Explanation

Vega measures the sensitivity of an option's price to changes in implied volatility.

For European options with the same underlying, strike price, and time to expiration:

• Call and put options have the same vega

This is because:

• Both calls and puts benefit from increased volatility
• The vega formula is identical for both call and put options
• Put-call parity relationship ensures that volatility affects both options equally

Given:

• Same underlying
• Same strike price (100)
• Same remaining maturity (1 month)
• Same contract size (1,000 shares)

The vega of Option 1 (call) is equal to the vega of Option 2 (put).

Therefore, option B is correct: the vega of Option 1 is equal to Option 2.