stock-options

A Rust library for calculating option pricing Greeks using the Black-Scholes and Bjerksund-Stensland models.

Features

• Black-Scholes Model: Calculate Greeks for European-style options
• Bjerksund-Stensland Model: Calculate Greeks for American-style options with early exercise
• Complete Greeks Suite: Delta, Gamma, Theta, Vega, and Rho
• Batch Calculation: Calculate all Greeks at once with all_greeks()
• Type-Safe: Strongly typed OptionType enum prevents errors
• Zero Dependencies on NumPy/SciPy: Pure Rust implementation using statrs

Installation

Add this to your Cargo.toml:

[dependencies]
stock-options = { git = "https://github.com/ajokela/stock-options" }

Usage

Basic Example

use stock_options::{black_scholes, bjerksund_stensland, OptionType};

fn main() {
    // Parameters
    let s = 100.0;      // Current stock price
    let k = 105.0;      // Strike price
    let t = 0.5;        // Time to expiration (years)
    let r = 0.05;       // Risk-free interest rate
    let sigma = 0.2;    // Volatility
    let q = 0.01;       // Dividend yield

    // Calculate Black-Scholes delta for a call option
    let delta = black_scholes::delta(s, k, t, r, sigma, q, OptionType::Call).unwrap();
    println!("Black-Scholes Call Delta: {:.4}", delta);

    // Calculate Black-Scholes delta for a put option
    let put_delta = black_scholes::delta(s, k, t, r, sigma, q, OptionType::Put).unwrap();
    println!("Black-Scholes Put Delta: {:.4}", put_delta);
}

Calculate All Greeks at Once

use stock_options::{black_scholes, OptionType};

fn main() {
    let greeks = black_scholes::all_greeks(
        100.0,              // Stock price
        105.0,              // Strike price
        0.5,                // Time to expiration
        0.05,               // Risk-free rate
        0.2,                // Volatility
        0.01,               // Dividend yield
        OptionType::Call
    ).unwrap();

    println!("Delta: {:.4}", greeks.delta);
    println!("Gamma: {:.4}", greeks.gamma);
    println!("Theta: {:.4} (per day)", greeks.theta);
    println!("Vega:  {:.4}", greeks.vega);
    println!("Rho:   {:.4} (per 1% rate change)", greeks.rho);
}

American Options with Bjerksund-Stensland

use stock_options::{bjerksund_stensland, OptionType};

fn main() {
    // American options can be exercised early, which affects their pricing
    let american_greeks = bjerksund_stensland::all_greeks(
        100.0,              // Stock price
        95.0,               // Strike price
        1.0,                // Time to expiration
        0.05,               // Risk-free rate
        0.25,               // Volatility
        0.02,               // Dividend yield
        OptionType::Put
    ).unwrap();

    println!("American Put Greeks:");
    println!("  Delta: {:.4}", american_greeks.delta);
    println!("  Gamma: {:.4}", american_greeks.gamma);
    println!("  Theta: {:.4}", american_greeks.theta);
    println!("  Vega:  {:.4}", american_greeks.vega);
    println!("  Rho:   {:.4}", american_greeks.rho);
}

API Reference

Types

OptionType

pub enum OptionType {
    Call,
    Put,
}

Greeks

pub struct Greeks {
    pub delta: f64,
    pub gamma: f64,
    pub theta: f64,  // Per day
    pub vega: f64,
    pub rho: f64,    // Per 1% change in interest rate
}

Black-Scholes Functions (European Options)

All functions take the following parameters:

• s: f64 - Current price of the underlying asset
• k: f64 - Strike price of the option
• t: f64 - Time to expiration in years
• r: f64 - Risk-free interest rate (e.g., 0.05 for 5%)
• sigma: f64 - Volatility of the underlying asset (e.g., 0.2 for 20%)
• q: f64 - Dividend yield (e.g., 0.01 for 1%)
• option_type: OptionType - Call or Put (where applicable)

Bjerksund-Stensland Functions (American Options)

Same parameters as Black-Scholes functions.

The Greeks Explained

Model Comparison

License

This project is licensed under the BSD 3-Clause License - see the LICENSE file for details.

References

• Black, F., & Scholes, M. (1973). The Pricing of Options and Corporate Liabilities. Journal of Political Economy, 81(3), 637-654.
• Bjerksund, P., & Stensland, G. (2002). Closed Form Valuation of American Options. Discussion paper 2002/09, Norwegian School of Economics.