How to Forecast Stock Volatility with GARCH Models in Python

May 14, 2026

What’s the question?

Historical volatility — the standard deviation of past returns — is backward-looking by definition. It tells you how much a stock moved, not how much it is likely to move tomorrow. For risk management, options pricing, and position sizing, the relevant quantity is forward-looking volatility. The question is whether past return behavior contains enough structure to forecast future volatility, and specifically whether volatility shocks persist (cluster) or dissipate quickly. A stock where a single large move predicts continued elevated volatility requires different risk management than one where shocks fade rapidly back to baseline.

The approach

The GARCH(1,1) model — Generalized Autoregressive Conditional Heteroskedasticity — is the standard parametric model for volatility forecasting. It decomposes the conditional variance (the variance of tomorrow’s return, given today’s information) into three components: a long-run baseline variance (omega), the impact of yesterday’s squared return shock (alpha), and the persistence of yesterday’s conditional variance (beta). The sum alpha + beta is called persistence: values near 1.0 mean volatility shocks decay slowly (strong clustering), while values well below 1.0 mean shocks dissipate quickly.

Four stocks with different volatility profiles are tested: Apple (AAPL), Nvidia (NVDA), ExxonMobil (XOM), and JPMorgan (JPM). One year of daily returns is fitted to a GARCH(1,1) specification using maximum likelihood estimation. The model then forecasts next-day volatility, which is compared against historical annualized volatility to classify the current regime as HIGH (forecast exceeds historical by 20%+), LOW (forecast is 20%+ below historical), or NORMAL.

import xfinlink as xfl
import pandas as pd
import numpy as np
from arch import arch_model

xfl.set_api_key("your_key")  # free at https://xfinlink.com/signup

tickers = ["AAPL", "NVDA", "XOM", "JPM"]
df = xfl.prices(tickers, period="1y", fields=["close", "return_daily"])

for ticker in tickers:
    t = df[df["ticker"] == ticker].sort_values("date")
    returns = t["return_daily"].dropna() * 100  # scale to percent
    model = arch_model(returns, vol="Garch", p=1, q=1, dist="Normal", rescale=False)
    result = model.fit(disp="off")
    alpha, beta = result.params["alpha[1]"], result.params["beta[1]"]
    persistence = alpha + beta
    forecast = result.forecast(horizon=1)
    next_vol = np.sqrt(forecast.variance.iloc[-1, 0])
    ann_vol = next_vol * np.sqrt(252)
    hist_vol = returns.std() * np.sqrt(252)
    regime = "HIGH" if ann_vol > hist_vol * 1.2 else ("LOW" if ann_vol < hist_vol * 0.8 else "NORMAL")
    print(f"{ticker}: persistence={persistence:.4f} forecast={ann_vol:.1f}% hist={hist_vol:.1f}% regime={regime}")

Output:

=== GARCH(1,1) Volatility Forecast ===

  AAPL:
    GARCH params: omega=1.3003  alpha=0.0909  beta=0.2600  persistence=0.3509
    Forecast next-day vol: 1.38% daily = 22.0% annualized
    Historical vol:        22.5% annualized
    Regime: NORMAL

  NVDA:
    GARCH params: omega=1.9419  alpha=0.0875  beta=0.4749  persistence=0.5624
    Forecast next-day vol: 2.05% daily = 32.6% annualized
    Historical vol:        33.5% annualized
    Regime: NORMAL

  XOM:
    GARCH params: omega=0.0120  alpha=0.0305  beta=0.9682  persistence=0.9987
    Forecast next-day vol: 1.91% daily = 30.3% annualized
    Historical vol:        23.6% annualized
    Regime: HIGH

  JPM:
    GARCH params: omega=0.0083  alpha=0.0000  beta=0.9992  persistence=0.9992
    Forecast next-day vol: 1.61% daily = 25.6% annualized
    Historical vol:        21.1% annualized
    Regime: HIGH

What this tells us

The persistence parameter divides these four stocks into two distinct volatility regimes. AAPL (persistence = 0.35) and NVDA (persistence = 0.56) exhibit low to moderate persistence, meaning that after a volatility shock — a large daily move in either direction — the elevated volatility fades relatively quickly back toward its long-run level. Their forecast volatilities (22.0% and 32.6%) are close to their historical volatilities (22.5% and 33.5%), confirming that both stocks are currently in a normal volatility state.

XOM and JPM tell a fundamentally different story. Both have persistence values near 1.0 (0.999 for each), indicating extreme volatility clustering — once these stocks begin moving, the elevated volatility tends to self-perpetuate. The GARCH model reflects this by forecasting volatility substantially above the historical average: XOM’s forecast of 30.3% annualized exceeds its 23.6% historical vol by 28%, and JPM’s 25.6% forecast exceeds its 21.1% historical vol by 21%. Both are classified as HIGH regime.

The near-zero omega values for XOM (0.012) and JPM (0.008), combined with beta values near 1.0, mean that the long-run variance contributes almost nothing to the forecast. Tomorrow’s volatility is almost entirely determined by today’s volatility — a purely autoregressive process. In contrast, AAPL’s large omega (1.30) relative to its beta (0.26) means the long-run baseline dominates, producing mean-reverting volatility behavior.

So what?

For position sizing and risk management, the practical implication is direct. If you are using historical volatility to set position sizes or stop-loss levels, you are underestimating current risk for XOM and JPM by approximately 25–30%. The GARCH forecast provides a more accurate estimate of near-term risk because it incorporates the clustering effect. For AAPL and NVDA, historical volatility is an adequate proxy because their volatility mean-reverts quickly. The regime classification (NORMAL vs. HIGH) can serve as a simple signal: when a stock enters a HIGH volatility regime, reduce position size or widen stops to account for the persistence of elevated moves.