Calculate the theoretical price for the sampp500 index


The spot index value = 2,280.90

SP CME S&P 500 FUTURES

SETTLEMENT PRICES AS OF 01/30/17 06:00 PM (CST)

MTH/      ------------- DAILY -----------------------    PT                ----- PRIOR DAY --

STRIKE    OPEN     HIGH      LOW      LAST     SETT    CHGE EST.VOL     SETT     VOL     INT

MAR17 2283.10 2285.30B 2264.00   2275.80   2276.00 -13.10     1798 2289.10    4146 64465

JUN17 2273.30 2273.30   2259.00A 2270.00B 2270.90 -13.10       16 2284.00     485    1764

SEP17    ----    ---- 2254.70A 2265.70B 2266.60 -13.10           2279.70              22

DEC17     ----    ---- 2251.20A 2262.20B 2263.10 -13.10          2276.20

MAR18     ----    ---- 2257.10A 2268.10B 2269.00 -13.10          2282.10

JUN18     ----    ---- 2263.00A 2274.00B 2274.90 -13.10          2288.00

SEP18     ----    ---- 2268.90A 2279.90B 2280.80 -13.10          2293.90

DEC18     ----    ----   2258.00A 2269.00B 2269.90 -13.10          2283.00

DEC19     ----    ----   2281.10A 2292.10B 2293.00 -13.10          2306.10

DEC20     ----     ----      ----      ----   2316.10 -13.10          2329.20

DEC21     ----     ----      ----      ----   2339.20 -13.10          2352.30

TOTAL                                                          EST.VOL           VOLUME OPEN INT

TOTAL                                                             1814             6304    66241

(a) Calculate the theoretical price for the S&P500 index futures maturing in December 2017. Assume that the dividend yield on the index is 1.5% per year continuously compounded. Use the above quotes to determine whether there is an arbitrage opportunity. If there is an opportunity, show how the arbitrage would be made, using a payoff table. Assume that the futures contract expires at the end of the month, and use a T-bill rate of 0.70% per year continuously compounded. What are the potential problems with the arbitrage?

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Financial Management: Calculate the theoretical price for the sampp500 index
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