Volatility Arbitrage

Volatility arbitrage is a strategy that buys options whose implied volatility looks too low, or sells options whose implied volatility looks too high, compared with a forecast of the volatility that will actually occur. The options are delta hedged, so that profit comes from the difference between implied and realised volatility rather than from direction. Despite the name, it is not riskless arbitrage: it depends on forecasts that can be wrong and on hedging that is imperfect.

The core idea#

When you buy an option and delta hedge it continuously, your profit is approximately:

P&L ≈ ½ × Σ gamma × S² × (σ²_realised - σ²_implied) × Δt

In words: you earn the difference between realised and implied variance, weighted by the option's dollar gamma over its life. Long options profit if realised exceeds implied; short options profit if implied exceeds realised. See Gamma Scalping and Delta Hedging.

The steps#

1. Forecast volatility for the option's life.
2. Compare with implied volatility across strikes and expiries.
3. Trade the gap: buy options where implied is below your forecast, sell where it is above.
4. Delta hedge regularly.
5. Close or roll as the gap closes or expiry nears.

Forecasting volatility#

Research generally finds implied volatility is a useful but upwardly biased forecast of realised volatility for equity indices, because of the volatility risk premium.

Sources of mispricing#

• Supply and demand imbalances: heavy option buying for hedging or speculation inflates implied volatility; structured product issuance and overwriting can depress it.
• Slow adjustment after regime changes.
• Event mispricing: the market over or underestimates the size of an announcement.
• Relative mispricing between related underlyings or between options and variance swaps.

Why it is not true arbitrage#

• Forecast error: realised volatility can differ greatly from any forecast.
• Path dependence: profit depends on when moves happen. A big move when gamma is small (far from the strike or far from expiry) contributes little.
• Discrete hedging: hedging daily rather than continuously adds noise.
• Costs: spreads and commissions on options and hedges.
• Jumps: sudden gaps can overwhelm hedges.
• Implied volatility moves create mark to market gains and losses before expiry.

Variance swaps as cleaner tools#

Because option based volatility arbitrage depends on gamma along the path, many professionals prefer variance swaps, whose payoff depends directly on realised variance regardless of where the price moves. See Variance and Volatility Swaps.

Who does it#

Volatility arbitrage is practised by hedge funds, bank trading desks and options market makers, who have the forecasting models, low costs and infrastructure needed to hedge efficiently. Individual traders can apply the principles, but costs and hedging discipline are major challenges. See Volatility Trading.

Frequently asked questions#

What is volatility arbitrage?#

A strategy that trades delta hedged options when implied volatility differs from a forecast of realised volatility, aiming to profit from the gap.

Is volatility arbitrage risk free?#

No. It depends on volatility forecasts, which can be wrong, and on hedging that is never perfect.

How do traders forecast volatility?#

With historical realised volatility, GARCH and similar models, information from implied volatility itself and adjustments for known events.

Next, learn the cleanest volatility instruments in Variance and Volatility Swaps.