On November 8 2023, the S&P 500 index is at 1,300, the continuously compounded dividend yield is 3% p.a, and the continuously compounded risk-free rate is 5.2% p.a.

Assume the transaction cost is zero.

a) What is the theoretical futures price for a December contract that expires on 18th

December 2023?

b) If on November 8 2023, the futures contract is priced at 1,320, is there any arbitrage opportunity? If yes, show the overall profit from this opportunity assuming that the arbitrage transaction will be executed by borrowing $20 million, the multiplier of S&P is 250, and the S&P index stood at 1340 on December18.