13 releases
0.0.13 | Feb 1, 2023 |
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0.0.12 | Jan 29, 2023 |
0.0.11 | Dec 20, 2022 |
0.0.2 | Oct 4, 2022 |
#109 in Math
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SLoC
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
- Automatic Differentiation
- Option Pricers
- Stochastic Processes and Short Rate Models
- Bonds
- Distributions
- Mathematics
- Helper Functions and Macros
- How-tos
- 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
Dependencies
~8.5MB
~171K SLoC