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Relative value volatility

Trading the difference between an option's implied volatility and the volatility the trader expects to be realised, with the price exposure hedged away.

The pure form is: sell options you think are expensive in volatility terms, hedge the delta continuously, and collect the difference between what you sold and what the underlying delivers. The reverse for options you think are cheap.

It is usually called volatility arbitrage, but it is not riskless. The hedging is imperfect, the model that produced the implied volatility may be wrong, and the position can be right about eventual realised volatility while being liquidated on a mark-to-market loss along the way. The discipline it demands is continuous delta-hedging and honest accounting of transaction costs.

Example: XYZ 30-day options imply 28% while your estimate of realised volatility is 21%. Sell the straddle, hedge daily, and the position earns if XYZ chops. It loses if XYZ trends, even if the eventual realised figure comes in at 21%, because your rebalancing happened at the wrong prices.

Related: gamma-scalping, implied-vs-realized, delta-hedging, index-dispersion

See it drawn

Original diagrams for the ideas on this page. Illustrative, not real market data.

How a call option's delta changes with the underlying priceAn S-shaped curve rising from zero, passing through about a half at the strike, and flattening near one.Delta of a call option1.000.5008090110120Out of the moneyAt the moneyIn the money1.00 means it moves one-for-one with the stockdelta ≈ 0.50 at the strikeStrike 100Underlying price
Delta across the range of prices. Delta says how much a call's price moves for a one-point move in the stock. Far below the strike it is near 0 and the option barely reacts; at the strike it is about 0.50; far above it approaches 1 and tracks the stock.

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