 0). Computes e^(-r·τ) · Φ(d2).
• binaryPutPrice — Black-Scholes price of a binary put (pays 1 if spot < strike at expiry, else 0).
• binaryDelta — first-order sensitivity to the underlying price. Returns both call and put delta in a single call.
• binaryGamma — second-order sensitivity to the underlying price (rate of change of delta). Returns both call and put.
• binaryTheta — sensitivity to time, expressed per day. Returns both call and put.
• binaryVega — sensitivity to volatility, expressed per 1% change in vol. Returns both call and put.

This rounds out the binary options surface alongside the existing vanilla options support.

Use cases

Binary options are the natural pricing primitive for any discrete, yes/no payoff. On-chain, the most obvious application is prediction markets — fair-value pricing for binary outcome shares (e.g. "will price > X at time T?") on Polymarket-style protocols. The same math underpins depeg and catastrophic-event insurance: protocols that pay out a fixed amount if a stablecoin breaks its peg, an oracle price crosses a threshold, or a similar discrete event occurs.

Beyond that, binary pricing is what structured yield products need when they sell binaries to collect premium income — price and Greeks drive the risk management. Binaries also work as threshold-based hedges against specific triggers (liquidation levels, oracle bands, knock-out barriers) and as the pricing layer for conditional rewards and incentives that depend on an observable on-chain condition being met by a deadline.

See the DeFiMath GitHub repo for full source and usage examples.