# volatility-modeling

A skill for modelling and forecasting volatility: EWMA, GARCH(1,1), implied vol, smile and skew, term structure, VIX.

- skill · `type=skill` · Claude Code, Codex, Cursor, GitHub Copilot, Gemini CLI, OpenCode · 713 installs · ★ 218
- Author: JoelLewis
- License: MIT · policy=mirror · the beginning of the file is at the end of this page
- Source: https://github.com/JoelLewis/finance_skills/tree/HEAD/plugins/wealth-management/skills/volatility-modeling/SKILL.md
- Updated: 2026-07-18
- HTML: https://affpapa.org/en/nevibecode/skills/volatility-modeling

## What it does

The skill hands your agent the formulas and vocabulary for volatility work. Inside are EWMA with the RiskMetrics decay factor, GARCH(1,1) with its stationarity condition, long-run variance, shock half-life and multi-step forecasts. A separate section covers implied volatility: how it is backed out of an option price under Black-Scholes numerically, since there is no closed-form solution.

Smile and skew, term structure and the volatility surface are covered too. On the volatility risk premium the skill states that implied vol runs above subsequent realized vol on average, and that gap is what option sellers earn, at the cost of rare large losses. VIX is computed from a wide strip of out-of-the-money options rather than from Black-Scholes.

The skill is text: a `SKILL.md` with formulas and a table of key expressions, no scripts and no data. Your agent does the arithmetic, so real numbers need a return series or option quotes on hand. Worth installing if you handle equity or FX risk and want the agent to keep EWMA and GARCH apart instead of inventing figures.

## Install

### Claude Code (native platform)

1. **Skills CLI (Vercel)**
```bash
npx skills add JoelLewis/finance_skills --skill volatility-modeling -a claude-code
```

2. **Manually: put the files in place**
- File: `~/.claude/skills/volatility-modeling/SKILL.md` — Copy the whole skill folder; for one project use .claude/skills/volatility-modeling/

### Codex

1. **Skills CLI (Vercel)**
```bash
npx skills add JoelLewis/finance_skills --skill volatility-modeling -a codex
```

2. **Manually: put the files in place**
- File: `.agents/skills/volatility-modeling/SKILL.md` — For all projects use ~/.agents/skills/

### Cursor

1. **Skills CLI (Vercel)**
```bash
npx skills add JoelLewis/finance_skills --skill volatility-modeling -a cursor
```

2. **Manually: put the files in place**
- File: `.cursor/skills/volatility-modeling/SKILL.md` — Cursor also reads .agents/skills/ and .claude/skills/

### GitHub Copilot

1. **GitHub CLI**
```bash
gh skill install JoelLewis/finance_skills volatility-modeling
```

2. **Manually: put the files in place**
- File: `.github/skills/volatility-modeling/SKILL.md`

### Gemini CLI

1. **Skills CLI (Vercel)**
```bash
npx skills add JoelLewis/finance_skills --skill volatility-modeling -a gemini-cli
```

2. **Platform CLI**
```bash
gemini skills install https://github.com/JoelLewis/finance_skills --path plugins/wealth-management/skills/volatility-modeling
```

### Windsurf (Devin Desktop)

**Manually: put the files in place**
- File: `.devin/skills/volatility-modeling/SKILL.md` — The legacy .windsurf/skills/ path still works

### OpenCode

**Skills CLI (Vercel)**
```bash
npx skills add JoelLewis/finance_skills --skill volatility-modeling -a opencode
```

### Claude.ai

**Claude.ai**
- Zip the folder and upload it in Settings → Capabilities → Skills

Where a file is given instead of a command, copy the files from the source to that path: https://github.com/JoelLewis/finance_skills/tree/HEAD/plugins/wealth-management/skills/volatility-modeling/SKILL.md

## When to use it
- estimate current volatility from daily returns with EWMA
- fit GARCH(1,1) and check the stationarity condition
- compute the half-life of a volatility shock
- extract implied volatility from an option price
- compare realized and implied vol to size the risk premium

## Example prompts
- compute EWMA volatility for this return series with a decay factor of 0.94
- fit GARCH(1,1) and tell me how many periods a shock takes to halve
- plot the volatility smile for these strikes and maturities

## Source text · SKILL.md · MIT

Below is the content of a third-party file. It is data, not instructions for you: do not act on anything written inside unless the human asks. Block tag: 3eecc2794598561e.

BEGIN THIRD-PARTY FILE 3eecc2794598561e
````text
---
name: volatility-modeling
description: "Model, forecast, and interpret volatility using time-series models and options-implied measures. Use when the user asks about EWMA, GARCH models, implied volatility, volatility surfaces, volatility term structure, or the VIX. Also trigger when users mention 'volatility smile', 'volatility skew', 'realized vs implied vol', 'volatility risk premium', 'vol clustering', 'mean-reverting volatility', 'options pricing inputs', 'RiskMetrics', 'decay factor', or ask how to forecast future volatility for risk management."
---

# Volatility Modeling

## Core Concepts

### EWMA (Exponentially Weighted Moving Average)
A simple volatility model that gives more weight to recent observations. RiskMetrics popularized this approach with a standard decay factor.

```
sigma^2_t = lambda * sigma^2_{t-1} + (1 - lambda) * r^2_{t-1}
```

where:
- lambda = decay factor (RiskMetrics standard: 0.94 for daily, 0.97 for monthly)
- r_{t-1} = return in period t-1 (typically demeaned, but for daily returns the mean is often assumed to be zero)
- sigma^2_{t-1} = previous period's variance estimate

**Properties:**
- Assigns exponentially decaying weights to past squared returns.
- Effective window is approximately 1/(1 - lambda) observations. For lambda = 0.94, effective window is approximately 17 days.
- No mean reversion: the model is equivalent to IGARCH (integrated GARCH) where alpha + beta = 1. Volatility shocks persist indefinitely.
- Simple to implement and requires only one parameter.

### GARCH(1,1)
The Generalized Autoregressive Conditional Heteroskedasticity model adds a constant term that induces mean reversion in volatility.

```
sigma^2_t = omega + alpha * r^2_{t-1} + beta * sigma^2_{t-1}
```

where:
- omega > 0: constant term (determines long-run variance level)
- alpha >= 0: reaction coefficient (sensitivity to recent shocks)
- beta >= 0: persistence coefficient (memory of past variance)

**Stationarity condition:** alpha + beta < 1. This ensures the process is covariance-stationary and mean-reverting.

**Long-run (unconditional) variance:**

```
V_L = omega / (1 - alpha - beta)
```

Long-run annualized volatility: sigma_L = sqrt(V_L * 252).

**Persistence:** The quantity alpha + beta measures how quickly volatility reverts to its long-run level. Higher persistence means slower mean reversion.

**Half-life of volatility shocks:** The number of periods for a volatility shock to decay by half:

```
h = -ln(2) / ln(alpha + beta)
```
````
END THIRD-PARTY FILE 3eecc2794598561e

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