Volatility in Derivatives Markets

📊 Volatility Models in Quant Finance — Master These! ⚡ Volatility modeling isn’t just about plugging into Black-Scholes. It’s about capturing the true behavior of markets — smiles, skews, jumps, and roughness. Here are the most widely used volatility models, from classical to cutting-edge: ➡️ Black-Scholes (Constant Volatility) Simple and closed-form. Assumes volatility stays constant — often too simplistic for real markets. ➡️ Local Volatility (Dupire Model) Volatility is a deterministic function of time and asset price. Fits the entire implied vol surface, but can overfit. ➡️ Stochastic Volatility (Heston, Hull-White, etc.) Volatility evolves as its own random process. Captures skew and mean reversion in volatility. ➡️ SABR Model Designed for rates and FX. Combines stochastic volatility with power-law dynamics, capturing smiles and shifts. ➡️ Stochastic Local Volatility (SLV) Combines local and stochastic vol. Flexible and fits market prices well — used heavily in exotic option desks. ➡️ GARCH / EGARCH / NGARCH Models Volatility estimated from historical returns. Common in risk management, but less suited for option pricing. ➡️ Jump-Diffusion Models (e.g., Merton) Adds jumps to the price process. Captures sudden spikes in volatility that diffusion models miss. ➡️ Variance Gamma / CGMY Models Pure jump processes — no Brownian motion. Good at modeling heavy tails and kurtosis in returns. ➡️ Rough Volatility (e.g., Rough Heston) Volatility behaves like a rough fractional process. Matches high-frequency data better than any other model. ➡️ Markov-Regime Switching Models Volatility switches between regimes (e.g., calm ↔ crisis). Useful for modeling sudden changes in market conditions. ➡️ Stochastic Volatility with Jumps (SVJ) Combines stochastic vol with price jumps — extremely useful in equity and credit markets. 💡 Whether you’re building a volatility surface, pricing exotics, or forecasting market risk, these models are your toolbox. #QuantFinance #VolatilityModeling #RiskManagement #HestonModel #SABR #RoughVolatility #SLV #GARCH #OptionPricing #ExoticOptions #QuantResearch

When Finance Breaks Calculus, The Power of Quadratic Variation In the real world, asset prices don’t move smoothly, they bounce, jolt, and stutter with every tick. The concept of quadratic variation flips this expectation upside down and explains why we need entirely new tools to model financial markets. 1. Why Classical Calculus Doesn’t Work ➤ In school, we’re taught that a function is “well-behaved” if it’s continuous and has a derivative. This works for things like temperature curves or car speed, ➤ But in quant finance, asset prices modeled by Brownian motion (the foundation of many models) are continuous but wildly irregular. You can’t pin down a rate of change, the path is too jagged, ➤ This is why we say Brownian motion has “infinite variation” in any interval. You can’t apply normal derivatives or integrals to it, they simply don’t exist in the way we’re used to, 2. What Is Quadratic Variation (In Plain Terms)? ➤ Think of it as a way to measure how rough a process is. Instead of measuring the slope, we measure how erratic the path is over time, ➤ For smooth functions, this erraticness approaches zero. But for Brownian motion, it builds steadily, it accumulates volatility, ➤ This property forces us to replace traditional calculus with stochastic calculus, which is designed to handle uncertainty, jumps, and randomness at a foundational level, 3. Why This Matters in Quantitative Finance ➤ Option Pricing: Every time you price a vanilla or exotic derivative using models like Black-Scholes, Heston, or SABR, you’re relying on stochastic integrals, which only work because quadratic variation tells us how to integrate randomness, ➤ Portfolio Hedging: Delta-hedging strategies use simulated price paths to estimate and neutralize risk. Without recognizing that asset prices are not smooth, hedges become inaccurate and can cause large PnL swings, ➤ Risk Management: Monte Carlo engines simulate thousands of price paths using Brownian motion. If you assume these paths behave like ordinary curves, your entire Value at Risk (VaR) or Expected Shortfall (ES) framework breaks, 4. A Practical Analogy from Industry ➤ Imagine a trader at a major investment bank running a derivatives desk. Every night, their models recalibrate based on fresh market data, curves, volatilities, correlations. Underneath it all, the simulation engine assumes the price paths are based on stochastic processes with well-defined quadratic variation, ➤ If you removed that concept, your model would either explode in volatility or become completely blind to actual risk, like measuring earthquake risk by just looking at average wind speeds, ➤ This is why even the most advanced desks in firms like Goldman Sachs, Morgan Stanley, or hedge funds like Citadel and Two Sigma bake this concept into the core of their modeling libraries, #QuantitativeFinance #QuadraticVariation #StochasticCalculus #BrownianMotion #Derivatives #RiskModeling

🧨 Triple Witching, De-Fanged: How $6 Trillion in Derivatives Expire Four Fridays a year (March, June, September, December) feel like Wall Street’s version of a full-moon party: stock-index futures, index options, and single-stock/ETF options all die on the same afternoon. 1️⃣ Core Concept — What, When, Why the Spooky Name? • Three giant stopwatches—futures, index options, equity options—hit 00 : 00 together. • 1980s floor traders called the hour “bewitched,” so the nickname stuck. • In June 2025, roughly $6.5 trillion of contracts will vanish in one session. 2️⃣ Market Mechanics in Plain English • Dealer Gamma Unwind – Market makers are short options; as gamma spikes into expiry, they yank hedges, jolting prices. • Institutional Rolling – Asset managers close June futures, open September, spraying algos all day. • Options Pinning – Index hovers near “max-pain” strikes (huge open-interest magnets) until contracts die. • Witching Hour – 3–4 p.m. ET delivers the biggest spikes in volume and spreads. 3️⃣ How It Shows Up on the Tape • Volume: S&P futures trade about 2× a normal Friday; equities add ~1.5 billion shares. • Volatility: Intraday realized vol jumps ~40 %, then mean-reverts by Tuesday. • Spreads: Bid-ask gaps balloon in the final 30 minutes—market orders become landmines. 4️⃣ Why the Noise Rarely Lasts • Twenty-five-year data show an average triple-witch return of –0.04 %—statistically flat. • By Monday afternoon, the index is almost exactly where a random walk would predict. • Translation: fireworks intraday, no lasting trend. 5️⃣ India’s Perpetual “Mini Witching” • Last-Thursday monthly expiry already collapses all four contract types into one session. • Weekly index options replay the drama most Thursdays (moving to Tuesday for NSE from 1 Sep 2025). • Result: Indian traders live with a functional “triple witching” monthly, plus weekly aftershocks. 6️⃣ Investor Impact — Who Should Care? • Long-Horizon Investors – Stay diversified; ignore the strobe lights. • Active Equity Traders – Avoid late-day market orders; tighten stops; manage slippage. • Derivatives Specialists – Expiry is opportunity and risk; edge comes from gamma maps, OI heat-screens, strict sizing. 7️⃣ Practical Option Set-Ups (Illustrative Only) • Harvest IV Crush: Zero-DTE iron condor, exit an hour before the bell. • Ride a Vol Spike: ATM long straddle, gamma-scalp every ±0.25 % move. • Exploit Pinning: Broken-wing butterfly at max-pain strike • Institutional Roll Mimic: Futures calendar spread—sell expiring, buy next. 🔔 Takeaway — Fireworks or Minefield? For most investors, triple witching is a quarterly light show best watched from the safety of a long-term portfolio. For nimble intraday traders it’s fertile but treacherous ground. Edge exists—if you trade defined-risk structures, follow real-time data, and know when to walk away. Follow Quantace Research Disclosures :https://lnkd.in/d58vgQwk

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