Delta Hedging for ITM Call Option

This interview question focuses on delta hedging for a deep in-the-money European call option as it approaches expiry, after you have already been running a hedge for most of the option's life. The setup asks you to reason qualitatively about how the option's delta evolves when the underlying stock drifts lower over a period close to maturity, and to translate that view into concrete trading actions in the underlying. It is the kind of scenario-based question often used in sell-side derivatives or options market-making interviews to see whether candidates can connect option Greeks to actual hedge adjustments.

To answer well, you need a clear grasp of how delta behaves as a function of moneyness and time to expiry, and how this interacts with the recent price path of the underlying. The problem leans on intuition about theta and gamma, and understanding how they compete when the option is already deep in-the-money but time is short and the underlying is moving. Interviewers are watching for consistent reasoning about the direction of delta's change and the corresponding buy/sell flows required to remain delta-neutral.

What it tests

The delta of an option measures the sensitivity of the option's price to changes in the price of the underlying asset. For European options, delta evolves over time due to both the passage of time (theta decay) and movements in the underlying asset's price. As expiration approaches, the delta of an in-the-money call option approaches 1, reflecting the increasing likelihood that the option will be exercised, while the delta of an out-of-the-money call approaches 0. The interplay between time decay and price movement means that delta is not static: time decay pushes the delta of in-the-money calls higher, while a falling underlying price pulls it lower. The dominant effect depends on the option's moneyness and the magnitude of the price move relative to the time remaining.