Consider a European call and a European put on a non- dividend-paying stock. Both the...
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Consider a European call and a European put on a non- dividend-paying stock. Both the call and the put will expire in two years and have the same strike prices of $110. The stock currently sells for $115. The risk-free rate is 3% per annum. The price of the call is $15, and the price of the put is $5. Is there an arbitrage? If so, what is the arbitrage profit today? (Consider an arbitrage strategy where we long or short one contract each for both call and put, and the net cash flow in year 2 is zero) There is no arbitrage. $1.406 $1.493 $1.527 The following is an attempt to prove that it is never optimal to exercise early an American call option on a continuous- dividend paying stock. The option has the strike price K, and the expiration date T. Which of the following steps is incorrect? Let Ct be the option price and St be the stock price at time t. q(>0) is the dividend yield, and r(>0) is the risk-free rate per annum. (1) If Ct > St K for all t( Ct. Using the put-call parity, it follows that Ct > P+ + Ste-9(T-t) - Ke-r(T-t). (3) The inequality in (2) can be rewritten as C+ 2 Pt+ (St K) + (St Ste=9(T-1)) + (K Ke=r(T-1)). (4) Because pt is non-negative, and (St Se-q(Tt)) and (K Ke-r(Tt)) are all positive for every t( (St K)
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