---
title: "Extreme Value Theory-Based Value At Risk"
method: POST
path: "/portfolios/analysis/value-at-risk/estimation/extreme-value-theory-based"
tags: ["Portfolio Analysis / Risk Measures / Value At Risk Estimation"]
---

# Extreme Value Theory-Based Value At Risk

`POST /portfolios/analysis/value-at-risk/estimation/extreme-value-theory-based`

## Request

- Base URL: `https://api.portfoliooptimizer.io/v1`
- URL: `https://api.portfoliooptimizer.io/v1/portfolios/analysis/value-at-risk/estimation/extreme-value-theory-based`
- Auth: API key in header `X-API-Key`

Compute the value at risk of a portfolio using extreme value theory to model the lower tail of the portfolio returns.

References
* [Valerie Chavez-Demoulin, Armelle Guillou, Extreme quantile estimation for beta-mixing time series and applications, Insurance: Mathematics and Economics, Volume 83, 2018, Pages 59-74](https://www.sciencedirect.com/science/article/abs/pii/S0167668718300192)
* [Mhamed-Ali El-Aroui, Jean Diebolt, On the use of the peaks over thresholds method for estimating out-of-sample quantiles, Computational Statistics & Data Analysis, Volume 39, Issue 4, 2002, Pages 453-475](https://www.sciencedirect.com/science/article/abs/pii/S0167947301000871)
* [David E. Giles, Hui Feng & Ryan T. Godwin (2016) Bias-corrected maximum likelihood estimation of the parameters of the generalized Pareto distribution, Communications in Statistics - Theory and Methods, 45:8, 2465-2483](http://dx.doi.org/10.1080/03610926.2014.887104)
* [de Haan, L., Mercadier, C. & Zhou, C. Adapting extreme value statistics to financial time series: dealing with bias and serial dependence. Finance Stoch 20, 321–354 (2016)](https://link.springer.com/article/10.1007/s00780-015-0287-6)

## Request body

- object
  - `confidenceLevel` number: The confidence level
  - `evtQuantileEstimationMethod` 'gpdQuantileEstimation' | 'weissmanHeavyTailedQuantileEstimation': The extreme value theory-based quantile estimation method to use
  - `portfolios` object[], required
    - `portfolioValues` number[], required: portfolioValues[t] is the value of the portfolio at the time t

## Response `200`

OK

- object
  - `portfolios` object[], required
    - `portfolioValueAtRisk` number, required: The empirical value at risk of the portfolio, in (logarithmic return) percentage
    - `portfolioArithmeticValueAtRisk` number, required: The empirical value at risk of the portfolio, converted from logarithmic return percentage to arithmetic return percentage

## Changes

- **2026-02-08** `ac51d393c9a9`: 1 info
  - endpoint added

[Operation history](https://skmtc.dev/portfoliooptimizer/apis/portfolio-optimizer/changes/portfolios/analysis/value-at-risk/estimation/extreme-value-theory-based/post.md)

---

[API](https://skmtc.dev/portfoliooptimizer/apis/portfolio-optimizer.md) - [All operations](https://skmtc.dev/portfoliooptimizer/apis/portfolio-optimizer/llms.txt) - [OpenAPI document](https://skmtc.dev/portfoliooptimizer/apis/portfolio-optimizer/revisions/9d075aa717bf?raw)