ECMC71-11Mid2A

# ECMC71-11Mid2A - UNIVERSITY OF TORONTO SCARBOROUGH...

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UNIVERSITY OF TORONTO SCARBOROUGH DEPARTMENT OF MANAGEMENT MGTC71: Introduction to Derivatives Markets Term Test-2 (Solutions) A. Mazaheri Instructions : This is a closed book examination. You are allowed one side of a one 4”x6" crib card and the use of a calculator. Show all your work otherwise you will not get full credit . Make sure you allocate time appropriately . You have 2 hour. Good Luck! NAME: _____________________________________________ ID#: _____________________________________________ Answer all the following 4 questions: Q-1 _______________ (18 points) Q-2 _______________ (20 points) Q-3 ________________ (12 points) Q-4 _______________ (20 points) Total _____________ (70 points)

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2 Question-1 (18 Points) Short questions . a) [5 Points] In the binomial model the risk neutral probability cannot be more than the unity? True/False explain why? Answer: False, the risk neutral probability is not a real probability. It is the probability that makes the expected return from holding the stock equal to the risk-free. Therefore it can be more than one if: u e d u d e P rT rT > => > - - = 1 b) [5 Points] Use graphs to explain why – in the absence of dividend – an American put option might be early exercised while an American call might not. Solution: Call: The lower bound is a S-PV(K) which is higher than S-K therefore the time value is always positive => It is always better to sell the American call than to exercise it. Call: PV(K) K
3 Put: The lower bound is a PV(K)-S which is lower than K-S therefore the time value can be negative => The deep in the money put options will be exercised – have negative time value. PV(K) K

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4 c) [8 Points] Consider the following option strategy: Long one call with \$100 strike price, bought for \$6 Long one call with \$90 strike price, bought for \$20 Short one call with \$105 strike price, sold for \$8 Short one call with \$95 strike price, sold for \$16 Show in a table the payoff and profit of the strategy and then graph the payoff. Briefly explain the bet behind the strategy. Solution: St<=90 90<St<=95 95<St<=100 100<St>105 St>105 Long 1 Call 100 0 0 0 St-100 St-100 Long 1 Call 90 0 St-90 St-90 St-90 St-90 Short 1 Call 105 0 0 0 0 -(St-105) Short 1 Call 95 0 0 -(St-95) -(St-95) -(St-95) Payoff 0 St-90 5 St-95 10 Cost 24-26=-2 Profit -2 St-92 3 St-97 8 This is a bullish bet very much like bull spread.
5 Question-2 . [20 points] Companies A and B face the following borrowing costs: Fixed rate Floating rate A 7% 6-m LIBOR B 9% 6-m LIBOR + 1% a) [5 Points] Explain any comparative advantage A and/or B may have in fixed rate and/or floating borrowing. If the two sides decide to engage in a swap what would be is maximum gain possible?

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## This note was uploaded on 07/20/2011 for the course MGMT 71 taught by Professor Mazaheri during the Spring '11 term at University of Toronto.

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ECMC71-11Mid2A - UNIVERSITY OF TORONTO SCARBOROUGH...

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