Options Pricing

Black-Scholes options pricing and Greeks calculations.

Overview

The financial-calc crate provides complete Black-Scholes-Merton model implementation including:

European call/put pricing
All five Greeks (delta, gamma, theta, vega, rho)
Implied volatility calculation
Standard normal CDF/PDF

Basic Usage

#![allow(unused)]
fn main() {
use financial_calc::options::{black_scholes_call, OptionParams};
use precision_core::Decimal;
use core::str::FromStr;

let params = OptionParams {
    spot: Decimal::from(100i64),           // Current price
    strike: Decimal::from(100i64),         // Strike price
    rate: Decimal::from_str("0.05")?,      // 5% risk-free rate
    time: Decimal::from_str("0.25")?,      // 3 months to expiry
    volatility: Decimal::from_str("0.2")?, // 20% annualized vol
};

let call_price = black_scholes_call(&params)?;
}

Greeks

Calculate all Greeks for risk management:

#![allow(unused)]
fn main() {
use financial_calc::options::{call_greeks, put_greeks};

let greeks = call_greeks(&params)?;

println!("Delta: {}", greeks.delta);  // Price sensitivity
println!("Gamma: {}", greeks.gamma);  // Delta sensitivity
println!("Theta: {}", greeks.theta);  // Time decay (per day)
println!("Vega: {}", greeks.vega);    // Vol sensitivity (per 1%)
println!("Rho: {}", greeks.rho);      // Rate sensitivity (per 1%)
}

Implied Volatility

Recover implied volatility from market prices using Newton-Raphson:

#![allow(unused)]
fn main() {
use financial_calc::options::implied_volatility;

let market_price = Decimal::from_str("10.5")?;
let iv = implied_volatility(
    market_price,
    &params,
    true,  // is_call
    None,  // max_iterations (default: 100)
    None,  // tolerance (default: 0.0001)
)?;
}

Put-Call Parity

The implementation satisfies put-call parity:

C - P = S - K * e^(-rT)

Both call and put prices are internally consistent.

Accuracy

Uses Hart approximation (1968) for normal CDF
Maximum CDF error: ~7.5×10⁻⁸
All calculations use deterministic decimal arithmetic

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