RustQuant

Rust library for quantitative finance tools.

Contact: rustquantcontact@gmail.com

Latest additions:

• Gap option and cash-or-nothing option pricers (currently adding more binary options)
• Asian option pricer (closed-form solution for continuous geometric average).
• Heston Model option pricer (uses the tanh-sinh quadrature numerical integrator).
• Tanh-sinh (double exponential) quadrature for evaluating integrals.
  • Plus other basic numerical integrators (midpoint, trapezoid, Simpson's 3/8).
• Characteristic functions and density functions for common distributions:
  • Gaussian, Bernoulli, Binomial, Poisson, Uniform, Chi-Squared, Gamma, and Exponential.

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.

Table of Contents

1. Automatic Differentiation
2. Option Pricers
3. Stochastic Processes and Short Rate Models
4. Bonds
5. Distributions
6. Mathematics
7. Helper Functions and Macros
8. How-tos
9. References

Automatic Differentiation

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

• 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 $m \gg n$

Option Pricers

• Closed-form price solutions:

  • Heston Model
  • Barrier
  • European Options
  • Greeks/Sensitivities
  • Lookback
  • Asian
    • Continuous Geometric Average
  • 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

Most will follow the notation and formulas in John C. Hull's Options, Futures, and Other Derivatives.

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

Distributions

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

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

Mathematics

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

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

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]));
}

Compute integrals:

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); 
}

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);
}

References:

• 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