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## Utilities for economic capital assignments for a loan portfolio
This library has a relatively opinionated API for creating a portfolio of loans and performing aggregate statistics (such as loan level risk contributions and expected values).
## Install
Add the following to your Cargo.toml:
`loan_ec = "0.1.2"`
## Use
A full example is in the [credit_faas_demo](https://github.com/phillyfan1138/credit_faas_demo).
Create instances of the Loan struct:
```rust
extern crate loan_ec;
//crate is needed for computing the complex domain
extern crate fang_oost;
let loan=Loan{
balance:1000.0, //dollar exposure
pd:0.03, //annualized probability of default
lgd:0.5,//expected value of loss given default
weight:vec![0.4, 0.6],//must add to one, represents exposure to macro variables
r:0.5, //loss in a liquidity event, as a fraction of the balance
lgd_variance:0.3,//variance of the loss given default
num:1000.0//number of loans that have these attributes
};
```
Then add to the portfolio:
```rust
//the higher this number, the more accurate the numerical approximation, but the slower it will run
let num_u:usize=256;
//the truncation of the distribution for numerical purposes
let x_min=-100000.0;
let x_max=0.0;//the maximum of the distribution
let mut ec=loan_ec::EconomicCapitalAttributes::new(
num_u,
weight.len()
);
let u_domain:Vec<Complex<f64>>=fang_oost::get_u_domain(
num_u, x_min, x_max
).collect();
//the characteristic function for the random variable for LGD...in this case, degenerate (a constant)
let lgd_fn=|u:&Complex<f64>, l:f64, _lgd_v:f64|(-u*l).exp();
//cf enhancement for ec
let liquid_fn=loan_ec::get_liquidity_risk_fn(lambda, q);
let log_lpm_cf=loan_ec::get_log_lpm_cf(&lgd_fn, &liquid_fn);
ec.process_loan(&loan, &u_domain, &log_lpm_cf);
//keep adding until there are no more loans left...
```
Retrieve the (discretized) characteristic function for the portfolio:
```rust
//variance of macro variables
let variance=vec![0.3, 0.4];
//in this example, macro variables are Gamma distributed
-(1.0-v*u).ln()/v
}).sum::<Complex<f64>>().exp()
};
let final_cf:Vec<Complex<f64>>=ec.get_full_cf(&v_mgf);
```
Using the characteristic function, obtain any number of metrics including expected shortfall and value at risk (from my [cf_dist_utils](https://github.com/phillyfan1138/cf_dist_utils_rust) repository).
```rust
let quantile=0.01;
let (
expected_shortfall,
value_at_risk
)=cf_dist_utils::get_expected_shortfall_and_value_at_risk_discrete_cf(
quantile,
x_min,
x_max,
max_iterations,
tolerance,
&final_cf
);
```