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Delta-Hedged Gains and the Negative Market Volatility Risk Premium

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What they found

The authors isolate the volatility risk premium by looking at delta-hedged option positions on the S&P 500 from 1988 to 1995. If volatility risk were not priced, a continuously delta-hedged long option should break even; instead it consistently lost money, and the losses were larger when implied volatility was high and after market drops. This shows that the market charges a negative premium for volatility risk: investors pay to be long volatility because it pays off in bad states. The result held across strikes and maturities and was not driven by jumps alone.

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.

What you can use

  • Even a perfectly delta-hedged long option loses money on average; the premium is in the volatility, not the direction.
  • Implied volatility exceeds subsequent realized volatility on average, which is the source of returns for option sellers.
  • The premium is largest after sell-offs when fear is high, which is when selling volatility is most profitable and most dangerous.

Caveats

Index options in a relatively short sample; delta hedging in practice is discrete and costly. Technical.

Tags: options, variance-risk-premium, delta-hedging, implied-volatility

Summaries are our own reading of the paper, not the authors' words. Educational only, not advice. Discuss it in Book Club.