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Midterm-2-Solutions - FINE 448 Derivatives and Risk...

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FINE 448 - Derivatives and Risk Management Summer 2007, Version A2 Midterm # 2, 90 minutes. Wednesday June 13th 2007 Prof. Chayawat Ornthanalai Part A: Short questions (2 points each) The correct answer is bolded. Question A1 When the stock pays no dividend, it is never optimal to exercise an American put option. a) True b) False c) Cannot say d) Only if the dividend yield is less than the interest rate Question A2 Your current portfolio consists of one long position in each of the three European call options with three di/erent strike prices on an underlying stock that pays no dividend. These call options have maturity of one year and deltas of 0.4, 0.5, and 0.6 respectively. What would be the delta of a portfolio that consists of one long position in each of the three European put options on these identical three strike prices and maturity. a) -0.9 b) -1.3 c) -1.4 d) -1.5 e) -1.6 f) None of the above 1
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Question A3 Six-month put options with strike prices of $35 and $42 cost $4 and $8 ; respectively. What is the maximum loss (not payo/) when a bear spread is created from the calls? a) $3 : 5 b) $5 : 0 c) $7 : 0 d) $6 : 0 e) $ 4 : 0 f) None of the above Question A4 What can you infer on the gamma of a portfolio consisting of one long position in a call option and one short position in its underlying? a) It is equal or less than zero b) It is equal or greater than zero c) It is greater than one d) It is less than minus one e) It is equal to zero f) None of the above Question A5 Assume log normal distribution on the stock price. The current stock price is S 0 = $250 ; and you estimated the annualized volatility of ° and annualized mean ± of to be 20% and 13% respectively : The riskfree rate in the market is 7% per annum. What is the subjective real probability that the stock price will be below $255 one year from now. a) 0.390 b) 0.326 c) 0.674 d) 0.610 e) 0.450 f) Not enough information is given. 2
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Question A6 When is it that the European option prices computed using the binomial trees are the same as the European option prices computed using the Black-Scholes-Merton formula? a) When the stock pays no dividend b) When the options are in-the-money c) When the maturity of the options approaches in°nity. This is also known as perpetual calls or puts d) When the number of binomial tree step approaches in°nity e) When the underlying asset of the options are foreign exchange rate f) None of the above Question A7 Assume log normal distribution on the stock price. The current stock price is S 0 = $1000 with annualized volatility of ° = 30% : The riskfree rate in the market is 7% per annum. What is the risk-neutral probability that a put option with a strike price $ 1050 with maturity of 2 years will expire in-the-money. a) 0.82 b) 0.56 c) 0.61 d) 0.43 e) 1.00 f) None of the above 3
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Part B: Short questions ( 5 points each ) Please show your works in the provided space and write down your °nal answers on the blank line at the end of each question. Please be as concise as possible. Unless
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