User:Gxti, CC BY 3.0 · CC-BY-3.0 · Wikimedia Commons
Delta is the rate of change of option value per dollar move in the underlying. Delta hedging means buying or selling shares so the portfolio's instantaneous P&L from a small underlying move is zero. It only kills the linear term β convexity (gamma) leaks through, which is what dynamic hedging captures.
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Worked example
You sell one call option contract on a stock at strike $\$100$. The contract covers $100$ shares, and the call's delta is $0.5$. How many shares should you buy or sell to be delta-hedged?
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Practice 1 of 3Type a fraction, decimal, or expression β mathjs parses it.
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Reflection
Why does delta-hedging fail to capture gamma exposure? What kind of P&L does an unhedged short-gamma position produce when markets are quiet vs volatile?
