quantrs

Quantrs is a tiny quantitative finance library for Rust. It is designed to be as intuitive and easy to use as possible so that you can work with derivatives without the need to write complex code or have a PhD in reading QuantLib documentation. The library is still in the early stages of development, and many features are not yet implemented.

Please check out the documentation here.

Features

Options Pricing

Quantrs supports options pricing with various models for both vanilla and exotic options as well as options trading strategies for both basic options spreads and non-directional strategies.

Click to see supported models

	Black-Scholes	Black-76	Lattice	³Monte-Carlo	Finite Diff	Heston
European	✅	✅	✅	✅	⏳	⏳
American	❌	❌	✅	❌ (L. Sq.)	⏳	❌
Bermudan	❌	❌	✅	❌ (L. Sq.)	❌ (complex)	❌
¹Basket	⏳ (∀component)	❌	⏳ (approx.)	⏳	❌	❌
¹Rainbow	✅ (∀component)	❌	✅	✅	❌	❌
²Barrier	❌ (mod. BSM)	❌	⏳	⏳	⏳	⏳
²Double Barrier	❌ (mod. BSM)	❌	⏳	⏳	❌ (complex)	⏳
²Asian (fixed strike)	❌ (mod. BSM)	❌	❌	✅	⏳	⏳
²Asian (floating strike)	❌ (mod. BSM)	❌	❌	✅	⏳	⏳
²Lookback (fixed strike)	❌	❌	❌	✅	⏳	⏳
²Lookback (floating strike)	✅	❌	❌	✅	⏳	⏳
²Binary Cash-or-Nothing	✅	❌	✅	✅	❌ (mod. PDE)	⏳
²Binary Asset-or-Nothing	✅	❌	✅	✅	❌ (mod. PDE)	⏳
Greeks (Δ,ν,Θ,ρ,Γ)	✅	✅	⏳	❌	❌	❌
Implied Volatility	✅	⏳	⏳	❌	❌	❌

¹ "Exotic" options with standard exercise style; only differ in their payoff value
² Non-vanilla path-dependent "exotic" options
³ MC simulates underlying price paths based on geometric Brownian motion for Black-Scholes models and both arithmetic or geometric average price paths for Asian and Lookback options
✅ = Supported, ⏳ = Planned / In progress, ❌ = Not supported / Not applicable

Click to see supported strategies

Strategy Name	Type	Description
Covered Call	Income	Long stock + short call
Protective Put	Hedging	Long stock + long put
Guts	Volatility	Long ITM call + long ITM put
Straddle	Volatility	Long ATM call + long ATM put
Strangle	Volatility	Long OTM call + long OTM put
Butterfly Spread	¹Spread	Long ITM call, short two ATM calls, long OTM call (or all puts)
Iron Butterfly	¹Spread	Short straddle + long wings
Christmas Tree Butterfly	¹Spread	Long 1 ATM call, short 3 OTM calls, long 2 high-strike OTM calls (or all puts)
Condor Spread	¹Spread	Long low-strike ITM call, short ITM call, short OTM call, long high-strike OTM call (or all puts)
Iron Condor	¹Spread	Short strangle + long wings
Calendar Spread	²Time Spread	Long far-expiry ATM call + short near-expiry ATM call (or all puts)
Diagonal Spread	³Time Spread	Short near-expiry OTM call + long far-expiry further OTM call (or all puts)
Back Spread	Directional	Long 2 OTM calls + short 1 ATM call (or all puts)

¹ Also referred to as 'vertical'
² Also referred to as 'horizontal'
³ Also referred to as 'diagonal'

Usage

Add this to your Cargo.toml:

[dependencies]
quantrs = "0.1.6"

Now if you want to e.g., calculate the arbitrage-free price of a binary cash-or-nothing call using the Black-Scholes model, you can:

use quantrs::options::*;

// Create a new instrument with a spot price of 100 and a dividend yield of 2%
let instrument = Instrument::new().with_spot(100.0).with_cont_yield(0.02);

// Create a new Cash-or-Nothing binary call option with:
// - Strike price (K) = 85
// - Time to maturity (T) = 0.78 years
let option = BinaryOption::cash_or_nothing(instrument, 85.0, 0.78, Call);

// Create a new Black-Scholes model with:
// - Risk-free interest rate (r) = 5%
// - Volatility (σ) = 20%
let model = BlackScholesModel::new(0.05, 0.2);

// Calculate the price of the binary call option using the Black-Scholes model
println!("Price: {}", model.price(&option));

// Calculate first order greeks for the option
println!("{:?}", Greeks::calculate(&model, &option));

This will output:

Price: 0.8006934914644723
Greeks { delta: 0.013645840354947947, gamma: -0.0008813766475726433, theta: 0.17537248302290848, vega: -1.3749475702133236, rho: 0.4398346243436515 }

Plotting

Quantrs also supports plotting option prices and strategies using the plotters backend.

E.g., Plot the P/L of a slightly skewed Condor spread consisting of fixed-strike Asian calls using the Monte-Carlo model with the geometric average price path:

Click to see example code

use quantrs::options::*;

// Create a new instrument with a spot price of 100 and a dividend yield of 2%
let instrument = Instrument::new().with_spot(100.0).with_cont_yield(0.02);

// Create a vector of fixed-strike Asian calls options with different strike prices
let options = vec![
    AsianOption::fixed(instrument.clone(), 85.0, 1.0, Call),
    AsianOption::fixed(instrument.clone(), 95.0, 1.0, Call),
    AsianOption::fixed(instrument.clone(), 102.0, 1.0, Call),
    AsianOption::fixed(instrument.clone(), 115.0, 1.0, Call),
];

// Create a new Monte-Carlo model with:
// - Risk-free interest rate (r) = 5%
// - Volatility (σ) = 20%
// - Number of simulations = 10,000
// - Number of time steps = 252
let model = MonteCarloModel::geometric(0.05, 0.2, 10_000, 252);

// Plot a breakdown of the Condor spread with a spot price range of [80,120]
model.plot_strategy_breakdown(
    "Condor Example",
    model.condor(&options[0], &options[1], &options[2], &options[3]),
    80.0..120.0,
    "examples/images/strategy.png",
    &options,
);

See the documentation for more information and examples.

Benchmarks

Compared to other popular and well-maintained (i.e., actively developed, well-documented, and feature-rich) options pricing libraries, quantrs competes well in terms of performance: E.g., for pricing a European call with the Merton Black-Scholes model, quantrs is:

• 87x faster than py_vollib
• 29x faster than QuantLib (python bindings)
• 15x faster than RustQuant
• 3x faster than Q-Fin
• 1.7x slower than QuantLib (cpp)

Library	Mean Execution Time (μs)	Median Execution Time (μs)	Standard Deviation (μs)	Operations / Second (OPS)
quantrs	0.0971	0.0970	0.0007	10,142,000
py_vollib	8.5341	8.5210	0.8129	117,176
QuantLib (py)	2.8551	2.8630	0.9391	350,250
RustQuant	1.4777	1.4750	0.0237	676,727
Q-Fin	0.2900	0.2906	0.0448	3,447,870
QuantLib (cpp)	0.0556	n.a.	n.a.	17,958,600

You can find the benchmarks at quantrs.pages.dev/report.

Published benchmarks have been measured on a selfhosted VM with 32 GB RAM, AMD Ryzen 7 PRO 6850U @ 2.70GHz, and Manjaro Linux x86_64

Minimum supported Rust version (MSRV)

This crate requires a Rust version of 1.77.0 or higher. Increases in MSRV will be considered a semver non-breaking API change and require a version increase (PATCH until 1.0.0, MINOR after 1.0.0).

Outlook

See OUTLOOK.md for a list of planned features and improvements.

Contributing

If you find any bugs or have suggestions for improvement, please open a new issue or submit a pull request.

Disclaimer

This library is not intended for professional use. It is a hobby project and should be treated as such.

License

This project is licensed under either of:

• MIT license or
• Apache License, Version 2.0

at your option.

---

© Carlo Bortolan

Carlo Bortolan  ·  GitHub carlobortolan  ·  contact via [email protected]