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# Fang-Oosterlee Library for Rust

Implements [Fang-Oosterlee](https://mpra.ub.uni-muenchen.de/8914/4/MPRA_paper_8914.pdf) algorithm in Rust.  While the algorithm originally was used for option pricing, it can be used for a variety of use cases.  For example, it can be used to compute the Value at Risk of a distribution, the density of a distribution, and the partial expectation.

It requires a characteristic function computed at various specific intervals.  A utility function is provided which converts an analytical characteristic function into a vector.

Documentation is at [docs.rs](https://docs.rs/fang_oost/0.15.0/fang_oost/)


## Use
Put the following in your Cargo.toml:

```toml
[dependencies]
fang_oost = "0.15"
```

Import and use:

```rust
extern crate num_complex;
extern crate fang_oost;
extern crate rayon;
use rayon::prelude::*;
use num_complex::Complex;

let num_x = 1024;
let num_u = 256;
let x_min = -20.0;
let x_max = 25.0;
let mu=2.0;
let sigma:f64=5.0;
let norm_cf = |u:&Complex<f64>|(u*mu+0.5*u*u*sigma*sigma).exp();
let x_domain=fang_oost::get_x_domain(num_x, x_min, x_max);
//computes discrete gaussian characteristic function
let discrete_cf=fang_oost::get_discrete_cf(num_u, x_min, x_max, &norm_cf);
let result=fang_oost::get_expectation_single_element_real(
    x_min, x_max, x, &discrete_cf,
     |u_im, x, k|{
         if k==0{x-x_min} else { ((x-x_min)*u_im).sin()/u_im }
     }
);
```

## Related Crates

* [Option Pricing with Fang Oost](https://crates.io/crates/fang_oost_option)
* [Distribution Utilities (including CDF, VaR, and Expected Shortfall)](https://crates.io/crates/cf_dist_utils)

## Benchmarks

View benchmarks at https://danielhstahl.github.io/fang_oost_rust/report/index.html.