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QUESTION 4 4.1. Use put-call parity to show that the cost of a butterfly spread created from European puts is identical to the cost of a butterfly spread created from European calls. 4.2. A stock price is currently $50. Over each of the next two 3-month periods it is expected to go up by 6% or down by 5%. The risk-free interest rate is 5% per annum with continuous compounding, what is the value of a 6- month European call option with a strike price of $51? For the situation considered above, what is the value of a 6-month European put option with a strike price of $51? Verify that the European call and European put prices satisfy put-call parity. If the put option were American, would it ever be optimal to exercise it early at any of the nodes on the tree? 4.3 TOTAL 33.3% Continued overleaf... QUESTION 4 4.1. Use put-call parity to show that the cost of a butterfly spread created from European puts is identical to the cost of a butterfly spread created from European calls. 4.2. A stock price is currently $50. Over each of the next two 3-month periods it is expected to go up by 6% or down by 5%. The risk-free interest rate is 5% per annum with continuous compounding, what is the value of a 6- month European call option with a strike price of $51? For the situation considered above, what is the value of a 6-month European put option with a strike price of $51? Verify that the European call and European put prices satisfy put-call parity. If the put option were American, would it ever be optimal to exercise it early at any of the nodes on the tree? 4.3 TOTAL 33.3% Continued overleaf