A Black-Scholes options pricer in Rust, compiled to WASM

What Black-Scholes computes

The Black-Scholes model prices European options on a non-dividend-paying underlying. Given five market inputs — spot price (S), strike (K), time to expiry (T), risk-free rate (r), and implied volatility (σ) — the formula produces a fair-value price plus five sensitivity measures called the Greeks: Delta (Δ, price sensitivity to spot), Gamma (Γ, rate of change of delta), Theta (Θ, daily time decay), Vega (sensitivity to volatility), and Rho (ρ, sensitivity to the risk-free rate). The formula is closed-form — no simulation, no iteration — so it is fast and deterministic for a given set of inputs.

The formulas here follow the standard derivation from Fischer Black and Myron Scholes (1973), with the cumulative normal distribution approximated via the Abramowitz and Stegun 26.2.17 rational polynomial (maximum absolute error 7.5×10⁻⁸). All arithmetic is IEEE 754 double-precision.

Why Rust compiled to WASM, not JavaScript

A JavaScript implementation would be concise and fully sufficient for this level of precision. The reason to use Rust compiled to WebAssembly here is signal rather than necessity: the Network tab shows a .wasm binary loading, the JavaScript glue is generated automatically by wasm-pack, and the Rust source is the specification — not a translation layer that can diverge from intent.

The other consideration is correctness in the tail. Rust’s type system makes the degenerate cases explicit. When T ≤ 0 or σ ≤ 0 the function returns the intrinsic value rather than NaN or a panic. The #[wasm_bindgen] entry point deserialises its input with serde-wasm-bindgen; if the input is malformed it returns zeroed output rather than throwing. That boundary hardening is easier to express and verify in Rust than in hand-written JavaScript.

The compiled binary is 62 KB raw, 27 KB gzipped — smaller than most hero images. It loads with client:visible, so it only fetches when the island scrolls into view. The compute itself is sub-millisecond on any device capable of loading the page.

How to read the Greeks

Move the sliders and watch the readout update. A few reference points:

• Delta is the hedge ratio. A call with delta 0.50 gains roughly $0.50 per $1.00 spot move. At-the-money calls have delta near 0.5; deeply in-the-money calls approach 1.0. Put deltas are negative and range from 0 to −1.
• Gamma is highest at-the-money near expiry — that is where the hedge ratio changes most rapidly per spot move.
• Theta shows as a negative number for long options: holding the option costs you time decay each day. Long gamma positions pay theta; short gamma positions collect it.
• Vega (per 1% volatility move) is largest for at-the-money options with time remaining. It collapses as expiry approaches.
• Rho matters most for longer-dated options; its effect is small at the low interest-rate levels typical of recent history.

Live pricer

Adjust spot price, strike, time to expiry, rate, and volatility below. The call and put prices update instantly via the WASM module — no network request, no server, no latency.

The source for the Rust crate is at apps/api/crates/blackscholes-wasm/src/lib.rs in the portfolio repository. Unit tests cover the ATM textbook values from Hull’s Options, Futures, and Other Derivatives, put-call parity across four parameter sets, deep-OTM price approaching zero, and deep-ITM put delta approaching −1.