RustQuant

Rust library for quantitative finance tools.

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.

Features

Below is a checklist of features that are:

• currently implemented, or
• I would like to implement in the future.

Automatic Differentiation

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

• 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 $m \gg n$
• 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 $m \ll n$

Option Pricers

• Closed-form price solutions:

  • Barrier
  • European Options
  • Greeks/Sensitivities
  • Lookback
  • Heston Model
  • Basket
  • Rainbow
  • American
  • Heston Model

• 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

Stochastic Processes and Short Rate Models

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

• Brownian Motion
• Geometric Brownian Motion
  • $dX_t = \mu X_t dt + \sigma X_t dW_t$
  • Models: Black-Scholes (1973), Rendleman-Bartter (1980)
• Cox-Ingersoll-Ross (1985)
  • $dX_t = (\theta - \alpha X_t)dt + \sqrt{r_t} \sigma dW_t$
• Ornstein-Uhlenbeck process
  • $dX_t = \theta(\mu - X_t)dt + \sigma dW_t$
  • Models: Vasicek (1977)
• Ho-Lee (1986)
  • $dX_t = \theta_t dt + \sigma dW_t$
• Hull-White (1990)
  • $dX_t = (\theta - \alpha X_t)dt + \sigma_t dW_t$
• Black-Derman-Toy (1990)
  • $d\ln(X) = \left[ \theta_t + \frac{\sigma_t'}{\sigma_t}\ln(X) \right]dt + \sigma_t dW_t$
  • $d\ln(X) = \theta_t dt + \sigma dW_t$
• Merton's model (1973)
  • $X_t = X_0 + at + \sigma W_t^*$
  • $dX_t = adt + \sigma dW_t^*$

Bonds

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

Mathematics & Statistics

• Risk-Reward Measures (Sharpe, Treynor, Sortino, etc)
• Standard Normal Distribution (Distribution/Density functions, and generation of variates)
• Numerical Integration (needed for Heston model)
• Interpolation
• Newton-Raphson

Helper Functions/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:

Compute gradients:

use RustQuant::autodiff::*;

fn main() {
    // Create a new Tape.
    let t = Tape::new();

    // Assign variables.
    let x = t.var(0.5);
    let y = t.var(4.2);

    // Define a function.
    let z = x * y + x.sin();

    // Accumulate the gradient.
    let grad = z.accumulate();

    println!("Function = {}", z);
    println!("Gradient = {:?}", grad.wrt([x, y]));
}

Price options:

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);
}

Generate stochastic processes:

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.trajectories);
}