The correct answer is B: Buy the futures contract and sell the underlying. This situation represents an index arbitrage opportunity. The parity condition between the equity index price and the futures contract price is not met, which can be exploited for potential arbitrage profit. The theoretical value of the futures price is calculated using the formula:

$\text{Price} (F_0,t) = S_0 \times e^{(r - q) \times t}$

where:

• $S_0$ is the current spot price of the index (USD 3,625),
• $r$ is the continuously compounded risk-free rate (5% per year),
• $q$ is the continuously compounded dividend yield (2% per year),
• $t$ is the time to expiration in years (15 months, or 1.25 years).

Plugging in the values, we get:

$\text{Theoretical futures price} = 3625 \times e^{(0.05 - 0.02) \times 1.25} = 3625 \times e^{0.03 \times 1.25} = 3625 \times e^{0.0375} \approx 3763.52$

Since the current futures price (USD 3,759.52) is higher than the theoretical futures price (USD 3,763.52), an arbitrageur would sell the futures contract and buy the underlying equity index to lock in a profit. This is because the market price of the futures contract is above its theoretical value, indicating that the futures contract is overpriced relative to the underlying index. By selling the overpriced futures and buying the underpriced underlying, the arbitrageur can profit from the price discrepancy once the market corrects itself.