Answer-first summary for fast verification
Answer: $2,475.12
Over the six-month period from June 30th to December 31st, the average dividend yield is: \[ \bar q = \frac{4\%\times 4 + 7\%\times 2}{6} = 5\% \] Using the cost-of-carry formula with continuous compounding: \[ F_0 = S_0 e^{(r-q)T} \] where \(S_0 = 2500\), \(r=3\%\), \(q=5\%\), and \(T=0.5\). Thus: \[ F_0 = 2500\, e^{(0.03-0.05)0.5} = 2475.12 \] So the nearest theoretical futures price is **$2,475.12**.
Author: Manit Arora
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718.1. Assume that the risk-free rate is 3.0% per annum with continuous compounding and that the dividend yield on a stock index varies throughout the year. In January, April, July, and October, dividends are paid at a rate of 7.0% per annum. In other months, dividends are paid at a rate of 4.0% per annum. Suppose that the value of the index on June 30th is 2,500. Which is nearest to the theoretical futures price for a contract deliverable on December 31st? (this question is inspired by Hull's EOC Problem 5.11)
A
$2,450.50
B
$2,475.12
C
$2,602.03
D
$2,708.22
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