A Rust library for quantitative finance tools. Also the largest option pricing library in Rust.

🎯 I want to hit a stable v0.1.0 by the end of 2023, so any feedback, suggestions, or contributions are strongly welcomed!

Email me at: RustQuantContact@gmail.com

Join the Discord server: https://discord.gg/tQcM77h8vr

📰 Latest features

See CHANGELOG.md for a full list of changes.

🔗 Automatic Differentiation

Reverse (Adjoint) Mode Automatic Differentiation.

Currently only gradients can be computed. Suggestions on how to extend the functionality to Hessian matrices are definitely welcome.

Additionally, only functions $f: \mathbb{R}^n \rightarrow \mathbb{R}$ (scalar output) are supported. However, you can manually apply the differentiation to multiple functions that could represent a vector output.

• Reverse (Adjoint) Mode
  • Implementation via Operator and Function Overloading.
  • Useful when number of outputs is smaller than number of inputs.
    • i.e for functions $f:\mathbb{R}^n \rightarrow \mathbb{R}^m$, where $m \ll n$
• Forward (Tangent) Mode
  • Implementation via Dual Numbers.
  • Useful when number of outputs is larger than number of inputs.
    • i.e. for functions $f:\mathbb{R}^n \rightarrow \mathbb{R}^m$, where $m \gg n$

useRustQuant::autodiff::*;fnmain(){// Create a new Graph to store the computations.let g = Graph::new();// Assign variables.let x = g.var(69.);let y = g.var(420.);// Define a function.let f = {let a = x.powi(2);let b = y.powi(2);
a + b + (x * y).exp()};// Accumulate the gradient.let gradient = f.accumulate();println!("Function = {}", f);println!("Gradient = {:?}", gradient.wrt([x, y]));}

You can also generate Graphviz (dot) code to visualize the computation graphs:

println!("{}", graphviz(&graph,&variables));

The computation graph from computing Black-Scholes Greeks is:

It is clearly a work in progress, but gives a general idea of how the computation graph is structured.

If you want to improve the visualization, please feel free to submit a PR!

📊 Data

Methods for reading and writing data from/to various sources (CSV, JSON, Parquet). Can also download data from Yahoo! Finance.

You can:

• Download data from Yahoo! Finance into a Polars DataFrame.
• Compute returns on the DataFrame you just downloaded.

useRustQuant::data::*;use time::macros::date;fnmain(){// New YahooFinanceData instance.// By default, date range is: 1970-01-01 to present.letmut yfd = YahooFinanceData::new("AAPL".to_string());// Can specify custom dates (optional).
yfd.set_start_date(time::macros::datetime!(2019 - 01 - 010:00UTC));
yfd.set_end_date(time::macros::datetime!(2020 - 01 - 010:00UTC));// Download the historical data.
yfd.get_price_history();// Compute the returns.// Specify the type of returns to compute (Simple, Logarithmic, Absolute)// You don't need to run .get_price_history() first, .compute_returns()// will do it for you if necessary.
yfd.compute_returns(ReturnsType::Logarithmic);println!("Apple's quotes: {:?}", yfd.price_history);println!("Apple's returns: {:?}", yfd.returns);}

Apple's quotes: Some(shape: (252, 7)┌────────────┬───────────┬───────────┬───────────┬───────────┬────────────┬───────────┐│ date ┆ open ┆ high ┆ low ┆ close ┆ volume ┆ adjusted ││ --- ┆ --- ┆ --- ┆ --- ┆ --- ┆ --- ┆ --- ││ date ┆ f64 ┆ f64 ┆ f64 ┆ f64 ┆ f64 ┆ f64 │╞════════════╪═══════════╪═══════════╪═══════════╪═══════════╪════════════╪═══════════╡│ 2019-01-02 ┆ 38.7225 ┆ 39.712502 ┆ 38.557499 ┆ 39.48 ┆ 1.481588e8 ┆ 37.994499 ││ 2019-01-03 ┆ 35.994999 ┆ 36.43 ┆ 35.5 ┆ 35.547501 ┆ 3.652488e8 ┆ 34.209969 ││ 2019-01-04 ┆ 36.1325 ┆ 37.137501 ┆ 35.950001 ┆ 37.064999 ┆ 2.344284e8 ┆ 35.670372 ││ 2019-01-07 ┆ 37.174999 ┆ 37.2075 ┆ 36.474998 ┆ 36.982498 ┆ 2.191112e8 ┆ 35.590965 ││ … ┆ … ┆ … ┆ … ┆ … ┆ … ┆ … ││ 2019-12-26 ┆ 71.205002 ┆ 72.495003 ┆ 71.175003 ┆ 72.477501 ┆ 9.31212e7 ┆ 70.798401 ││ 2019-12-27 ┆ 72.779999 ┆ 73.4925 ┆ 72.029999 ┆ 72.449997 ┆ 1.46266e8 ┆ 70.771545 ││ 2019-12-30 ┆ 72.364998 ┆ 73.172501 ┆ 71.305 ┆ 72.879997 ┆ 1.441144e8 ┆ 71.191582 ││ 2019-12-31 ┆ 72.482498 ┆ 73.419998 ┆ 72.379997 ┆ 73.412498 ┆ 1.008056e8 ┆ 71.711739 │└────────────┴───────────┴───────────┴───────────┴───────────┴────────────┴───────────┘)

Apple's returns: Some(shape: (252, 7)┌────────────┬────────────┬───────────────┬───────────────┬───────────────┬──────────────┬──────────────┐│ date ┆ volume ┆ open_logarith ┆ high_logarith ┆ low_logarithm ┆ close_logari ┆ adjusted_log ││ --- ┆ --- ┆ mic ┆ mic ┆ ic ┆ thmic ┆ arithmic ││ date ┆ f64 ┆ --- ┆ --- ┆ --- ┆ --- ┆ --- ││ ┆ ┆ f64 ┆ f64 ┆ f64 ┆ f64 ┆ f64 │╞════════════╪════════════╪═══════════════╪═══════════════╪═══════════════╪══════════════╪══════════════╡│ 2019-01-02 ┆ 1.481588e8 ┆ null ┆ null ┆ null ┆ null ┆ null ││ 2019-01-03 ┆ 3.652488e8 ┆ -0.073041 ┆ -0.086273 ┆ -0.082618 ┆ -0.104924 ┆ -0.104925 ││ 2019-01-04 ┆ 2.344284e8 ┆ 0.003813 ┆ 0.019235 ┆ 0.012596 ┆ 0.041803 ┆ 0.041803 ││ 2019-01-07 ┆ 2.191112e8 ┆ 0.028444 ┆ 0.001883 ┆ 0.014498 ┆ -0.002228 ┆ -0.002229 ││ … ┆ … ┆ … ┆ … ┆ … ┆ … ┆ … ││ 2019-12-26 ┆ 9.31212e7 ┆ 0.000457 ┆ 0.017709 ┆ 0.006272 ┆ 0.019646 ┆ 0.019646 ││ 2019-12-27 ┆ 1.46266e8 ┆ 0.021878 ┆ 0.013666 ┆ 0.011941 ┆ -0.00038 ┆ -0.00038 ││ 2019-12-30 ┆ 1.441144e8 ┆ -0.005718 ┆ -0.004364 ┆ -0.010116 ┆ 0.005918 ┆ 0.005918 ││ 2019-12-31 ┆ 1.008056e8 ┆ 0.001622 ┆ 0.003377 ┆ 0.014964 ┆ 0.00728 ┆ 0.00728 │└────────────┴────────────┴───────────────┴───────────────┴───────────────┴──────────────┴──────────────┘)

Read/write data

useRustQuant::data::*;fnmain(){// New `Data` instance.letmut data = Data::new(
format:DataFormat::CSV,// Can also be JSON or PARQUET.
path:String::from("./file/path/read.csv"))// Read from the given file. 
data.read().unwrap();// New path to write the data to. 
data.path = String::from("./file/path/write.csv")
data.write().unwrap();println!("{:?}", data.data)}

📊 Distributions

PDFs, CDFs, MGFs, CFs, and other ditrubution related functions for common distributions.

Probability density/mass functions, distribution functions, characteristic functions, etc.

• Gaussian
• Bernoulli
• Binomial
• Poisson
• Uniform (discrete & continuous)
• Chi-Squared
• Gamma
• Exponential

📈 Instruments

Various implementations for instruments like `Bonds` and `Options`, and the pricing of them. Others coming in the future (swaps, futures, CDSs, etc).

📉 Bonds

• Prices:
  • The Vasicek Model
  • The Cox, Ingersoll, and Ross Model
  • The Hull–White (One-Factor) Model
  • The Rendleman and Bartter Model
  • The Ho–Lee Model
  • The Black–Derman–Toy Model
  • The Black–Karasinski Model
• Duration
• Convexity

💸 Option Pricing

• Closed-form price solutions:

  • Heston Model
  • Barrier
  • European
  • Greeks/Sensitivities
  • Lookback
  • Asian: Continuous Geometric Average
  • Forward Start
  • Bachelier and Modified Bachelier
  • Generalised Black-Scholes-Merton
  • Basket
  • Rainbow
  • American

• Lattice models:

  • Binomial Tree (Cox-Ross-Rubinstein)

The stochastic process generators can be used to price path-dependent options via Monte-Carlo.

• Monte Carlo pricing:
  • Lookback
  • Asian
  • Chooser
  • Barrier

useRustQuant::options::*;fnmain(){letVanillaOption = EuropeanOption{initial_price:100.0,strike_price:110.0,risk_free_rate:0.05,volatility:0.2,dividend_rate:0.02,time_to_maturity:0.5,};let prices = VanillaOption.price();println!("Call price = {}", prices.0);println!("Put price = {}", prices.1);}

📐 Mathematics

Fast Fourier Transform (FFT), numerical integration (double-exponential quadrature), optimisation/root-finding (gradient descent, Newton-Raphson), and risk-reward metrics.

Optimization and Root Finding

• Gradient Descent
• Newton-Raphson

Note: the reason you need to specify the lifetimes and use the type Variable is because the gradient descent optimiser uses the RustQuant::autodiff module to compute the gradients. This is a slight inconvenience, but the speed-up is enormous when working with functions with many inputs (when compared with using finite-difference quotients).

useRustQuant::optimisation::GradientDescent;// Define the objective function.fnhimmelblau<'v>(variables:&[Variable<'v>]) -> Variable<'v>{let x = variables[0];let y = variables[1];((x.powf(2.0) + y - 11.0).powf(2.0) + (x + y.powf(2.0) - 7.0).powf(2.0))}fnmain(){// Create a new GradientDescent object with:// - Step size: 0.005 // - Iterations: 10000// - Tolerance: sqrt(machine epsilon)let gd = GradientDescent::new(0.005,10000, std::f64::EPSILON.sqrt());// Perform the optimisation with:// - Initial guess (10.0, 10.0),// - Verbose output.let result = gd.optimize(&himmelblau,&vec![10.0,10.0],true);// Print the result.println!("{:?}", result.minimizer);}

Integration

• Numerical Integration (needed for Heston model, for example):
  • Tanh-Sinh (double exponential) quadrature
  • Composite Midpoint Rule
  • Composite Trapezoidal Rule
  • Composite Simpson's 3/8 Rule

useRustQuant::math::*;fnmain(){// Define a function to integrate: e^(sin(x))fnf(x:f64) -> f64{(x.sin()).exp()}// Integrate from 0 to 5.let integral = integrate(f,0.0,5.0);// ~ 7.18911925println!("Integral = {}", integral);}

Risk-Reward Metrics

• Risk-Reward Measures (Sharpe, Treynor, Sortino, etc)

🔮 Machine Learning

Currently only linear regression is implemented (and working on logistic regression). More to come in the future.

Regression

• Linear (using QR or SVD decomposition)
• Logistic (via IRLS, adding MLE in the future).

💰 Money

Implementations for `Cashflows`, `Currencies`, and `Quotes`, and similar objects.

• Cashflow
• Currency
• Money
• Quote
• Leg

📈 Stochastic Processes and Short Rate Models

Can generate Brownian Motion (standard, arithmetic and geometric) and various short-rate models (CIR, OU, Vasicek, Hull-White, etc).

The following is a list of stochastic processes that can be generated.

• Brownian Motions:
  • Standard Brownian Motion
    • $dX(t) = dW(t)$
  • Arithmetic Brownian Motion
    • $dX(t) = \mu dt + \sigma dW(t)$
  • Geometric Brownian Motion
    • $dX(t) = \mu X(t) dt + \sigma X(t) dW(t)$
  • Fractional Brownian Motion
• Cox-Ingersoll-Ross (1985)
  • $dX(t) = \left[ \theta - \alpha X(t) \right] dt + \sigma \sqrt{r_t} dW(t)$
• Ornstein-Uhlenbeck process
  • $dX(t) = \theta \left[ \mu - X(t) \right] dt + \sigma dW(t)$
• Ho-Lee (1986)
  • $dX(t) = \theta(t) dt + \sigma dW(t)$
• Hull-White (1990)
  • $dX(t) = \left[ \theta(t) - \alpha X(t) \right]dt + \sigma dW(t)$
• Extended Vasicek (1990)
  • $dX(t) = \left[ \theta(t) - \alpha(t) X(t) \right] dt + \sigma dW(t)$
• Black-Derman-Toy (1990)
  • $d\ln[X(t)] = \left[ \theta(t) + \frac{\sigma'(t)}{\sigma(t)}\ln[X(t)] \right]dt + \sigma_t dW(t)$

useRustQuant::stochastics::*;fnmain(){// Create new GBM with mu and sigma.let gbm = GeometricBrownianMotion::new(0.05,0.9);// Generate path using Euler-Maruyama scheme.// Parameters: x_0, t_0, t_n, n, sims, parallel.let output = (&gbm).euler_maruyama(10.0,0.0,0.5,10,1,false);println!("GBM = {:?}", output.paths);}

📆 Time and Date

Time and date functionality. Mostly the `DayCounter` for pricing options and bonds.

• DayCounter

🤝 Miscellaneous Functions and Macros

Various helper functions and macros.

A collection of utility functions and macros.

• Plot a vector.
• Write vector to file.
• Cumulative sum of vector.
• Linearly spaced sequence.
• assert_approx_equal!

✔️ How-tos

Guides for using RustQuant.

See /examples for more details. Run them with:

cargo run --example automatic_differentiation

I would not recommend using RustQuant within any other libraries for some time, as it will most likely go through many breaking changes as I learn more Rust and settle on a decent structure for the library.

🙏 I would greatly appreciate contributions so it can get to the v1.0.0 mark ASAP.

📖 References

References and resources used for this project.

• John C. Hull - Options, Futures, and Other Derivatives
• Damiano Brigo & Fabio Mercurio - Interest Rate Models - Theory and Practice (With Smile, Inflation and Credit)
• Paul Glasserman - Monte Carlo Methods in Financial Engineering
• Andreas Griewank & Andrea Walther - Evaluating Derivatives - Principles and Techniques of Algorithmic Differentiation
• Steven E. Shreve - Stochastic Calculus for Finance II: Continuous-Time Models
• Espen Gaarder Haug - Option Pricing Formulas
• Antoine Savine - Modern Computational Finance: AAD and Parallel Simulations

Disclaimer: This is currently a free-time project and not a professional financial software library. Nothing in this library should be taken as financial advice, and I do not recommend you to use it for trading or making financial decisions.