ADMS4503-Final-Sample2-Sol

ADMS4503-Final-Sample2-Sol - ADMS4503 Derivative Securities...

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ADMS4503 – Derivative Securities Sample 2 YORK UNIVERSITY Atkinson School of Administrative Studies DERIVATIVE SECURITIES AK/ADMS 4503.03 FINAL EXAMINATION Solution Nabil Tahani INSTRUCTIONS 1. Allowed material: Textbook, lectures notes and a calculator. 2. This examination contains 5 questions on 5 pages (including this cover page and the Normal Distribution table at the end) and carries a total mark of 40 points . 3. Answer all questions in the examination booklet provided. 4. If you have to make any assumptions, state them clearly. Unrealistic assumptions, or those inconsistent with the information provided in the question, will not be accepted. 5. You must show all your work, including formulas and details, in order to receive full credit. Final Examination 1
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ADMS4503 – Derivative Securities Sample 2 Question 1 (8 marks) You own shares of XTS that are currently trading at $100. A European put option written on XTS with a $100 strike price that expires in three months is priced at $6. The equivalent call option is priced at $8. (a) What is the continuously compounded annual interest rate implied by these prices? (2 marks) (b) A quick check of the price of three-month T-bills on The Wall Street Journal web site reveals that this T-bill is trading at $97.50. What arbitrage would you undertake? Show all the details. (3 marks) (c) A quick check of the price of three-month T-bills on The Wall Street Journal web site reveals that this T-bill is trading at $99. What arbitrage would you undertake? Show all the details. (3 marks) Solution (a) Given these prices, the put-call parity relationship implies that the price of the synthetic T-bill is $98. % 0811 . 8 100 98 ln 25 . 0 1 98 $ = = = + = = r Ke p c S Ke Ke S p c rT rT rT (b) The synthetic T-bill (i.e. long stock, long put and short call) is overpriced, at $98, according to the prices given above. Thus, there is an arbitrage opportunity for the investor. To capture the $.50 profit implied by these prices, the investor should simultaneously sell the synthetic T-bill and purchase the traded T-bill, locking in a sure profit equal to 98 - 97.50 = $0.50 today, or equivalently $0.5128 in three months. Here are the details: Today - Short sell one stock, sell one put and buy one call, creating a cash inflow of $98 - Buy a three-month T-bill for $97.50 - The net profit today is $0.50 In three months - Buy back one stock at S(T), thus a cash flow of – S(T) - Either the long call or the short put will be exercised, yielding a cash flow equal to S(T) - $100 - The T-bill pays the face value of $100 Final Examination 2
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ADMS4503 – Derivative Securities Sample 2 - The total cash flow at the maturity is then zero Note that a three-month T-bill price of $97.5 implies an interest rate of 10.1271% per annum continuously compounded. The net profit of $0.50 today is equivalent to 0.50 x exp(10.1271% x 0.25) = $0.5128. (c) The synthetic T-bill is under-priced, at $98, according to the prices given
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This note was uploaded on 12/17/2010 for the course ADMS 4503 taught by Professor Nabil during the Fall '10 term at York University.

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ADMS4503-Final-Sample2-Sol - ADMS4503 Derivative Securities...

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