Delta-hedging

Quantitative Finance Glossary

Continuous rebalancing of the underlying position to keep the portfolio delta-neutral: hold -Δ_t shares against a long option. In the BSM idealisation rebalancing is continuous and frictionless, perfectly replicating the payoff at cost equal to the BSM price. In practice, rebalancing is discrete (incurring gamma slippage proportional to tfrac12Gamma,(Δ S)^2 per step) and pays transaction costs, so dealers hedge at intervals that trade off these two; the canonical analysis is Leland (1985), who derives a vol-adjusted BSM with proportional costs.

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