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Advanced Proof

Delta-Neutral Hedging: The Dynamics of the Hedge Ratio

Students often confuse Δ \Delta as a constant. In reality, Δ \Delta is time-varying and price-dependent. The 'Gamma' risk—the second-order derivative 2V/S2 \partial^2 V / \partial S^2 —implies that the hedge ratio must be dynamically updated as S S fluctuates to maintain neutrality.
Institutional Reference: Advanced Stochastic Processes
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