ActuaryUtilities.jl

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ActuaryUtilities.jl

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Common functions in actuarial and financial routines

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# ActuaryUtilities

[![Stable](https://img.shields.io/badge/docs-stable-blue.svg)](https://docs.juliaactuary.org/ActuaryUtilities/stable/)
[![Dev](https://img.shields.io/badge/docs-dev-blue.svg)](https://docs.juliaactuary.org/ActuaryUtilities/dev/)
![CI](https://github.com/JuliaActuary/ActuaryUtilities.jl/workflows/CI/badge.svg)
[![Codecov](https://codecov.io/gh/JuliaActuary/ActuaryUtilities.jl/branch/master/graph/badge.svg)](https://codecov.io/gh/JuliaActuary/ActuaryUtilities.jl)

## Quickstart

```julia
using ActuaryUtilities

cfs = [5, 5, 105]
times    = [1, 2, 3]

discount_rate = 0.03

present_value(discount_rate, cfs, times)           # 105.65
duration(Macaulay(), discount_rate, cfs, times)    #   2.86
duration(discount_rate, cfs, times)                #   2.78
convexity(discount_rate, cfs, times)               #  10.62
```

## Features

A collection of common functions/manipulations used in Actuarial Calculations.

### Financial Maths

- `duration`:
  - Calculate the `Macaulay`, `Modified`, or `DV01` durations for a set of cashflows
  - Calculate the `KeyRate(time)` (a.k.a. `KeyRateZero`) duration or `KeyRatePar(time)` duration
- `convexity` for price sensitivity
- Flexible interest rate models via the [`FinanceModels.jl`](https://github.com/JuliaActuary/FinanceModels.jl) package.
- `internal_rate_of_return` or `irr` to calculate the IRR given cashflows (including at timepoints like Excel's `XIRR`)
- `breakeven` to calculate the breakeven time for a set of cashflows
- `accum_offset` to calculate accumulations like survivorship from a mortality vector
- `spread` will calculate the spread needed between two yield curves to equate a set of cashflows

### Key Rate Sensitivities via Automatic Differentiation

Compute exact key rate durations, DV01s, and convexities using ForwardDiff through `ZeroRateCurve` from [FinanceModels.jl](https://github.com/JuliaActuary/FinanceModels.jl) -- machine-precision sensitivities in a single pass, no bump-and-reprice required.

```julia
using ActuaryUtilities, FinanceModels, FinanceCore

rates = [0.03, 0.03, 0.03, 0.03, 0.03]
tenors = [1.0, 2.0, 3.0, 4.0, 5.0]
zrc = ZeroRateCurve(rates, tenors)

# Works with amounts + times or Cashflow objects directly
cfs = Cashflow.([5.0, 5.0, 5.0, 5.0, 105.0], tenors)

# All key rate sensitivities in one AD pass
result = sensitivities(KeyRates(tenors), zrc, cfs)
result.value       # present value
result.durations   # key rate durations (vector)
result.convexities # cross-convexity matrix
```

- **`sensitivities`**: bundled value, key rate durations, and convexity matrix in a single AD pass
- **Two-curve decomposition**: separate `IR01` (risk-free) and `CS01` (credit spread) sensitivities
- **Do-block syntax**: custom valuation functions for rate-dependent instruments (callable bonds, floaters, caps/floors)
- **Hull-White stochastic model**: key rate sensitivities of Monte Carlo expected values, differentiating through the full simulation pipeline

```julia
using FinanceModels: ShortRate
using Random: Xoshiro

hw = ShortRate.HullWhite(0.1, 0.01, zrc)
hw_result = sensitivities(KeyRates(tenors), hw, cfs, tenors; n_scenarios=1000, rng=Xoshiro(42))
hw_result.durations   # key rate durations under stochastic dynamics
```

See the [Key Rate Sensitivities documentation](https://docs.juliaactuary.org/ActuaryUtilities/stable/sensitivities/) for details.

### Risk Measures

- Calculate risk measures for a given vector of risks:
  - `CTE` for the Conditional Tail Expectation
  - `VaR` for the percentile/Value at Risk
  - `WangTransform` for the Wang Transformation
  - `ProportionalHazard` for proportional hazards
  - `DualPower` for dual power measure

### Insurance mechanics

- `duration`:
  - Calculate the duration given an issue date and date (a.k.a. policy duration)
  
### Typed Rates

- functions which return a rate/yield will return a `FinanceCore.Rate` object. E.g. `irr(cashflows)` will return a `Rate(0.05,Periodic(1))` instead of just a `0.05` (`float64`) to convey the compounding frequency. This is compatible across the JuliaActuary ecosystem and can be used anywhere you would otherwise use a simple floating point rate.

A couple of other notes:

- `rate(...)` will return the scalar rate value from a `Rate` struct:

```julia-repl
julia> r = Rate(0.05,Periodic(1));

julia> rate(r) 
0.05
```

- You can still pass a simple floating point rate to various methods. E.g. these two are the same (the default compounding convention is periodic once per period):

```julia
discount(0.05,cashflows)

r = Rate(0.05,Periodic(1));
discount(r,cashflows)
```

- convert between rates with:

```julia
r = Rate(0.05,Periodic(1));

convert(Periodic(2),  r)   # convert to compounded twice per timestep
convert(Continuous(), r)   # convert to continuous compounding
```

For more on Rates, see [FinanceCore.jl](https://github.com/JuliaActuary/FinanceCore.jl). [FinanceModels.jl](https://github.com/JuliaActuary/FinanceModels.jl) also provides a rich and flexible set of yield models to use.

## Documentation

Full documentation is [available here](https://docs.juliaactuary.org/ActuaryUtilities/stable/).

## Examples

### Interactive, basic cashflow analysis

See [JuliaActuary.org for instructions](https://juliaactuary.org/tutorials/cashflowanalysis/) on running this example.

[![Simple cashflow analysis with ActuaryUtilities.jl](https://user-images.githubusercontent.com/711879/95857181-d646a280-0d20-11eb-8300-a4c226021334.gif)](https://juliaactuary.org/tutorials/cashflowanalysis/)

## Useful tips

Functions often use a mix of interest_rates, cashflows, and timepoints. When calling functions, the general order of the arguments is 1) interest rates, 2) cashflows, and 3) timepoints.

ActuaryUtilities.jl

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