https://github.com/jaantollander/conditionalvalueatrisk

Provides a concrete Julia implementation for computing the conditional value-at-risk (aka expected shortfall) for discrete probability distributions. Also works as a pseudocode for other languages.
https://github.com/jaantollander/conditionalvalueatrisk

coherent-risk-measure conditional-value-at-risk expected-shortfall risk-measure

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Provides a concrete Julia implementation for computing the conditional value-at-risk (aka expected shortfall) for discrete probability distributions. Also works as a pseudocode for other languages.

• Host: GitHub
• URL: https://github.com/jaantollander/conditionalvalueatrisk
• Owner: jaantollander
• License: mit
• Created: 2020-09-14T11:35:26.000Z (over 4 years ago)
• Default Branch: master
• Last Pushed: 2021-09-21T06:05:14.000Z (over 3 years ago)
• Last Synced: 2024-05-01T13:26:52.179Z (8 months ago)
• Topics: coherent-risk-measure, conditional-value-at-risk, expected-shortfall, risk-measure
• Language: Julia
• Homepage: https://jaantollander.com/post/measuring-tail-risk-using-conditional-value-at-risk/
• Size: 71.3 KB
• Stars: 2
• Watchers: 2
• Forks: 1
• Open Issues: 1
• Metadata Files:
  • Readme: README.md
  • License: LICENSE

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README

        
# Conditional Value-at-Risk

![](images/distributions.svg)

You can copy The Julia code from the file [`conditional-value-at-risk`](conditional-value-at-risk.jl). The example below describes the implementation and how to use it. This repository is related to my article [*Measuring Tail-Risk Using Conditional Value at Risk*](https://jaantollander.com/post/measuring-tail-risk-using-conditional-value-at-risk/), which discusses the definition, properties and implementation of conditional value at risk in more detail.

We can implement the value-at-risk and conditional value-at-risk functions in [Julia](https://julialang.org/) for discrete probability distributions as follow.

```julia

"""Value-at-risk."""

function value_at_risk(x::Vector{Float64}, f::Vector{Float64}, α::Float64)

    i = findfirst(p -> p≥α, cumsum(f))

    if i === nothing

        return x[end]

    else

        return x[i]

    end

end

"""Conditional value-at-risk."""

function conditional_value_at_risk(x::Vector{Float64}, f::Vector{Float64}, α::Float64)

    x_α = value_at_risk(x, f, α)

    if iszero(α)

        return x_α

    else

        tail = x .≤ x_α

        return (sum(x[tail] .* f[tail]) - (sum(f[tail]) - α) * x_α) / α

    end

end

```

Let us create a random discrete probability distribution.

```julia

normalize(v) = v ./ sum(v)

scale(v, low, high) = v * (high - low) + low

n = 10

x = sort(scale.(rand(n), -1.0, 1.0))

f = normalize(rand(n))

α = 0.05

```

Next, we assert that the inputs are valid. Note that the states `x` do not have to be unique for the formulation to work.

```julia

@assert issorted(x)

@assert all(f .≥ 0)

@assert sum(f) ≈ 1

@assert 0 ≤ α ≤ 1

```

Then, executing the function in Julia REPL gives us a result.

```text

julia> conditional_value_at_risk(x, f, α)

-0.9911100750623101

```