Futures Price = [Spot Price + PV of Cost of Carry - PV of Dividends]*Future Value Factor = [S + (C*e^-rt) + (D*e^-rt)]*e^rt
Where S = Spot Rate, e = constant (2.71828), r = Risk Free Rate, t = years to expiry
Applying the above formula,
Futures Price = 58.43, r = 0.03, t = 3/12 = 1/4, C = 0, D = 0
Therefore,
58.43 = [S + 0 +0]*e^0.03*1/4
58.43 = S*e^0.0075
58.43 = S*1.0075
Therefore, Current Spot Price = S = 58.43/1.0075 = $57.995
As per Put Call Parity, the prices of options with same strike price & expiry date are as follows:
Price of Call + PV of Exercise Price = Spot Price (Current Stock Price) + Price of Put
Interest Rate is assumed as continuous compounding
Therefore,
C + [55*(e^-0.0075)] = 57.995 + 2.85
C + [55*0.9925(from table)] = 60.845
Therefore, Price of Call = C = 60.845 – 54.5875 = 6.2575 = $6.26
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