Final answer:
The no-arbitrage futures price for a position in E-mini S&P 500 futures contracts is determined using the current S&P 500 index value, the continuously compounded rate, the continuous dividend yield, and the time to expiration. The futures price is calculated using an exponential formula, then adjusted for the number of contracts and the contract unit.
Step-by-step explanation:
The student has asked for the calculation of the no-arbitrage futures price for a position in E-mini S&P 500 futures contracts, given the value of the S&P 500 index, the continuously compounded rate, the continuous dividend yield, and the time to expiration of the futures contract.
To calculate the no-arbitrage futures price (F) of the position, we use the formula:
F = S * e(r - q) * t
where:
- S is the current value of the S&P 500 index (3565)
- r is the continuously compounded interest rate (4.7% or 0.047 as a decimal)
- q is the continuous dividend yield (2.6% or 0.026 as a decimal)
- t is the time to expiration in years (280/365, considering there are 365 days in a year)
The contract unit for each E-mini future is $50 multiplied by the S&P 500 index, and since the student considers trading 10 E-mini futures, we need to multiply the calculated futures price by 10 and the contract unit.
Based on the given information, the no-arbitrage futures price of one contract is:
F = 3565 * e(0.047 - 0.026) * (280/365)
After calculating F, we would then calculate the total position value by:
Total Position Value = F * $50 * 10
This calculation gives the no-arbitrage price of the total position in E-mini S&P 500 futures contracts that the student is considering.