Final answer:
The future price for a four-month contract on a stock index can be calculated using the cost-of-carry model, which includes the current index level, risk-free interest rate, and dividend yield. One month later, the value of the contract is updated using the same formula but with the new index level and remaining time to maturity.
Step-by-step explanation:
When calculating the futures price for a four-month contract on a stock index with the given parameters, we use the cost-of-carry model which takes into account the current stock index level, the risk-free interest rate, and the dividend yield. The formula for the futures price (F) is given by: F = Se(r - q)T, where S is the current index level, r is the risk-free interest rate with continuous compounding, q is the dividend yield, and T is the time to maturity in years. In this case, F = 350e(0.08 - 0.04)(4/12). After one month, the value of the contract is reassessed based on the new index level and the reduced time to maturity.
For part b) of the question, to determine the value of the futures contract one month later when the index is at 351 and other factors remain unchanged, we again apply the formula with the adjusted index level and time to maturity, which is now three months (0.25 years): F = 351e(0.08 - 0.04)(3/12).