function paramvar
paramvar(
mu: number,
sigma: number,
p?: number,
amount?: number,
period?: number,
): number

Parametric Value-At-Risk.

Parametric Value-At-Risk assuming returns are normally distributed. It can work with numbers, arrays, row vectors, and column vectors.

Examples

VaR with default parameters

import { assertEquals } from "jsr:@std/assert";

assertEquals(paramvar(0, 1), 1.6448536127562643);

VaR with arrays

import { assertEquals } from "jsr:@std/assert";

assertEquals(paramvar([0, 0, 0], [1, 2, 3]), [1.6448536127562643, 3.2897072255125286, 4.934560838268792]);

Parametric VaR for a single asset

import { assertEquals } from "jsr:@std/assert";

assertEquals(paramvar(0.0179, 0.023230487630602065), 0.020310751505285517);

Parameters

mu: number

mean value (def: 0)

sigma: number

standard deviation (def: 1)

optional
p: number

VaR confidence level in range [0,1] (def: 0.95)

optional
amount: number

portfolio/asset amount (def: 1)

optional
period: number

time horizon (def: 1)

Return Type

number

Parametric Value-At-Risk

paramvar(
mu: array,
sigma: array,
p?: number,
amount?: number,
period?: number,
): array

Parametric Value-At-Risk.

Parametric Value-At-Risk assuming returns are normally distributed. It can work with numbers, arrays, row vectors, and column vectors.

Examples

VaR with default parameters

import { assertEquals } from "jsr:@std/assert";

assertEquals(paramvar(0, 1), 1.6448536127562643);

VaR with arrays

import { assertEquals } from "jsr:@std/assert";

assertEquals(paramvar([0, 0, 0], [1, 2, 3]), [1.6448536127562643, 3.2897072255125286, 4.934560838268792]);

Parametric VaR for a single asset

import { assertEquals } from "jsr:@std/assert";

assertEquals(paramvar(0.0179, 0.023230487630602065), 0.020310751505285517);

Parameters

mu: array

mean value (def: 0)

sigma: array

standard deviation (def: 1)

optional
p: number

VaR confidence level in range [0,1] (def: 0.95)

optional
amount: number

portfolio/asset amount (def: 1)

optional
period: number

time horizon (def: 1)

Return Type

Parametric Value-At-Risk

paramvar(
mu: matrix,
sigma: matrix,
p?: number,
amount?: number,
period?: number,
): array | matrix

Parametric Value-At-Risk.

Parametric Value-At-Risk assuming returns are normally distributed. It can work with numbers, arrays, row vectors, and column vectors.

Examples

VaR with default parameters

import { assertEquals } from "jsr:@std/assert";

assertEquals(paramvar(0, 1), 1.6448536127562643);

VaR with arrays

import { assertEquals } from "jsr:@std/assert";

assertEquals(paramvar([0, 0, 0], [1, 2, 3]), [1.6448536127562643, 3.2897072255125286, 4.934560838268792]);

Parametric VaR for a single asset

import { assertEquals } from "jsr:@std/assert";

assertEquals(paramvar(0.0179, 0.023230487630602065), 0.020310751505285517);

Parameters

mu: matrix

mean value (def: 0)

sigma: matrix

standard deviation (def: 1)

optional
p: number

VaR confidence level in range [0,1] (def: 0.95)

optional
amount: number

portfolio/asset amount (def: 1)

optional
period: number

time horizon (def: 1)

Return Type

Parametric Value-At-Risk

Usage

import paramvar from "quants/paramvar.ts";