April 2, 2025. Trump announced tariffs on Chinese goods.
By April 7, Apple's stock had crashed 19% over three days, wiping out $640 billion in market capitalization. While most prediction models assumed a calm 1.76% volatility based on historical averages, AAPL's actual volatility exploded to 5% - nearly triple the expected level.
Traders using static volatility models were blindsided by the severity and persistence of the selloff. Those with dynamic volatility systems? They saw the storm building and sized their positions accordingly.
The difference? Understanding that volatility clusters - big moves follow big moves.
See AAPL's price estimates on MarketCrunch AI
TL;DR: Measuring Market Volatility the Smart Way
The Problem: Most prediction models use static historical volatility (like predicting weather by averaging last month's temperatures). This misses how volatility actually behaves - it clusters. Stormy market days tend to follow other stormy days.
Our Solution: A 3-step dynamic volatility system:
- ARCH Test [1]: Detect if volatility clustering exists
- Leverage Test [2]: Check if bad news hits harder than good news
- GARCH Model [3]: Auto-select optimal parameters daily
Real Impact: Using AAPL as a case study, we observe that during April 2025's volatility spike, realized volatility hit 5% while static models would have assumed a constant 1.76%. Our GARCH model captures these dramatic swings.
How We Use It: The GARCH forecast generates a volatility multiplier that scales our price predictions - smaller moves in calm markets and larger moves in volatile ones.
What's Next: Part 2 will reveal our 3-method calibration strategy that transforms these volatility-aware forecasts into trustworthy, actionable predictions.
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The stock market, much like the weather, has its seasons. Some days are calm and predictable, while others are stormy and turbulent. For any stock price prediction model, understanding this "mood" - what we call volatility - is just as important as predicting the direction of the price itself. A model that can't tell the difference between a calm sea and a hurricane is a model navigating blind.
Let's explore this concept using Apple (AAPL) as our case study, where we can see these principles play out in real market data.
The Problem with Static Thinking
Many models rely on a simple rearview mirror approach called historical volatility, which is just the standard deviation of an asset's past returns. This is like predicting tomorrow's weather by taking the average of the last month. It's not wrong, but it's dangerously incomplete.
Looking at AAPL's price chart and daily returns, we can immediately see why this static approach falls short:
Notice how AAPL's returns aren't randomly scattered - they show clear patterns. Large price movements tend to cluster together, like storm systems. The dramatic volatility spike in April 2025 wasn't an isolated event; it was part of a broader period of market turbulence that persisted for weeks.
This clustering behavior reveals a crucial fact about financial markets: volatility is not constant. It clusters. Stormy days are often followed by more stormy days, and calm periods tend to persist.
Visualizing Volatility Clustering
The concept of volatility clustering becomes crystal clear when we examine AAPL's squared returns over time:
The red dots highlight periods of exceptional volatility - notice how they don't appear randomly but cluster together. This isn't a coincidence; it's a fundamental characteristic of financial markets. When uncertainty strikes (whether from earnings announcements, market corrections, or economic news), it tends to persist for extended periods.
Compare this clustered pattern to the static historical volatility approach shown in our dynamic vs. static comparison:
The orange dashed line represents the traditional approach - a constant 1.76% volatility assumption based on historical averages. Meanwhile, the green line shows realized 21-day rolling volatility, which adapts to changing market conditions. During AAPL's volatile period in April 2025, realized volatility spiked to nearly 5%, while the historical average remained obliviously flat at 1.76%.
Our Three-Step Solution
To capture and forecast this market mood, we use a systematic process:
Step 1: Detecting the Signal - The ARCH Test
We first test whether volatility clustering exists - whether large market moves tend to be followed by more large moves, and calm periods by more calm periods. In our Apple case study, the data confirmed this pattern with clear statistical significance, validating the need for a dynamic volatility model over a static one.
Step 2: Understanding Asymmetry - The Leverage Effect Test
Next, we examine whether markets respond differently to positive versus negative shocks. This determines whether a symmetric model like GARCH is appropriate or if an asymmetric approach, such as EGARCH[4], is needed. In this case, a symmetric response was observed, supporting the use of GARCH.
Step 3: Building the Optimal Model - GARCH Parameter Selection
Finally, we evaluate multiple GARCH configurations on a ticker's data, using the Akaike Information Criterion (AIC) [5] to balance accuracy with simplicity. This process ensures we capture the essential volatility patterns without overfitting, producing a reliable forecast engine for varying market conditions.
This automated process ensures we capture the essential volatility patterns without overfitting to random fluctuations.
Generating the Volatility Forecast
Once the optimal GARCH model is selected, it's applied to generate volatility forecasts. The model combines recent market shocks with past volatility estimates to produce a forward-looking measure of expected volatility. This approach yields specific forecasts that reflect current market conditions, rather than vague "it might be volatile" statements.
The GARCH model uses this equation to forecast future volatility:
σ²ₜ₊₁ = ω + α₁ × εₜ² + β₁ × σₜ² + β₂ × σₜ₋₁² + β₃ × σₜ₋₂²
Where:
- ω (omega): The long-term baseline volatility level
- αᵢ (alpha): How much past price shocks affect future volatility
- βⱼ (beta): How much past volatility forecasts influence future predictions
- p: Number of past shock terms (ARCH terms)
- q: Number of past volatility terms (GARCH terms)
- εₜ: The return innovation (price shock) at time t
- σₜ: The conditional volatility at time t
This framework adapts automatically to different market conditions - whether we're dealing with a GARCH(1,1) for simpler patterns or higher-order models for more complex volatility dynamics.
Why This Matters for Stock Price Estimates
Traditional approach: "Apple will go up 1.5% tomorrow" (same prediction regardless of market conditions)
Our approach: "Apple will go up 1.5% tomorrow" × volatility multiplier = calibrated prediction that matches current market conditions
During calm markets, we predict smaller moves. During volatile markets, we predict larger moves. This volatility-scaling transforms static predictions into market-adaptive forecasts.
The True Challenge: Making It Reliable
We now have a system that can detect volatility patterns, understand their nature, and produce forecasts that adjust to market conditions. But volatility-aware predictions are still raw - they can carry biases, work well in normal markets, yet falter in extremes.
That's where calibration comes in. Like tuning a race car, calibration corrects a model's tendencies so it performs reliably in all conditions. The goal isn't just to be better than static forecasts - it's to ensure that when we predict a 30% chance of an outcome, it truly happens about 30% of the time.
Coming Next: From Forecast to Finish
In Part 2, we'll reveal our three-method calibration system that transforms volatility-aware forecasts into trustworthy, actionable predictions:
- The Adaptable Strategist - Different strategies for high vs. normal volatility periods
- The Hybrid Approach - Smooth blending of bias correction with volatility adjustments
- The Advanced Method - Machine learning-powered calibration incorporating multiple market factors
We'll show real performance data demonstrating how this multi-method approach delivers dramatically more accurate predictions than any single method.
Who are we?
MarketCrunch AI is built by a mission-driven team of engineers, quants, and researchers from MAANG, high-frequency trading, and applied ML labs. We've shipped real-time systems, tuned signals in microseconds, and built AI that scales under pressure.
Our goal? Level the playing field by turning raw market data into fast, explainable, and actionable insights for every investor.
References
[1] Bollerslev, Tim, Robert F. Engle, and Daniel B. Nelson. "ARCH models." Handbook of econometrics 4 (1994): 2959–3038.
[2] Figlewski, Stephen, and Xiaozu Wang. "Is the" Leverage effect" a leverage effect?." (2000).
[3] Bauwens, Luc, Sébastien Laurent, and Jeroen VK Rombouts. "Multivariate GARCH models: a survey." Journal of applied econometrics 21, no. 1 (2006): 79–109.
[4] Brandt, Michael W., and Christopher S. Jones. "Volatility forecasting with range-based EGARCH models." Journal of Business & Economic Statistics 24, no. 4 (2006): 470–486.
[5] Akaike, Hirotugu. "Akaike's information criterion." In International encyclopedia of statistical science, pp. 41–42. Springer, Berlin, Heidelberg, 2025.