nautilus_analysis/statistics/
value_at_risk.rs

1// -------------------------------------------------------------------------------------------------
2//  Copyright (C) 2015-2026 Nautech Systems Pty Ltd. All rights reserved.
3//  https://nautechsystems.io
4//
5//  Licensed under the GNU Lesser General Public License Version 3.0 (the "License");
6//  You may not use this file except in compliance with the License.
7//  You may obtain a copy of the License at https://www.gnu.org/licenses/lgpl-3.0.en.html
8//
9//  Unless required by applicable law or agreed to in writing, software
10//  distributed under the License is distributed on an "AS IS" BASIS,
11//  WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
12//  See the License for the specific language governing permissions and
13//  limitations under the License.
14// -------------------------------------------------------------------------------------------------
15
16//! Value at Risk statistic.
17
18use std::fmt::Display;
19
20use nautilus_core::correctness::check_predicate_true;
21use nautilus_model::position::Position;
22
23use crate::{Returns, statistic::PortfolioStatistic};
24
25/// Calculates the historical Value at Risk (`VaR`) of portfolio returns.
26///
27/// `VaR` is the loss threshold that returns are not expected to exceed at a given
28/// confidence level. This is the non-parametric (historical) estimator: the
29/// empirical quantile of the return distribution at `1 - confidence`.
30///
31/// `VaR(c) = quantile(returns, 1 - c)`
32///
33/// The quantile uses linear interpolation between closest ranks (matching
34/// `numpy.percentile`). `confidence` defaults to `0.95`. The result is expressed
35/// as a return (e.g. `-0.03` is a 3% loss threshold); more negative means greater
36/// risk. Returns `NaN` for an empty series.
37///
38/// # References
39///
40/// - Jorion, P. (2007). *Value at Risk: The New Benchmark for Managing Financial Risk*
41///   (3rd ed.). McGraw-Hill.
42/// - J.P. Morgan/Reuters (1996). *RiskMetrics Technical Document* (4th ed.).
43#[expect(
44    clippy::doc_markdown,
45    reason = "citation contains proper nouns with intra-word capitals"
46)]
47#[repr(C)]
48#[derive(Debug, Clone)]
49#[cfg_attr(
50    feature = "python",
51    pyo3::pyclass(module = "nautilus_trader.analysis", from_py_object)
52)]
53#[cfg_attr(
54    feature = "python",
55    pyo3_stub_gen::derive::gen_stub_pyclass(module = "nautilus_trader.analysis")
56)]
57pub struct ValueAtRisk {
58    /// The confidence level `c` in `(0, 1)` (default: 0.95).
59    confidence: f64,
60}
61
62impl ValueAtRisk {
63    /// Creates a new checked [`ValueAtRisk`] instance.
64    ///
65    /// # Errors
66    ///
67    /// Returns an error if `confidence` is not finite and in the range `(0, 1)`.
68    pub fn new_checked(confidence: Option<f64>) -> anyhow::Result<Self> {
69        let confidence = confidence.unwrap_or(0.95);
70        check_predicate_true(
71            confidence.is_finite() && confidence > 0.0 && confidence < 1.0,
72            "confidence must be finite and in the range (0, 1)",
73        )?;
74        Ok(Self { confidence })
75    }
76
77    /// Creates a new [`ValueAtRisk`] instance.
78    ///
79    /// # Panics
80    ///
81    /// Panics if `confidence` is not finite and in the range `(0, 1)`.
82    #[must_use]
83    pub fn new(confidence: Option<f64>) -> Self {
84        Self::new_checked(confidence).expect("Invalid `confidence` for `ValueAtRisk`")
85    }
86}
87
88impl Display for ValueAtRisk {
89    fn fmt(&self, f: &mut std::fmt::Formatter<'_>) -> std::fmt::Result {
90        write!(f, "Value at Risk (confidence {})", self.confidence)
91    }
92}
93
94/// Returns the `q`-th percentile (`q` in `[0, 100]`) of `sorted_values` using
95/// linear interpolation between closest ranks, matching `numpy.percentile`.
96///
97/// `sorted_values` must be sorted ascending and non-empty.
98pub(crate) fn percentile_linear(sorted_values: &[f64], q: f64) -> f64 {
99    debug_assert!(
100        !sorted_values.is_empty(),
101        "percentile requires a non-empty slice"
102    );
103    let n = sorted_values.len();
104
105    let rank = (q / 100.0) * (n - 1) as f64;
106    let lower = rank.floor() as usize;
107    let upper = rank.ceil() as usize;
108    if lower == upper {
109        return sorted_values[lower];
110    }
111
112    let weight = rank - lower as f64;
113    (sorted_values[upper] - sorted_values[lower]).mul_add(weight, sorted_values[lower])
114}
115
116impl PortfolioStatistic for ValueAtRisk {
117    type Item = f64;
118
119    fn name(&self) -> String {
120        self.to_string()
121    }
122
123    fn calculate_from_returns(&self, raw_returns: &Returns) -> Option<Self::Item> {
124        if !self.check_valid_returns(raw_returns) {
125            return Some(f64::NAN);
126        }
127
128        let returns = self.downsample_to_daily_bins(raw_returns);
129        let mut values: Vec<f64> = returns.values().copied().collect();
130        values.sort_by(f64::total_cmp);
131
132        let alpha = 1.0 - self.confidence;
133        Some(percentile_linear(&values, alpha * 100.0))
134    }
135
136    fn calculate_from_realized_pnls(&self, _realized_pnls: &[f64]) -> Option<Self::Item> {
137        None
138    }
139
140    fn calculate_from_positions(&self, _positions: &[Position]) -> Option<Self::Item> {
141        None
142    }
143}
144
145#[cfg(test)]
146mod tests {
147    use std::collections::BTreeMap;
148
149    use nautilus_core::{UnixNanos, approx_eq};
150    use rstest::rstest;
151
152    use super::*;
153
154    fn create_returns(values: &[f64]) -> BTreeMap<UnixNanos, f64> {
155        let mut new_return = BTreeMap::new();
156        let one_day_in_nanos = 86_400_000_000_000;
157        let start_time = 1_600_000_000_000_000_000;
158
159        for (i, &value) in values.iter().enumerate() {
160            let timestamp = start_time + i as u64 * one_day_in_nanos;
161            new_return.insert(UnixNanos::from(timestamp), value);
162        }
163
164        new_return
165    }
166
167    #[rstest]
168    fn test_name() {
169        let var = ValueAtRisk::new(None);
170        assert_eq!(var.name(), "Value at Risk (confidence 0.95)");
171    }
172
173    #[rstest]
174    fn test_empty_returns() {
175        let var = ValueAtRisk::new(None);
176        let returns = create_returns(&[]);
177        let result = var.calculate_from_returns(&returns);
178        assert!(result.is_some());
179        assert!(result.unwrap().is_nan());
180    }
181
182    #[rstest]
183    fn test_value_at_risk_calculation() {
184        // sorted: [-0.10, -0.08, -0.05, -0.03, -0.02, 0.01, 0.015, 0.02, 0.03, 0.04]
185        // alpha = 0.05, rank = 0.05 * 9 = 0.45
186        // VaR = -0.10 + (-0.08 - -0.10) * 0.45 = -0.091
187        let var = ValueAtRisk::new(Some(0.95));
188        let returns = create_returns(&[
189            0.02, -0.05, 0.01, -0.08, 0.03, -0.02, 0.04, -0.10, 0.015, -0.03,
190        ]);
191        let result = var.calculate_from_returns(&returns).unwrap();
192        assert!(approx_eq!(f64, result, -0.091, epsilon = 1e-12));
193    }
194
195    #[rstest]
196    #[case(Some(0.0))]
197    #[case(Some(1.0))]
198    #[case(Some(1.5))]
199    #[case(Some(-0.5))]
200    #[case(Some(f64::NAN))]
201    #[case(Some(f64::INFINITY))]
202    fn test_new_checked_rejects_invalid_confidence(#[case] confidence: Option<f64>) {
203        assert!(ValueAtRisk::new_checked(confidence).is_err());
204    }
205
206    #[rstest]
207    #[case(None)]
208    #[case(Some(0.5))]
209    #[case(Some(0.99))]
210    fn test_new_checked_accepts_valid_confidence(#[case] confidence: Option<f64>) {
211        assert!(ValueAtRisk::new_checked(confidence).is_ok());
212    }
213}
nautilus_analysis/statistics/value_at_risk.rs

nautilus_analysis/statistics/
value_at_risk.rs
