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.