PracticeFinal

# PracticeFinal - IEOR 4404 Practice Final Exam Simulation...

This preview shows pages 1–4. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: IEOR 4404 Practice Final Exam Simulation December 8, 2008 Prof. Mariana Olvera-Cravioto 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 log-normal 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 log-normal distribution is given below....
View Full Document

## This note was uploaded on 12/20/2010 for the course IEOR E4404 taught by Professor Marianaolvera-cravioto during the Spring '08 term at Columbia.

### Page1 / 13

PracticeFinal - IEOR 4404 Practice Final Exam Simulation...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online