Answer: The book has a long position in up-and-out call options.

## Explanation A **negative delta** in an options book with only long positions is possible with certain exotic options that have **negative delta characteristics** even when held long. ### Key Concepts: - **Delta**: Measures the sensitivity of an option's price to changes in the underlying asset price - **Standard options**: Long calls have positive delta, long puts have negative delta - **Exotic options**: Can have non-standard delta behavior ### Analysis of Options: **Option C - Up-and-out call options**: - These are **barrier options** that become worthless if the underlying price reaches a predetermined barrier level - When the underlying price approaches the barrier, the option's value decreases as the probability of knockout increases - This creates a **negative delta** effect - as the underlying price rises toward the barrier, the option loses value - Therefore, long positions in up-and-out calls can have negative delta **Other options analysis**: - **A. Up-and-in calls**: Have positive delta (standard call behavior once activated) - **B. Binary options**: Typically have positive delta for calls, negative for puts - **D. Down-and-out calls**: Have positive delta (standard call behavior until barrier is hit) ### Conclusion: Up-and-out call options are the only ones among the choices that can exhibit negative delta when held long, making option C the correct explanation.

Author: LeetQuiz .