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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](./CHANGELOG.md) for a full list of changes.
# Table of Contents
1. [Automatic Differentiation](#autodiff) - Reverse (Adjoint) Mode Automatic Differentiation.
2. [Data](#data) - Methods for reading and writing data from/to various sources (`CSV`, `JSON`, `PARQUET`). Can also download data from Yahoo! Finance.
3. [Distributions](#distributions) - PDFs, CDFs, MGFs, CFs, and other ditrubution related functions for common distributions.
4. [Instruments](#instruments) - Various implementations for instruments like `Bonds` and `Options`, and the pricing of them. Others coming in the future (swaps, futures, CDSs, etc).
5. [Mathematics](#maths) - Numerical integration (double-exponential quadrature), root finding (gradient descent, Newton-Raphson), and risk-reward metrics.
6. [Machine Learning](#ml) - Currently only linear regression is implemented (and working on logistic regression). More to come in the future.
7. [Money](#money) - Implementations for `Cashflows`, `Currencies`, and `Quotes`, and similar objects.
8. [Stochastic Processes](#stochastics) - Can generate Brownian Motion (standard, arithmetric and geometric) and various short-rate models (CIR, OU, Vasicek, Hull-White, etc).
9. [Time and Dates](#time) - Time and date functionality. Mostly the `DayCounter` for pricing options and bonds.
10. [Utilities/Helpers](#helpers) - Various helper functions and macros.
11. [How-tos](#howto) - How to do various things with RustQuant.
12. [References](#references) - References and resources used for this project.
## :link: Automatic Differentiation <a name="autodiff"></a>
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.
- [x] 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 $m \gg n$
```rust
use RustQuant::autodiff::*;
fn main() {
// Create a new Graph to store the computations.
let g = Graph::new();
// Assign variables.
let x = g.var(0.5);
let y = g.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]));
}
```
## :bar_chart: Data <a name="data"></a>
You can download data from Yahoo! Finance into a Polars `DataFrame`.
```rust
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();
println!("Apple's quotes: {:?}", yfd.price_history)
}
```
```bash
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 │
└────────────┴───────────┴───────────┴───────────┴───────────┴────────────┴───────────┘)
```
### Read/write data
```rust
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)
}
```
## :bar_chart: Distributions <a name="distributions"></a>
Probability density/mass functions, distribution functions, characteristic functions, etc.
- [x] Gaussian
- [x] Bernoulli
- [x] Binomial
- [x] Poisson
- [x] Uniform (discrete & continuous)
- [x] Chi-Squared
- [x] Gamma
- [x] Exponential
## :chart_with_upwards_trend: Instruments <a name="instruments"></a>
### :chart_with_downwards_trend: Bonds <a name="bonds"></a>
- Prices:
- [x] The Vasicek Model
- [x] The Cox, Ingersoll, and Ross Model
- [x] 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 <a name="options"></a>
- Closed-form price solutions:
- [x] Heston Model
- [x] Barrier
- [x] European
- [x] Greeks/Sensitivities
- [x] Lookback
- [x] Asian: Continuous Geometric Average
- [x] Forward Start
- [ ] Basket
- [ ] Rainbow
- [ ] American
- Lattice models:
- [x] Binomial Tree (Cox-Ross-Rubinstein)
The stochastic process generators can be used to price path-dependent options via Monte-Carlo.
- Monte Carlo pricing:
- [x] Lookback
- [ ] Asian
- [ ] Chooser
- [ ] Barrier
```rust
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);
}
```
## :triangular_ruler: Mathematics <a name="maths"></a>
## Optimization and Root Finding
- [x] Gradient Descent
- [x] 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).
```rust
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):
- [x] Tanh-Sinh (double exponential) quadrature
- [x] Composite Midpoint Rule
- [x] Composite Trapezoidal Rule
- [x] Composite Simpson's 3/8 Rule
```rust
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
- [x] Risk-Reward Measures (Sharpe, Treynor, Sortino, etc)
## :crystal_ball: Machine Learning <a name="ml"></a>
### Regression
- [x] Linear (using QR or SVD decomposition)
- [ ] Logistic (using MLE or IRLS). Work in progress.
## :moneybag: Money <a name="money"></a>
- `Cashflows`
- `Currencies`
- `Quotes`
## :chart_with_upwards_trend: Stochastic Processes and Short Rate Models <a name="stochastics"></a>
The following is a list of stochastic processes that can be generated.
- [x] Brownian Motion
- [x] Arithmetic Brownian Motion
- $dX(t) = \mu dt + \sigma dW(t)$
- [x] Geometric Brownian Motion
- $dX(t) = \mu X(t) dt + \sigma X(t) dW(t)$
- Models: Black-Scholes (1973), Rendleman-Bartter (1980)
- [x] Cox-Ingersoll-Ross (1985)
- $dX(t) = \left[ \theta - \alpha X(t) \right] dt + \sigma \sqrt{r_t} dW(t)$
- [x] Ornstein-Uhlenbeck process
- $dX(t) = \theta \left[ \mu - X(t) \right] dt + \sigma dW(t)$
- Models: Vasicek (1977)
- [x] Ho-Lee (1986)
- $dX(t) = \theta(t) dt + \sigma dW(t)$
- [x] Hull-White (1990)
- $dX(t) = \left[ \theta(t) - \alpha X(t) \right]dt + \sigma dW(t)$
- [x] Extended Vasicek (1990)
- $dX(t) = \left[ \theta(t) - \alpha(t) X(t) \right] dt + \sigma dW(t)$
- [x] Black-Derman-Toy (1990)
- $d\ln[X(t)] = \left[ \theta(t) + \frac{\sigma'(t)}{\sigma(t)}\ln[X(t)] \right]dt + \sigma_t dW(t)$
- $d\ln[X(t)] = \theta(t) dt + \sigma dW(t)$
```rust
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);
}
```
## :handshake: Helper Functions and Macros <a name="helpers"></a>
A collection of utility functions and macros.
- [x] Plot a vector.
- [x] Write vector to file.
- [x] Cumulative sum of vector.
- [x] Linearly spaced sequence.
- [x] `assert_approx_equal!`
## :heavy_check_mark: How-tos <a name="howto"></a>
See [/examples](./examples) for more details. Run them with:
```bash
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.
## :book: References: <a name="references"></a>
- 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*