RustQuant 0.0.26

Rust library for quantitative finance tools.

:dart: I want to hit a stable and legitimate v1.0.0 by the end of 2023, so any and all feedback, suggestions, or contributions are strongly welcomed!

Contact: rustquantcontact@gmail.com

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.

:newspaper: Latest features

See CHANGELOG.md for a full list of changes.

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 $m \gg n$

use RustQuant::autodiff::*;

fn main() {
    // 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!

You can:

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

use RustQuant::data::*;
use time::macros::date;

fn main() {
    // New YahooFinanceData instance.
    // By default, date range is: 1970-01-01 to present.
    let mut yfd = YahooFinanceData::new("AAPL".to_string());

    // Can specify custom dates (optional).
    yfd.set_start_date(time::macros::datetime!(2019 - 01 - 01 0:00 UTC));
    yfd.set_end_date(time::macros::datetime!(2020 - 01 - 01 0:00 UTC));

    // 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

use RustQuant::data::*;

fn main() {
    // New `Data` instance.
    let mut 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)
}

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

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

:chart_with_downwards_trend: 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

:money_with_wings: Option Pricing

• Closed-form price solutions:

  • Heston Model
  • Barrier
  • European
  • Greeks/Sensitivities
  • Lookback
  • Asian: Continuous Geometric Average
  • Forward Start
  • 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

use RustQuant::options::*;

fn main() {
    let VanillaOption = 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);
}

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).

use RustQuant::optimisation::GradientDescent;

// Define the objective function.
fn himmelblau<'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))
}

fn main() {
    // 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

use RustQuant::math::*;

fn main() {
    // Define a function to integrate: e^(sin(x))
    fn f(x: f64) -> f64 {
        (x.sin()).exp()
    }

    // Integrate from 0 to 5.
    let integral = integrate(f, 0.0, 5.0);

    // ~ 7.18911925
    println!("Integral = {}", integral); 
}

Risk-Reward Metrics

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

Regression

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

• Cashflow
• Currency
• Money
• Quote
• Leg

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)
  • $d\ln[X(t)] = \left[ \theta(t) + \frac{\sigma'(t)}{\sigma(t)}\ln[X(t)] \right]dt + \sigma_t dW(t)$

use RustQuant::stochastics::*;

fn main() {
    // 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);
}

• DayCounter

A collection of utility functions and macros.

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

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.

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

• 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