Question

1. A European-style put option on Cyan Inc. with three months until expiration and an exercise price of $55 is trading at $2.85. A forward contract on Cyan stock with three months until expiration has a forward price of $58.43 and the risk-free rate is 3%. What is the no-arbitrage price of a European-style call on Cyan stock with three months until expiration and an exercise price of $55? (2 points)

Answer 1

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