ADMS4503-Assignment2-F10-Sol

ADMS4503-Assignment2-F10-Sol - AP/ADMS 4503 3.0 Derivative...

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Page 1 AP/ADMS 4503 3.0 Derivative Securities Fall 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 (6 marks) The CAD/GBP spot exchange rate is 1.6412 (i.e. GBP 1 = CAD 1.6412). The 6- month 1.64-strike call on CAD/GBP is selling at CAD 0.0670. The risk-free rates in Canada and the UK are respectively 3.15% and 3.6% per annum continuously compounded. All options considered in this question are European-style and each option is on GBP 62,500. (a) What is the theoretical price of the 6-month put on CAD/GBP? (2 marks) (b) The 6-month put is selling at CAD 0.0650 in the market, show how you can benefit from this arbitrage opportunity. Show all details. (4 marks) Solution (a) The call-put parity for currency options gives us: 0694 . 0 ) 5 . 0 % 15 . 3 exp( 64 . 1 ) 5 . 0 % 6 . 3 exp( 6412 . 1 0670 . 0 ) exp( ) exp( 0 = × × + × × = × + × = p p rT K T r S c p f (b) The market price of the put, CAD 0.0650, is lower than its fair price of CAD 0.0694, so there is an arbitrage. One should take a long put at the market price of CAD 0.0650 and synthetically create a short put at the cost of CAD 0.0694. The net profit today would be 62,500 x (0.0694 – 0.0650) = CAD 278.10 today , or CAD 282.52 if compounded at 3.15% for 6 months . Here are the arbitrage details: Today - Buy a 6-month put at CAD 0.0650, so you pay CAD 4,062.50
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ADMS4503 3.0 Assignment #2 Page 2 - Sell a 6-month call at CAD 0.0670, so you receive CAD 4,187.50 - Borrow CAD 62,500 x exp(-3.15%*0.5) x 1.64 = CAD 100,898.27 at 3.15% for six months - Buy GBP 62,500 x exp(-3.6%*0.5) = GBP 61,385.06 spot at CAD 100,745.17, and invest the GBP at 3.6% for six months - The total net cash inflow today is then CAD 278.10 In six months
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This note was uploaded on 12/17/2010 for the course ATKINSON adms 4503 taught by Professor Nabil during the Fall '10 term at York University.

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ADMS4503-Assignment2-F10-Sol - AP/ADMS 4503 3.0 Derivative...

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