• Download time series data from Yahoo! Finance.
• Read (write) from (to) .csv, .json, and .parquet files, using Polars DataFrames.
• Arithmetic Brownian Motion generator.
• Gamma, exponential, and chi-squared distributions.
• Forward start option pricer (Rubinstein 1990 formula).
• 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.

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

:link: Automatic Differentiation

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

• [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 $m \gg n$

:moneywithwings: Option Pricers

• 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

:chartwithupwards_trend: Stochastic Processes and Short Rate Models

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

• [x] Brownian Motion
• [x] Arithmetic Brownian Motion
  • $dXt = \mu dt + \sigma dWt$
• [x] Geometric Brownian Motion
  • $dXt = \mu Xt dt + \sigma Xt dWt$
  • Models: Black-Scholes (1973), Rendleman-Bartter (1980)
• [x] Cox-Ingersoll-Ross (1985)
  • $dXt = (\theta - \alpha Xt)dt + \sqrt{rt} \sigma dWt$
• [x] Ornstein-Uhlenbeck process
  • $dXt = \theta(\mu - Xt)dt + \sigma dW_t$
  • Models: Vasicek (1977)
• [ ] Ho-Lee (1986)
  • $dXt = \thetat dt + \sigma dW_t$
• [ ] Hull-White (1990)
  • $dXt = (\theta - \alpha Xt)dt + \sigmat dWt$
• [ ] Black-Derman-Toy (1990)
  • $d\ln(X) = \left[ \thetat + \frac{\sigmat'}{\sigmat}\ln(X) \right]dt + \sigmat dW_t$
  • $d\ln(X) = \thetat dt + \sigma dWt$
• [ ] Merton's model (1973)
  • $Xt = X0 + at + \sigma W_t^$
  • $dXt = adt + \sigma dWt^$

:chartwithdownwards_trend: Bonds

• Prices:
  • [X] The Vasicek Model
  • [x] 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

:bar_chart: Distributions

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

:triangular_ruler: Mathematics

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

:handshake: Helper Functions and Macros

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!

:heavycheckmark: How-tos

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.

Download data from Yahoo! Finance:

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)

} ```

Compute gradients:

```rust 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:

```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);

} ```

Price options:

```rust use RustQuant::options::*;

fn main() { let VanillaOption = EuropeanOption { initialprice: 100.0, strikeprice: 110.0, riskfreerate: 0.05, volatility: 0.2, dividendrate: 0.02, timeto_maturity: 0.5, };

let prices = VanillaOption.price();

println!("Call price = {}", prices.0);
println!("Put price = {}", prices.1);

} ```

Generate stochastic processes:

```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.trajectories);

} ```

:book: 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