How does volatility arbitrage work, and how do traders profit from the gap between implied and realized volatility?

Volatility arbitrage exploits the difference between implied volatility (priced into options) and the trader's forecast of future realized volatility. The trader takes a position in options and continuously delta-hedges the directional exposure, leaving a pure bet on whether actual volatility will exceed or fall short of the implied level.\n\nCore Mechanism:\n\nIf IV > Expected RV: Sell options (short volatility), delta-hedge -> collect premium\nIf IV < Expected RV: Buy options (long volatility), delta-hedge -> gamma profits exceed theta decay\n\n`mermaid\ngraph TD\n A[\"Implied Vol = 28%
Forecast Realized Vol = 34%\"] --> B{\"IV < RV Forecast\"}\n B --> C[\"Buy ATM Straddle
on Wellford Corp
Cost: $4.80\"]\n C --> D[\"Delta-Hedge Daily
Buy/sell shares to stay delta-neutral\"]\n D --> E{\"Actual RV?\"}\n E -->|\"RV = 36%
(above IV)\"| F[\"Gamma P&L > Theta
Net Profit\"]\n E -->|\"RV = 22%
(below IV)\"| G[\"Theta > Gamma P&L
Net Loss\"]\n`\n\nP&L Decomposition:\n\nDaily delta-hedged P&L (for a long gamma position):\n\nP&L_daily = 0.5 x Gamma x S^2 x (realized_move^2 - implied_move^2)\n\nwhere implied_move^2 = (IV^2 / 252) and realized_move^2 = actual daily return^2.\n\nWorked Example:\n\nGranville Trading buys a 1-month ATM straddle on Wellford Corp (S = $120, IV = 28%, premium = $4.80 per share, gamma = 0.042).\n\nDaily theta cost: $4.80 / 21 trading days = $0.229/day\n\nDay 1: Stock moves +$2.40 (+2.0%)\n- Gamma P&L: 0.5 x 0.042 x (2.40)^2 = +$0.121\n- Net Day 1: $0.121 - $0.229 = -$0.108\n\nDay 2: Stock moves -$3.60 (-3.0%)\n- Gamma P&L: 0.5 x 0.042 x (3.60)^2 = +$0.272\n- Net Day 2: $0.272 - $0.229 = +$0.043\n\nThe trade profits when daily moves consistently exceed the implied daily move of $120 x 28% / sqrt(252) = $2.12.\n\nRisks of Vol Arb:\n- Model risk: Gamma and delta estimates depend on the pricing model\n- Discrete hedging: Hedging once per day vs continuous creates hedging error\n- Jump risk: Large gaps (earnings, events) can cause losses beyond what gamma captures\n- Transaction costs: Frequent delta adjustments erode gamma profits\n- Vega risk: If IV moves against you before the trade plays out, mark-to-market losses can force early exit\n\nKey Exam Points:\n- Vol arb is a bet on realized vs implied, not on direction\n- The trader must accurately forecast realized volatility, which is itself uncertain\n- Professional vol arb desks typically run hundreds of positions to diversify idiosyncratic risk\n\nPractice volatility strategies in our CFA Derivatives question bank.