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Unformatted text preview: IEOR 4404 Practice Final Exam Simulation December 8, 2008 Prof. Mariana OlveraCravioto Page 1 of 13 Practice Final Exam This exam is open book/notes/handouts/homework. You are allowed to use a calculator, but not a computer. Write all answers clearly and in complete sentences. All answers should be supported by analysis or an argument. This exam has a total of 120 points and you have 3 hours to complete it. This examination consists of 13 printed pages. First Name: Last Name: I II III Total Honor Code I resolve i ) not to give or receive aid during this examination, and ii ) to take an active part in seeing that other students uphold this Honor Code. Signature: 2 IEOR 4404, Practice Final Exam Problem I [20 points] Suppose that you are interested in modeling the price of a stock that is assumed to evolve as a geometric Brownian motion. According to this model, the price of the stock at the beginning of the k th day you observe is S k = S exp { X 1 + X 2 + ··· + X k } where the X i ’s are iid normal random variables. In order to estimate the mean and variance of the X i ’s you record the price of the stock for 30 days, that is, you collect the values S ,S 1 ,...,S 30 . (a) [10 pts] Describe the steps you would follow to find the parameters μ and σ 2 of the normal distribution that best fits the X i ’s implied by your observations. Note that the data you have are not the X i ’s themselves. IEOR 4404, Practice Final Exam 3 (b) [10 pts] Note that if X ∼ Normal( μ,σ 2 ), then Y = exp( X ), is a lognormal random variable with parameters ( μ,σ 2 ). Find the joint maximum likelihood estimators for μ and σ 2 . Assume that you have iid observations Y 1 ,...,Y n . The density function of the lognormal distribution is given below....
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This note was uploaded on 12/20/2010 for the course IEOR E4404 taught by Professor Marianaolveracravioto during the Spring '08 term at Columbia.
 Spring '08
 MarianaOlveraCravioto

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