ADMS4503-Final-Sample1-Sol

ADMS4503-Final-Sample1-Sol - ADMS4503 Derivatives and Fixed...

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ADMS4503 – Derivatives and Fixed Income Securities Sample 1 YORK UNIVERSITY Atkinson Faculty of Liberal and Professional Studies DERIVATIVES AND FIXED INCOME 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 – Derivatives and Fixed Income Securities Sample 1 Question 1 (10 marks) A stock selling at $85 is expected to pay a dividend of $3 in three months and has a volatility of 30%. Consider call and put options with a 6-month maturity and an $80 strike price. The risk-free rate is 5% per annum continuously compounded. Consider a three-step binomial tree. (a) Calculate the parameters of the binomial tree: u , d , a (i.e. growth factor) and p (risk-neutral probability) by matching the volatility. (2 marks) Answer 64.21422 15.12189 56.81215 Node Time: 0.0000 0.1667 0.3333 0.5000 Discount factor per step = 0.9917 Time step, dt = 0.1667 years, 60.83 days Growth factor per step, a = 1.0084 Probability of up move, p = 0.5035 Up step size, u = 1.1303 118.4626 Down step size, d = 0.8847 0 104.8072 0 95.71345 92.72593 1.798738 0 85 82.03727 5.4624 3.653131 75.56823 72.58071 9.269829 7.419294 23.18785 (b) Use the binomial tree to price the put option if it is European. (3 marks) Answer See the tree above. We must first generate the stock prices net of the PV of the dividend and then add back the PV of the dividend up to 3 months, that is the first and second nodes only. (c) Without using a Binomial tree, what is the price of the corresponding European Call? (2 marks) Answer The call price can be computed using the Call-Put parity for European options: Final Examination 2
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ADMS4503 – Derivatives and Fixed Income Securities Sample 1 4749 . 9 $ ) 5 . 0 % 5 exp( 80 $ 9627 . 2 $ 85 $ 4624 . 5 $ ) exp( ) ( 0 = × × + = × × + = c c T r K D PV S p c (d) Use the binomial tree to price the put option if it is American. (3 marks) Answer 118.4626 0 104.8072 0 95.71345 92.72593 1.798738 0 85 82.03727 5.6234 3.653131 75.56823 72.58071 9.59672 7.419294 64.21422 15.78578 56.81215 23.18785 Node Time: 0.0000 0.1667 0.3333 0.5000 Question 2 (8 marks) A European-style Barrier call option pays off ) 80 , 0 max( T S in one year’s time if the terminal stock price in one year is less (and not equal) than $100 . The stock spot price is $90, its volatility is 20% and it pays no dividend. The risk-free rate is 3% per annum continuously compounded. Consider a four-step binomial tree.
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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-Final-Sample1-Sol - ADMS4503 Derivatives and Fixed...

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