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Page 1 AP/ADMS 4503 3.0 Derivative Securities Fall 2009 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) Potash stock sells at \$104 and is not expected to pay any dividend over the next year. The 3-month \$100-strike call is selling at \$9.93. The risk-free rate is 4% per annum continuously compounded. Options considered here are assumed to be of European style. (a) What is the theoretical price of the 3-month put? (2 marks) (b) The 3-month put is selling at \$2.75 in the market. How would you undertake this arbitrage opportunity? Show all details. (3 marks) Solution (a) The call-put parity for index options gives us: 93 . 4 \$ ) 25 . 0 % 4 exp( 100 104 93 . 9 ) exp( 0 = × × + = × + = p p rT K S c p (b) The market price of the put is lower than its fair price, so there is an arbitrage. The net profit in 3 months is (4.93 – 2.75) x exp(4% x 0.25) = \$2.21 . Here are the details: Today - Buy the stock at \$104 - Buy one put at \$2.75 - Sell one call at \$9.93 - Borrow \$96.82 for 3 months at 4% (Note: 96.82 = 104+2.75–9.93) - The total cash flow today is zero

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ADMS4503 3.0 Assignment #2 Page 2 In three months
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