How does a trader implement delta hedging for a long call option in discrete time?

• A. Short or buy underlying shares to offset the option's delta, rebalance as delta changes, and factor in costs, funding and slippage.
• B. Hedge using only options and no underlying trading.
• C. Hedge by waiting for expiration; no rebalancing.
• D. Hedge by adjusting only implied volatility input.

Answer: (B)

Delta hedging a long call in discrete time means offsetting the option’s positive delta with a position in the underlying and rebalancing as that delta changes. Since a long call has a positive delta, you would take an opposite position in the underlying—typically short shares—to push the net portfolio delta toward zero at the hedging moment. But delta isn’t static: as the underlying moves (and as time passes), the option’s delta shifts (that's gamma), so you must rebalance at discrete intervals or after notable moves to keep the hedge approximately neutral.

Important practical points: you’re not just trading to match delta; you also face costs from executing trades, the funding cost of carrying the short underlying, and the possibility of slippage if fills aren’t perfect. These factors mean the hedge is approximate in discrete time, but it materially reduces directional risk from movements in the underlying.

Context for why other ideas don’t work as a standalone hedge: hedging with only options doesn’t eliminate delta risk because options themselves have nonzero delta; waiting until expiration leaves you unhedged for a long period; adjusting only the input for implied volatility does not address the actual price movement risk of the underlying.