Wiener Process Ito ’s Lemma Derivation of Black-Scholes Solving Black-Scholes Introduction to Financial Derivatives Understanding the Stock Pricing Model 22M:303:002 Understanding the Stock Pricing Model 22M:303:002 Wiener Process Ito ’s Lemma Derivation of Black-Scholes Stock Pricing Model Solving Black-Scholes Recall our stochastic dierential equation to model stock prices: dS = σ dX + µ dt S where µ is known as the asset ’s drift ‚ a measure of the average rate
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Examination Name: Course: Date: Final Examination in Statistics (M.A.Ed./M.A.N.) 1.The scores of 15 masteral students in Statistics were 80‚85‚78‚90‚91‚98‚95‚98‚95‚74‚71‚72‚98‚99‚and 87. Find the measures of central tendency‚ the range‚ the variance‚ and the standard deviation. 2. In the performance evaluation of teachers‚ if the dean’s evaluation is given a weight of 5‚ self-evaluation is 2‚ peer’s evaluation is 2‚ and student’s evaluation is 1 and the teacher’s rating is 90‚ 95
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Mid-Exam for Statistics 2 for IBA 12 March 2013; duration: two hours It is NOT allowed to use a graphical‚ programmable calculator; only a simple pocket calculator is allowed. Write the answers to the questions on the attached answering form (on pages 7 and 8); only the answers‚ no derivations. (For this midterm‚ only the final answers to each individual question count.) This mid-exam contains 8 pages: 4 pages with information and three exercises‚ 1 page with a few formulae and 2 pages for
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Location Location Income ($1000) Size Years Credit Balance($) Urban 1 54 3 12 4016 Rural 3 30 2 12 3159 Suburban 2 32 4 17 5100 Suburban 2 50 5 14 4742 Rural 3 31 2 4 1864 Urban 1 55 2 9 4070 Rural 3 37 1 20 2731 Urban 1 40 2 7 3348 Suburban 2 66 4 10 4764 Urban 1 51 3 16 4110 Urban 1 25 3 11 4208 Urban 1 48 4 16 4219 Rural 3 27 1 19 2477 Rural 3 33 2 12 2514 Urban 1 65 3 12 4214 Suburban 2 63 4 13 4965 Urban 1 42 6 15 4412 Urban 1 21 2 18 2448 Rural 3 44 1 7 2995 Urban 1 37 5
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for each question (no explanation is needed)‚ put your answers in the table on page 4. 1. Suppose you have a sample x1 ‚ x2 ‚ . . . ‚ xn from a population. Which of the following has different unit as sample mean? (A). population mean (B). sample variance (C). standard error (D). single observation xi for i = 1‚ 2‚ . . . ‚ n 2. In paired t-test with sample size n1 = n2 = 20‚ you have H0 : µ = 0 vs. Ha : µ < 0‚ the t-statistic is 3.4. what is the p-value? (A). 1 - pt(3.4‚ 20) (B). 1 - pt(3.4‚ 19)
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24.32% 3.15% Foreign Equity 14.44% 12.42% 30.87% 3.83% Bonds 11.10% 5.40% 10.83% 0.58% REITs 13.54% 9.44% 9.91% 0.94% Commodities 18.43% 10.05% 24.07% 2.42% Total 100.00% 10.92% 0.815960738 Portfolio Mean Return 10.92% Portoflio Variance 0.90% Portfolio S.D 9.46% Calculation of Covariance (Do Not Alter Formula) Correlation Matrix US Equity Foreign Equity Bonds REITs Commodities US Equity 1 0.62 0.25 0.56 -0.02 Foreign
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M2 Group Assignment Instructions Complete the Assignment‚ name it as GroupXX_Assign2.xls (where XX is your Group Name)‚ and upload and submit to the instructor through Dropbox. Do not enter anything in the spreadsheet cells that are black‚ labeled “Grader”. You must complete this assignment without the assistance of persons other than the members of your Group. You may use any other resources you deem necessary. Answer the questions below by placing the appropriate graph and/or answers in the designated
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Background Is being physically strong still important in today’s workplace? In our current high-tech world one might be inclined to think that only skills required for computer work such as reading‚ reasoning‚ abstract thinking‚ etc. are important for performing well in many of today’s jobs. There are still‚ however‚ a number of very important jobs that require‚ in addition to cognitive skills‚ a significant amount of strength to be able to perform at a high level. Take‚ for example‚ the job
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to a camp. If 15% of the children in the school are first graders‚ and the 18 children are selected at random from among all 6 grades at the school‚ find the mean and variance of the number of first graders chosen? The mean is 2.7‚ and the variance is 2.3. n = 18 p = .15 q = .85 Mean = np = 18 x .15 = 2.7 Variance = npq = (18 x .15 x .85) = 2.295 ≈ 2.3 3. A producer plans an outdoor regatta for May 3. The cost of the regatta is $8000‚ which includes advertising‚ security‚ printing
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following is a random sample of six entertainment expenses (dinner costs for four people) from expense reports submitted by members of the sales force. $157‚ $132‚ $109‚ $145‚ $125‚ $139. Calculate the mean and sample variance(s^2) and standard deviation. Mean = 807/6 = 134.5. Sample Variance = (109925 – (807^2/6)/6-1 = (109925 – 108541)/5 = 1384/5 = 276.8. Standard Deviation = √276.8 = 16.6373. ***the 109925 is all values of x individually squared and then summed together. ***the 6-1 is because it
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