Understanding Volatility Clusters

GARCH(1,1) FOR VOLATILITY FORECASTING 📊 Constant volatility models assume market risk remains static, fundamentally missing the most obvious empirical fact in finance: volatility clusters. Large market moves follow large moves, while quiet periods persist - yet traditional models treat each day as independent. The GARCH (Generalized Autoregressive Conditional Heteroskedasticity) framework revolutionizes volatility forecasting by explicitly modeling time-varying conditional variance through just three parameters: omega (long-run variance), alpha (reaction to shocks), and beta (persistence). The fundamental paradigm shift: Traditional Models: "Volatility is constant or follows simple averages" GARCH(1,1): "Today's volatility emerges from both yesterday's shocks (α·ε²ₜ₋₁) and yesterday's conditional variance (β·σ²ₜ₋₁)" My empirical application to S&P 500 demonstrates transformative results: - Alpha coefficient of 0.142, beta of 0.809, persistence of 0.952 - Shock half-life of just 14 days vs permanent impact in random walk models - Superior MSE performance vs Historical Volatility and EWMA benchmarks - VaR violation rate of 1.1% (target: 1%) confirming accurate risk measurement - Long-run volatility convergence to 0.98% annualized This framework delivers three game-changing advantages: 📈 Volatility Clustering: Captures persistence while allowing mean reversion ⚡ Rapid Shock Response: Alpha parameter enables quick adaptation to market surprises 🎯 Parsimonious Power: Just 3 parameters outperform complex alternatives Real-world applications transforming risk management: - Dynamic VaR calculations responding to market conditions - Option pricing with accurate term structure of volatility - Portfolio optimization using conditional covariances - Capital allocation based on time-varying risk - Stress testing with realistic volatility dynamics - Derivatives hedging with adaptive risk measures How does your risk framework handle volatility clustering? Are you still assuming tomorrow's risk equals today's historical average? 🤔 #VolatilityForecasting #GARCH #RiskManagement #QuantitativeFinance #MarketRisk #FinancialModeling

Volatility is often blamed on fundamentals. This research challenges that. A new model shows that volatility can emerge entirely from the overlapping impact of metaorders without news, signal, or informed trading. Price movements arise mechanically from sequences of trades, whose effects follow a square-root law and decay over time. The model shows how the cumulative imbalance of buy and sell orders scales with time in a nonlinear way. When small trades dominate -> imbalances grow faster than linearly and show heavy-tailed behavior. As larger trades are weighted more -> the effect vanishes, and price behavior becomes close to random walk. And the data confirms this crossover. The result reframes how volatility and market impact are understood really. If volatility is driven by internal trade dynamics, not external information, then exec strategy, order structure, and flow correlations become key variables, and this is not what most models consider. Paper: https://lnkd.in/e3izh4c3 Authors: Guillaume Maitrier jean-philippe bouchaud No code

📊 Volatility tells part of the story. But fragility has a shape, and a memory. I tracked the TLT-IEF convexity spread and the clustering of SPY tails to see whether risk fades with volatility, or lingers in structure. Here’s what I uncovered: 🔹 Convexity stress flares when duration mismatches bite 🔹 ±2σ thresholds mark silent pressure points before liquidity strains surface 🔹 Tails don’t vanish with volatility spikes, they cluster, signalling fragility is persistent 🔹 Both signals show structure, not just surface noise It wasn’t calm. It was concealed stress. 👇 In this post: 🔹 TLT-IEF convexity spread (52-week z-score, with ±2σ bands) 🔹 SPY tail persistence (>±2σ returns across 26 weeks) 🔹 Stress periods mapped across major market events Volatility shows noise. Convexity and tails reveal structure. #Convexity #TailRisk #SystemicRisk #QuantStrategy #FinancePhD #MarketFragility #RiskSignals #MarketStructure

Beyond GARCH: Emergent Volatility Fields Every quantitative model of volatility from ARCH to GARCH and its many extensions relies on one implicit axiom: that today’s risk can be explained by yesterday’s noise. That assumption created an entire generation of models built on conditional variance: elegant, recursive, and completely blind to the geometry of modern markets. Volatility is not an accounting function of past returns. It’s an emergent property of how trust, liquidity, and leverage interact through time. Each of these variables carries its own probabilistic structure, its own rhythm, asymmetry, and breaking point. Fractal models revealed something extraordinary; volatility clusters across scales, as if the system remembered its own turbulence. But even those frameworks remained descriptive. They mapped complexity without reproducing its causes. At Quantis, we treat volatility as a field variable, not a historical statistic, a dependent surface that deforms under systemic stress, shaped by liquidity compression, feedback loops, and reflexivity. This is not another volatility forecast. It’s a redefinition of the space in which risk exists. When the field itself moves, risk stops being a number. It becomes geometry.  Figure – From Statistical Volatility to Emergent Risk Geometry Blue: Accounting volatility, reactive, backward-looking, based on weighted averages of past variance. Red: Emergent volatility, dynamic, self-generated, dependent on systemic state and network tension.

Intraday and Overnight Volatility Clustering Effect Volatility clustering has undergone extensive study within the daily timeframe. The paper delves into volatility clustering within intraday and overnight timeframes. It specifically investigates clustering within each timeframe and between them. - The paper investigates volatility clustering in global equity markets for both intraday and overnight returns.  - Volatility clustering is present across various time scales, from daily to longer periods.  - Overnight returns generally exhibit more pronounced volatility clustering compared to intraday returns.  - Cross clustering between intraday and overnight volatilities is relatively weak.  - Developed and emerging markets show consistent volatility clustering patterns. - The paper suggests a trading strategy of "buy on close and sell on opening" to arbitrage during significant overnight fluctuations, aiming to avoid negative returns caused by intraday volatility. - Long-term investment strategy recommendations include adopting a short position during intraday volatility clustering periods and a long position during overnight volatility clustering, as simultaneous large clustering in both types of volatility is unlikely. Reference: Xiaojun Zhao, Na Zhang, Yali Zhang, Chao Xu, Pengjian Shang, Equity markets volatility clustering: A multiscale analysis of intraday and overnight returns, Journal of Empirical Finance 77 (2024) 101487 #volatility #options #portfoliomanagement #quantitativefinance Abstract Volatility clustering, widely observed in daily equity market returns, has not been analyzed for high-resolution intraday and overnight returns, nor has its time scale dependency been systematically explored. This paper examines the volatility clustering of intraday and overnight returns in 15 global equity markets, both developed and emerging. Findings reveal universal volatility clustering in intraday and overnight returns across various time scales, from daily to monthly and beyond. It appears that the volatility clustering of overnight returns is even more pronounced than intraday returns. However, the cross clustering between two volatility series is generally weak within each market. These observations suggest both short- and long-term investment risks, providing meaningful insights for equity market investors’ risk management.

Why the Heston Model Matters in Modern Finance In financial markets, volatility is not constant. It changes over time, and understanding this behavior is crucial for option pricing, risk management, and strategic decision-making. One of the most celebrated models addressing this is the Heston Model, a breakthrough in how we think about stochastic volatility. 1 → What Is the Heston Model? The Heston Model is a stochastic volatility model where the variance (volatility squared) follows a mean-reverting process rather than remaining static. Instead of assuming that volatility is constant (as the Black-Scholes model does), Heston allowed volatility to move randomly and revert back to a long-term mean. It uses two coupled stochastic differential equations: → One for the asset price → One for the variance of the asset This captures how volatility itself is random but tends to revert toward a long-term average. 2 → Why Is It Important? → Captures Reality Better Markets exhibit volatility clustering: periods of high volatility followed by calmness. The Heston Model captures this beautifully. → More Accurate Option Pricing Since volatility isn’t constant, options priced under Black-Scholes assumptions can be mispriced. Heston corrects this, especially for out-of-the-money options. → Smile and Skew Effects Option implied volatilities show a “smile” or “skew” across strikes. The Heston Model can naturally produce these shapes, unlike simpler models. → Risk Management For hedging portfolios, understanding that volatility itself is uncertain helps design better dynamic hedging strategies. 3 → Real-World Relevance and Examples → Crypto Markets In crypto (like Bitcoin and Ethereum), volatility is high and fluctuating. Traders use Heston-based models to price options on crypto assets where simple models fail miserably. → Equity Derivatives Desks Big banks like Goldman Sachs, JP Morgan, and Morgan Stanley implement Heston dynamics for structured equity products and exotic options. → Volatility Trading Products Products like VIX options or variance swaps are sensitive to the dynamics of volatility itself. Heston gives a robust framework to model these instruments. → Insurance and Risk Consulting Financial institutions use the Heston framework to price guarantees in variable annuities where the underlying investments have volatile returns. 4 → Key Intuitions Behind the Model → Mean Reversion: Volatility is pulled back toward a long-term mean (like gravity). → Vol of Vol: The volatility itself is uncertain and can jump around, not smooth. → Correlation: In real markets, price and volatility often move inversely (market crashes lead to spikes in volatility). Heston captures this through negative correlation between the asset and variance. #Finance #QuantitativeFinance #CryptoFinance #Derivatives #OptionsTrading #RiskManagement #HestonModel #FinancialEngineering #Volatility #StochasticProcesses

💥 𝗛𝗮𝘃𝗲 𝘆𝗼𝘂 𝗲𝘃𝗲𝗿 𝗻𝗼𝘁𝗶𝗰𝗲𝗱 𝗵𝗼𝘄 𝗺𝗮𝗿𝗸𝗲𝘁𝘀 𝗰𝗮𝗻 𝗯𝗲 𝗰𝗮𝗹𝗺 𝗳𝗼𝗿 𝘄𝗲𝗲𝗸𝘀 — 𝘁𝗵𝗲𝗻 𝘀𝘂𝗱𝗱𝗲𝗻𝗹𝘆 𝗲𝘅𝗽𝗹𝗼𝗱𝗲 𝗶𝗻 𝘃𝗼𝗹𝗮𝘁𝗶𝗹𝗶𝘁𝘆? It's not random. 𝗜𝘁'𝘀 𝗮 𝗽𝗮𝘁𝘁𝗲𝗿𝗻. 𝗔𝗻𝗱 𝘆𝗼𝘂 𝗰𝗮𝗻 𝗺𝗼𝗱𝗲𝗹 𝗶𝘁. In my 𝘀𝗶𝘅𝘁𝗵 article of the 𝙁𝙞𝙣𝙖𝙣𝙘𝙞𝙖𝙡 𝙈𝙖𝙧𝙠𝙚𝙩 𝙐𝙣𝙘𝙤𝙫𝙚𝙧𝙚𝙙 𝙨𝙚𝙧𝙞𝙚𝙨 — “𝘍𝘰𝘳𝘦𝘤𝘢𝘴𝘵𝘪𝘯𝘨 𝘝𝘰𝘭𝘢𝘵𝘪𝘭𝘪𝘵𝘺: 𝘔𝘰𝘥𝘦𝘭𝘴, 𝘓𝘪𝘮𝘪𝘵𝘴, 𝘢𝘯𝘥 𝘗𝘳𝘢𝘤𝘵𝘪𝘤𝘢𝘭 𝘈𝘱𝘱𝘭𝘪𝘤𝘢𝘵𝘪𝘰𝘯𝘴” — I explore how volatility behaves in the real world, and how we can forecast it with models that actually respond to market conditions. 📉 Volatility is not constant — it clusters, shows memory, and reacts asymmetrically to shocks. This article reviews the full modeling spectrum: from EWMA to GARCH(1,1) and advanced extensions like EGARCH, GJR-GARCH, and Student-t GARCH. 🔍 What you’ll learn: • Why volatility forecasting is essential for VaR, CVaR, derivatives pricing, and risk targeting • How GARCH models work — and where they fall short • When to use asymmetry (GJR), fat tails (Student-t), or regime-switching approaches • What stochastic volatility and machine learning models add to the forecasting game 📊 With Python code examples, real market use cases, and visual diagnostics, this article connects the theory to the trading desk — one volatility spike at a time. ➡️ 𝗖𝗼𝗺𝗶𝗻𝗴 𝘂𝗽 𝗻𝗲𝘅𝘁:  𝗪𝗵𝗮𝘁 𝗶𝗳 𝗮𝗻 𝗼𝗽𝘁𝗶𝗼𝗻 𝗽𝗮𝘆𝗼𝗳𝗳 𝗱𝗲𝗽𝗲𝗻𝗱𝘀 𝗼𝗻 𝘁𝗵𝗲 𝗽𝗮𝘁𝗵 — 𝗻𝗼𝘁 𝗷𝘂𝘀𝘁 𝘁𝗵𝗲 𝗲𝗻𝗱? I’ll explore the world of exotic options — barrier, Asian, digital, binary, and more. We’ll break down how they’re structured, priced, and traded — and how path-dependence changes everything. #Volatility #Forecasting #GARCH #VaR #CVaR #RiskManagement #QuantitativeFinance #Derivatives #OptionsTrading #EGARCH #MachineLearning #StochasticVolatility #FinancialMarkets #ExoticOptions #FinancialMarketUncovered