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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 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) (b) Use the binomial tree to price the put option if it is European. (3 marks) (c) Without using a Binomial tree, what is the price of the corresponding European Call? (2 marks) (d) Use the binomial tree to price the put option if it is American. (3 marks) 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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