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ADMS4503 3.0 Assignment #2 Page 1 AP/ADMS4503 3.0 Derivative Securities Winter 2010 Assignment #2 Solutions Instructions: (1) This assignment is to be done individually . You must sign and submit the standard cover page supplied as the last page of this assignment. (2) This assignment is due in the last class . (3) The work can be typed or handwritten . If it is handwritten and too difficult to read due to messiness and poor handwriting, it will receive zero credit . (4) You must show all details to receive full credit . (5) This assignment contains 5 questions and carries a total of 30 points . Question 1 (5 marks) GS stock sells at \$156 and is expected to pay a \$0.35 dividend in 3, 6 and 9 months. The 175-strike 1-year call option on GS costs \$10.25. The risk-free rate is 4% p.a. continuously compounded. (a) What is the price of the 175-strike 1-year put option on GS? (2 marks) (b) Actually, the market put price is \$24.32. Show how you should undertake this arbitrage. Show all the details. (3 marks) Solution (a) Using the call-put parity, the call price is given by: 0292 . 1 \$ 35 . 0 35 . 0 35 . 0 ) ( 75 . 0 % 4 5 . 0 % 4 25 . 0 % 4 = + + = × × × e e e Div PV 4174 . 23 \$ 175 0292 . 1 156 25 . 10 1 % 4 0 = + + = + + = × e Ke D S c p rT (b) There is an arbitrage opportunity since the put is overpriced by the market: - Sell one put and one stock for a total of \$180.32 - Buy one call at \$10.25 - Invest the proceeds, \$170.07, at 4% for 1 year - In 1 year, either the short put or the long call will be exercised, which will give you S(T) - K - In 1 year, you pay the dividends compounded (i.e. \$1.0712) and buy back the stock at S(T) - Your investment grows to 177.0107 in 1 year

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