Explanation

For a call option on a stock paying continuous dividends, the delta is given by:

$\Delta_{call} = e^{-qT} \cdot N(d_1)$

Where:

• $q$ = continuous dividend yield = 1% = 0.01
• $T$ = time to maturity = 2 years
• $N(d_1)$ = 0.64

Substituting the values: $\Delta_{call} = e^{-0.01 \times 2} \times 0.64$ $\Delta_{call} = e^{-0.02} \times 0.64$ $\Delta_{call} = 0.9802 \times 0.64$ $\Delta_{call} = 0.6273 \approx 0.63$

Therefore, the correct delta is approximately 0.63.

Key Points:

• The delta of a call option is not simply $N(d_1)$ when there are dividends
• The dividend yield reduces the delta by the factor $e^{-qT}$
• Without dividends, delta would be 0.64, but with 1% dividend yield over 2 years, it's reduced to 0.63