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V-Lab

Volatility Forecast Chart User Guide

Visualize volatility forecasts across multiple horizons with risk metrics

Contents

  • Tool Overview

  • Essential Concepts

  • How to Use

  • Data Interpretation

  • Practical Applications

  • Understanding Data

  • Troubleshooting

  • Tips & Best Practices

Tool Overview

The Forecast Chart visualizes GARCH model predictions across time horizons from 1 day to 1 year. It shows mean reversion dynamics, computes risk metrics (VaR/ES), and allows scenario analysis with the tau multiplier for applicable models.

Horizon Explorer

Jump to specific forecast horizons (1d, 1w, 1m, 6m, 1y) with quick-access buttons.

Risk Metrics

View VaR and Expected Shortfall at 95% and 99% confidence levels for the selected horizon.

Convergence View

Watch the forecast curve converge from current volatility toward long-run levels over time.

Tau Adjustment

For models with tau parameters, adjust long-run volatility to explore different regime scenarios.

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Essential Concepts

These terms are essential for understanding the Forecast Chart:

Forecast Horizon

The number of days ahead for which volatility is predicted. V-Lab provides forecasts from 1 day to 252 days (1 year), with standard checkpoints at 1 day, 1 week (5 days), 1 month (22 days), 6 months (126 days), and 1 year.

Why it matters: Different horizons serve different purposes. Short-term forecasts (1d, 1w) are best for trading decisions; longer horizons (6m, 1y) help with strategic planning and show convergence to long-run levels.

Mean Reversion

The tendency for volatility to return toward its long-run average over time. When volatility is elevated, forecasts typically decline; when volatility is depressed, forecasts rise. The speed of mean reversion depends on persistence.

Why it matters: The forecast curve visualizes mean reversion. Watch it converge from current levels toward long-run volatility. Steep curves indicate fast reversion; flat curves indicate slow reversion.

Value-at-Risk (VaR)

A risk measure expressing the maximum expected loss over a given horizon at a given confidence level. VaR 95% means there's a 5% chance of losing more than this amount; VaR 99% means a 1% chance.

Why it matters: VaR translates volatility into loss estimates. If VaR 95% is -3.2% for a $100,000 position, you might lose more than $3,200 on about 1 in 20 days.

Expected Shortfall (ES / CVaR)

The average loss when VaR is exceeded. Also called Conditional VaR or Tail VaR. ES 95% is the average loss in the worst 5% of scenarios, capturing tail risk beyond VaR.

Why it matters: ES is more sensitive to extreme tail events than VaR. When markets crash, ES provides a better estimate of potential losses in severe scenarios.

Tau Parameter

In Spline-GARCH and MF2-GARCH models, tau captures long-run or slowly varying components of volatility. The tau multiplier in the forecast tool allows you to adjust this component for scenario analysis.

Why it matters: Adjusting tau lets you stress-test forecasts. What if long-run volatility doubles? The tau slider answers questions about structural regime changes.

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Tool Layout

The Forecast Chart tool has three main components:

  • Forecast Curve

    The main chart showing annualized volatility (y-axis) across forecast horizons in days (x-axis). The curve starts at current volatility and converges toward long-run levels. You can click anywhere on the curve to select that specific day and view its risk metrics.

  • Horizon Buttons

    Quick-access buttons to jump to standard horizons: 1d, 1w, 1m, 6m, 1y. Click to update the risk metrics panel for that horizon.

  • Risk Metrics Panel

    Shows VaR and ES at 95% and 99% confidence for the selected horizon. Updates when you click horizon buttons or adjust the tau slider.

  • Summary Metrics

    Located below the chart, displays three key reference values: 1-Year Forecast (where volatility is headed), Long-run Vol (the model's equilibrium level, shown in green), and Persistence (how slowly shocks decay).

  • Horizon Details

    In the tool panel, shows details for the selected day: the day number, forecast volatility (color-coded by stress level), difference from long-run, and percentage convergence toward long-run.

Using the Horizon Explorer

Click the horizon buttons to focus on specific forecast periods:

  • 1 Day (1d)

    Tomorrow's forecast. Most influenced by current conditions. Best for daily trading decisions and short-term risk limits.

  • 1 Week (1w)

    5-day average forecast. Smooths daily noise while reflecting current regime. Useful for weekly position sizing.

  • 1 Month (1m)

    22-day average forecast. Shows medium-term outlook. Compare to 1-week to see expected trend direction.

  • 6 Months (6m)

    126-day average forecast. Begins converging toward long-run volatility. Useful for strategic planning.

  • 1 Year (1y)

    252-day average forecast. Essentially the model's long-run volatility estimate. Compare to current levels for regime context.

Understanding Risk Metrics

The tool calculates Value-at-Risk and Expected Shortfall for the selected horizon:

  • VaR 95%

    The loss level exceeded only 5% of the time. For a $100 position with -3.2% VaR, expect to lose more than $3.20 on roughly 1 in 20 days.

  • VaR 99%

    The loss level exceeded only 1% of the time. More conservative than 95% VaR. Used for stress testing and regulatory capital calculations.

  • ES 95% (Expected Shortfall)

    Average loss when VaR 95% is exceeded. Also called CVaR. More sensitive to tail risk than VaR alone.

  • ES 99%

    Average loss in the worst 1% of scenarios. The most conservative standard measure. Important for stress testing.

Using the Tau Multiplier

For models with a tau parameter (Spline-GARCH, MF2-GARCH), the tau slider enables scenario analysis:

  • Adjusting the Slider

    Move from 0.5× to 2× to see how different long-run volatility levels affect forecasts. Higher multipliers simulate higher-volatility regimes. The slider background is color-coded to preview the resulting 1-year forecast at each setting.

  • Scenario Analysis

    Use tau adjustment to stress-test. What if long-run volatility increases 50%? How does that change your 6-month VaR? This helps plan for regime changes.

Hover and Click Interactions

The chart responds to mouse movements and clicks:

  • Hovering

    Move your mouse over the forecast curve to see a vertical line and tooltip showing: the day number, forecast volatility, difference from current volatility, and difference from long-run. Positive differences are shown in red/orange; negative in green.

  • Clicking

    Click anywhere on the chart to select that specific day. The tool panel will update to show the forecast details and risk metrics for your selected day.

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The shape of the forecast curve reveals important information about current market conditions and expected volatility evolution.

Interpreting Curve Patterns
  • Elevated and Decaying

    Current volatility above long-run average, forecast declining over time. Normal pattern after volatility spikes. Risk is elevated short-term but expected to normalize.

  • Depressed and Rising

    Current volatility below long-run average, forecast rising toward normal. Calm conditions expected to eventually give way to typical volatility levels.

  • Flat at Long-Run Level

    Current volatility near long-run average, forecast relatively flat. Stable regime with no significant changes expected.

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Risk Management

Use forecast volatility to set position sizes and risk limits. Higher predicted volatility warrants smaller positions or wider stop-losses. VaR estimates help quantify potential losses.

Trading Decisions

Check the forecast before large trades. If volatility is expected to decline, consider waiting for calmer conditions. Use VaR to size positions appropriately for your risk tolerance.

Options Analysis

Compare statistical volatility forecasts to implied volatility from options markets. The forecast term structure shows what your model expects. Divergences may signal trading opportunities.

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The Forecast Chart computes multi-step ahead predictions using the estimated GARCH model parameters.

How Forecasts are Calculated

For each horizon, the tool iterates the GARCH variance equation forward, starting from current conditional variance. Multi-day forecasts average the variance path. Results are converted to annualized volatility.

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Common Questions
Why is my forecast curve nearly flat?

A flat curve means current volatility is close to long-run volatility and the model expects little change. This is typical during stable market periods. The curve becomes steeper after volatility spikes.

Why is my VaR so high at longer horizons?

VaR scales with the square root of time for multi-day horizons. A 1-day VaR of 2% becomes roughly 4.5% over 5 days (2% × √5). Longer horizons have higher VaR even if volatility is mean-reverting.

Why don't I see the tau slider?

The tau slider only appears for models with a tau parameter (Spline-GARCH, MF2-GARCH). Standard GARCH, GJR-GARCH, and EGARCH don't have this parameter and won't show the slider.

Technical Questions
How is multi-day VaR calculated?

The tool computes the average variance forecast over the horizon, converts to volatility, then applies normal distribution quantiles. This assumes returns are approximately normal. Actual tail risks may be larger.

How do forecasts work for liquidity (ILLIQ) models?

For liquidity models, the forecast shows projected illiquidity rather than volatility. The interpretation is similar: elevated illiquidity forecasts suggest higher trading costs. VaR and ES are not computed for liquidity forecasts.

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Get the most out of the Forecast Chart tool with these recommendations.

Recommended Workflow
  • 1. Check Current vs Long-Run

    Compare the left edge (current) to the right edge (long-run) of the curve. This tells you whether volatility is stressed or calm relative to normal.

  • 2. Compare Horizons

    Click through 1d, 1w, 1m to see forecast evolution. Big differences between horizons indicate strong mean reversion expectations.

  • 3. Assess Risk Metrics

    Review VaR and ES for your relevant horizon. For daily trading, use 1d metrics. For position holding periods, match the horizon.

  • 4. Stress Test (if available)

    For models with tau, use the slider to explore regime scenarios. What if long-run volatility increases significantly?

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