Using & Understanding Mathematics: A Quantitative Reasoning Approach (7th Edition)
7th Edition
ISBN: 9780134705187
Author: Jeffrey O. Bennett, William L. Briggs
Publisher: PEARSON
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Textbook Question
Chapter 3.C, Problem 3QQ
Under the standard rules for counting significant digits, which of the following numbers has the most significant digits?
a. 1.02
b. 1.020
c. 0.000020
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Chapter 3 Solutions
Using & Understanding Mathematics: A Quantitative Reasoning Approach (7th Edition)
Ch. 3.A - The price of a meal at a four-star restaurant is...Ch. 3.A - The population of a town increases from 50,000 to...Ch. 3.A - Suppose the value of a home changed by -20% over...Ch. 3.A - Emily scored 50% higher on the SAT than Joshua....Ch. 3.A - The price of a movie ticket increased from $10 to...Ch. 3.A - Your receipt shows that you paid $47.96 for a new...Ch. 3.A - Consider this statement: “The interest rate on...Ch. 3.A - A friend has a textbook that originally cost $150....Ch. 3.A - You currently earn $1000 per month, but you are...Ch. 3.A - During high school, Elise won 30% of the swim...
Ch. 3.A - Describe the three basic uses of percentages. Give...Ch. 3.A - Distinguish between absolute and relative change....Ch. 3.A - Distinguish between absolute and relative...Ch. 3.A - Explain the difference between the key words of...Ch. 3.A - Explain the difference between the terms percent...Ch. 3.A - 6. Give an example to explain why, in general, it...Ch. 3.A - In many European countries, the percentage change...Ch. 3.A - The price of tuition has tripled since my parents...Ch. 3.A - I’ve decreased my caloric intake by 125% which has...Ch. 3.A - If you earn 20% more than I do, then I must earn...Ch. 3.A - If they raise taxes by 10% every year, in a decade...Ch. 3.A - We found that these rare cancers were 700% more...Ch. 3.A - The rate of return on our fund increased by 50%,...Ch. 3.A - My bank increased the interest rate on my savings...Ch. 3.A - Prob. 15ECh. 3.A - Prob. 16ECh. 3.A - Prob. 17ECh. 3.A - Prob. 18ECh. 3.A - Fractions, Decimals, Percentages. Express the...Ch. 3.A - Prob. 20ECh. 3.A - Prob. 21ECh. 3.A - Prob. 22ECh. 3.A - Fractions, Decimals, Percentages. Express the...Ch. 3.A - Fractions, Decimals, Percentages. Express the...Ch. 3.A - Prob. 25ECh. 3.A - Prob. 26ECh. 3.A - Fractions, Decimals, Percentages. Express the...Ch. 3.A - Prob. 28ECh. 3.A - Prob. 29ECh. 3.A - Prob. 30ECh. 3.A - Prob. 31ECh. 3.A - Prob. 32ECh. 3.A - Prob. 33ECh. 3.A - Compare the following pairs of numbers A and B in...Ch. 3.A - 31-36: Review of Ratios. Compare the following...Ch. 3.A - Review of Ratios. Compare the following pairs of...Ch. 3.A - Prob. 37ECh. 3.A - Prob. 38ECh. 3.A - Prob. 39ECh. 3.A - Percentages as Fractions in the following...Ch. 3.A - Prob. 41ECh. 3.A - Prob. 42ECh. 3.A - Salary Comparisons. Clint’s salary increased from...Ch. 3.A - 44. Population Comparison. Between the 2010 U.S....Ch. 3.A - Percentage Change. Find the absolute change and...Ch. 3.A - Percentage Change. Find the absolute change and...Ch. 3.A - Percentage Change. Find the absolute change and...Ch. 3.A - Percentage Change. Find the absolute change and...Ch. 3.A - Percentage Comparisons. Complete the following...Ch. 3.A - Percentage Comparisons. Complete the following...Ch. 3.A - Prob. 51ECh. 3.A - Percentage Comparisons. Complete the following...Ch. 3.A - Of versus More Than. Fill in the blanks in the...Ch. 3.A - Of versus More Than. Fill in the blanks in the...Ch. 3.A - Of versus More Than. Fill in the blanks in the...Ch. 3.A - Of versus More Than. Fill in the blanks in the...Ch. 3.A - 57-60: Prices and Sales. Fill in the blanks in the...Ch. 3.A - Prob. 58ECh. 3.A - Prob. 59ECh. 3.A - Prob. 60ECh. 3.A - Percentages of Percentages. Describe each of the...Ch. 3.A - 61-64: Percentages of Percentages. Describe each...Ch. 3.A - Percentages of Percentages. Describe each of the...Ch. 3.A - Percentages of Percentages. Describe each of the...Ch. 3.A - Care in Wording. Assume that 30% of city employees...Ch. 3.A - Ambiguous News. The average annual precipitation...Ch. 3.A - Solving Percentage Problems. Solve the following...Ch. 3.A - Solving Percentage Problems. Solve the following...Ch. 3.A - Solving Percentage Problems. Solve the following...Ch. 3.A - Solving Percentage Problems. Solve the following...Ch. 3.A - Shifting Reference Value. State whether the...Ch. 3.A - Prob. 72ECh. 3.A - Prob. 73ECh. 3.A - Shifting Reference Value. State whether the...Ch. 3.A - Prob. 75ECh. 3.A - Is It Possible? Determine whether the following...Ch. 3.A - Prob. 77ECh. 3.A - Prob. 78ECh. 3.A - 75-80: Is It Possible? Determine whether the...Ch. 3.A - 75-80: Is It Possible? Determine whether the...Ch. 3.A - 81. Average Percentages. Suppose you have an 80%...Ch. 3.A - Prob. 82ECh. 3.A - 83-86: Analyzing Percentage Statements. Assuming...Ch. 3.A - Prob. 84ECh. 3.A - 83-86: Analyzing Percentage Statements. Assuming...Ch. 3.A - Prob. 86ECh. 3.A - 87-90: Solving Percentage Problems. Solve the...Ch. 3.A - Prob. 88ECh. 3.A - Prob. 89ECh. 3.A - 87-90: Solving Percentage Problems. Solve the...Ch. 3.A - Percentages in the News. Answer the question that...Ch. 3.A - Percentages in the News. Answer the question that...Ch. 3.A - Percentages in the News. Answer the question that...Ch. 3.A - Prob. 94ECh. 3.A - 108. Stock Market Losses.
a. The largest...Ch. 3.A - Percentages. Find three recent news reports that...Ch. 3.A - Percentage Change. Find a recent news report that...Ch. 3.A - Prob. 98ECh. 3.B - 1. The number 300,000,000 is the same as a. 3 10 7...Ch. 3.B - Prob. 2QQCh. 3.B - Prob. 3QQCh. 3.B - 4. You are asked to estimate the total amount of...Ch. 3.B - 5. You are wondering how many dollar bills you’d...Ch. 3.B - 6. You are given some data and asked to calculate...Ch. 3.B - You are looking at a map with a scale of 1 inch =...Ch. 3.B - An NFL quarterback is offered a new contract...Ch. 3.B - You are running for mayor this year in a city with...Ch. 3.B - A lottery ticket on which the odds of winning are...Ch. 3.B - Briefly describe scientific notation. How is it...Ch. 3.B - Prob. 2ECh. 3.B - Prob. 3ECh. 3.B - Explain how we can use comparisons to put numbers...Ch. 3.B - 5. Describe three common ways of expressing the...Ch. 3.B - 6. Explain how we can use scaling to put numbers...Ch. 3.B - 7. Suppose that the Sun were the size of a...Ch. 3.B - 8. Describe several ways of putting each of the...Ch. 3.B - Prob. 9ECh. 3.B - I’ve seen about commercials on TV.Ch. 3.B - I work in an office building that is 300 feet...Ch. 3.B - In total, Americans spend about a billion dollars...Ch. 3.B - A popular local redtaurant serves 5 million...Ch. 3.B - The CEO of the company earned more money last year...Ch. 3.B - Prob. 15ECh. 3.B - Prob. 16ECh. 3.B - Review of Scientific Notation. In the following...Ch. 3.B - Review of Scientific Notation. In the following...Ch. 3.B - Prob. 19ECh. 3.B - Prob. 20ECh. 3.B - Prob. 21ECh. 3.B - Prob. 22ECh. 3.B - Prob. 23ECh. 3.B - Prob. 24ECh. 3.B - Prob. 25ECh. 3.B - 23-26: Using Scientific Notation. Rewrite the...Ch. 3.B - Prob. 27ECh. 3.B - Prob. 28ECh. 3.B - 29-32: Perspective Through Estimation. Use...Ch. 3.B - Perspective Through Estimation. Use estimation to...Ch. 3.B - Perspective Through Estimation. Use estimation to...Ch. 3.B - Prob. 32ECh. 3.B - Prob. 33ECh. 3.B - Prob. 34ECh. 3.B - Prob. 35ECh. 3.B - Order of Magnitude Estimates. Make order of...Ch. 3.B - Prob. 37ECh. 3.B - Prob. 38ECh. 3.B - Prob. 39ECh. 3.B - 41-48: Energy Comparisons. Use Table 3.1 to answer...Ch. 3.B - 41-48: Energy Comparisons. Use Table 3.1 to answer...Ch. 3.B - 41-48: Energy Comparisons. Use Table 3.1 to answer...Ch. 3.B - Prob. 43ECh. 3.B - Prob. 44ECh. 3.B - Prob. 45ECh. 3.B - Prob. 46ECh. 3.B - Prob. 47ECh. 3.B - Prob. 48ECh. 3.B - Scale Ratios. Find the scale ratios for the...Ch. 3.B - Prob. 50ECh. 3.B - Scale Model Solar System. The following table...Ch. 3.B - 54. Interstellar Travel. The fastest spaceships...Ch. 3.B - 53. Universal Timeline. According to modern...Ch. 3.B - Universal Clock. According to modern science,...Ch. 3.B - Prob. 55ECh. 3.B - Prob. 56ECh. 3.B - Prob. 57ECh. 3.B - Prob. 58ECh. 3.B - Prob. 59ECh. 3.B - Prob. 60ECh. 3.B - Making Numbers Understandable. Restate the...Ch. 3.B - Making Numbers Understandable. Restate the...Ch. 3.B - Cells in the Human Body. Estimates of the number...Ch. 3.B - Emissions. For every gallon of gasoline burned by...Ch. 3.B - Prob. 65ECh. 3.B - Wood for Energy? A total of about 180,000...Ch. 3.B - Stellar Corpses: White Dwarfs and Neutron Stars. A...Ch. 3.B - Until the Sun Dies. It took 65 million years from...Ch. 3.B - Personal Consumption. The Bureau of Economic...Ch. 3.B - Sampling Problems. Sampling techniques can be used...Ch. 3.B - Prob. 71ECh. 3.B - 72 – 75 : Sampling Problems. Sampling techniques...Ch. 3.B - Sampling Problems. Sampling techniques can be used...Ch. 3.B - 76. Energy Comparisons. Using data available from...Ch. 3.B - Prob. 75ECh. 3.B - Prob. 76ECh. 3.B - Prob. 77ECh. 3.B - Prob. 78ECh. 3.B - Prob. 79ECh. 3.B - Putting Numbers in Perspective. Find at least two...Ch. 3.B - Prob. 81ECh. 3.C - The $5.6 trillion surplus that government...Ch. 3.C - Under the standard rules for counting significant...Ch. 3.C - Under the standard rules for counting significant...Ch. 3.C - You are trying to measure the outside temperature...Ch. 3.C - You are trying to measure the outside temperature...Ch. 3.C - A testing service makes a error that causes all...Ch. 3.C - A testing service makes an error that causes all...Ch. 3.C - A digital scale shows that you weigh 112.7 pounds,...Ch. 3.C - At a particular moment, the U.S. National Debt...Ch. 3.C - Prob. 10QQCh. 3.C - Prob. 1ECh. 3.C - Prob. 2ECh. 3.C - Prob. 3ECh. 3.C - Distinguish between accuracy and precision. Give...Ch. 3.C - Why can it be misleading to give measurements with...Ch. 3.C - Prob. 6ECh. 3.C - Next year's federal deficit will be $443.45...Ch. 3.C - In many developing nations, official estimates of...Ch. 3.C - My height is 5 feet, 6.3980 inches.Ch. 3.C - Wilma used her paces to measure the dimensions of...Ch. 3.C - More precision is useless if the measurement is...Ch. 3.C - A $2 million error is a lot of money, but it...Ch. 3.C - Prob. 13ECh. 3.C - 13-14: Review of Rounding. In the following...Ch. 3.C - 15-26: Counting Significant Digits. State the...Ch. 3.C - Prob. 16ECh. 3.C - Prob. 17ECh. 3.C - Prob. 18ECh. 3.C - Prob. 19ECh. 3.C - Prob. 20ECh. 3.C - Prob. 21ECh. 3.C - Prob. 22ECh. 3.C - Counting Significant Digits. State the number of...Ch. 3.C - 15-26: Counting Significant Digits. State the...Ch. 3.C - 15-26: Counting Significant Digits. State the...Ch. 3.C - 17-28: Counting Significant Digits. State the...Ch. 3.C - Prob. 27ECh. 3.C - Prob. 28ECh. 3.C - Prob. 29ECh. 3.C - Prob. 30ECh. 3.C - Prob. 31ECh. 3.C - Prob. 32ECh. 3.C - Prob. 33ECh. 3.C - Prob. 34ECh. 3.C - Source of Error. Describe possible source of...Ch. 3.C - 33-38: Sources of Error. Describe possible sources...Ch. 3.C - 35-42: Source of Error. Describe possible source...Ch. 3.C - Source of Error. Describe possible source of...Ch. 3.C - Tax Audit. A tax auditor reviewing a tax return...Ch. 3.C - Prob. 40ECh. 3.C - Safe Air Travel. Before taking off, a pilot is...Ch. 3.C - Cutting Lumber. A lumber yard employee cuts 30...Ch. 3.C - Prob. 43ECh. 3.C - Prob. 44ECh. 3.C - Prob. 45ECh. 3.C - Prob. 46ECh. 3.C - 43-50: Absolute and Relative Errors. Find the...Ch. 3.C - 43-50: Absolute and Relative Errors. Find the...Ch. 3.C - 43-50: Absolute and Relative Errors. Find the...Ch. 3.C - Prob. 50ECh. 3.C - Prob. 51ECh. 3.C - Accuracy and Precision. For each pair of...Ch. 3.C - Prob. 53ECh. 3.C - Accuracy and Precision. For each pair of...Ch. 3.C - Prob. 55ECh. 3.C - Prob. 56ECh. 3.C - Prob. 57ECh. 3.C - Prob. 58ECh. 3.C - 55-62: Combining Numbers. Use the appropriate...Ch. 3.C - 59-66: Combining Numbers. Use the appropriate...Ch. 3.C - 55-62: Combining Numbers. Use the appropriate...Ch. 3.C - Prob. 62ECh. 3.C - Prob. 63ECh. 3.C - Prob. 64ECh. 3.C - Prob. 65ECh. 3.C - Prob. 66ECh. 3.C - Prob. 67ECh. 3.C - Prob. 68ECh. 3.C - Prob. 69ECh. 3.C - Prob. 70ECh. 3.C - 75. Propagation of Error. Suppose you want to cut...Ch. 3.C - 72. Analyzing a Calculation. According to 2015...Ch. 3.C - 77. Random and Systematic Errors. Find a recent...Ch. 3.C - Prob. 74ECh. 3.C - Prob. 75ECh. 3.C - Prob. 76ECh. 3.C - Prob. 77ECh. 3.D - Look at the gasoline price index in Table 3.2....Ch. 3.D - Prob. 2QQCh. 3.D - Prob. 3QQCh. 3.D - Prob. 4QQCh. 3.D - Prob. 5QQCh. 3.D - 6. Suppose we created a price index for computers,...Ch. 3.D - 7. Over the past three decades, the cost of...Ch. 3.D - Suppose your salary has been rising at a greater...Ch. 3.D - Prob. 9QQCh. 3.D - Prob. 10QQCh. 3.D - Prob. 1ECh. 3.D - What is the Consumer Price Index (CPI)? How is it...Ch. 3.D - Prob. 3ECh. 3.D - Prob. 4ECh. 3.D - Prob. 5ECh. 3.D - Even though my salary has remained the same for...Ch. 3.D - Benjamin Franklin said, “A penny saved is a penny...Ch. 3.D - The prices of cars have risen steadily, but when...Ch. 3.D - 9. When we chart today’s price of milk in 1995...Ch. 3.D - 10. The Consumer Price Index is a theoretical...Ch. 3.D - 11-16: Gasoline Price Index. Use Table 3.2 to...Ch. 3.D - Prob. 12ECh. 3.D - Prob. 13ECh. 3.D - Prob. 14ECh. 3.D - Prob. 15ECh. 3.D - Prob. 16ECh. 3.D - Understanding the CPI. Use Table 3.4 to answer the...Ch. 3.D - Understanding the CPI. Use Table 3.4 to answer the...Ch. 3.D - Understanding the CPI. Use Table 3.4 to answer the...Ch. 3.D - Understanding the CPI. Use Table 3.4 to answer the...Ch. 3.D - Understanding the CPI. Use Table 3.4 to answer the...Ch. 3.D - Understanding the CPI. Use Table 3.4 to answer the...Ch. 3.D - Understanding the CPI. Use Table 3.4 to answer the...Ch. 3.D - Understanding the CPI. Use Table 3.4 to answer the...Ch. 3.D - Understanding the CPI. Use Table 3.4 to answer the...Ch. 3.D - Understanding the CPI. Use Table 3.4 to answer the...Ch. 3.D - Housing Price Index. Realtors use an index to...Ch. 3.D - Housing Price Index. Realtors use an index to...Ch. 3.D - Housing Price Index. Realtors use an index to...Ch. 3.D - Housing Price Index. Realtors use an index to...Ch. 3.D - HealthCare Spending. Total spending on health care...Ch. 3.D - Airfare. According to the U.S. Bureau of...Ch. 3.D - Private College Cost. According to the College...Ch. 3.D - Public College Cost. According to the College...Ch. 3.D - Federal Minimum Wage. Use the following table,...Ch. 3.D - Federal Minimum Wage. Use the following table,...Ch. 3.D - Federal Minimum Wage. Use the following table,...Ch. 3.D - Federal Minimum Wage. Use the following table,...Ch. 3.D - Prob. 39ECh. 3.D - Prob. 40ECh. 3.D - Prob. 41ECh. 3.D - Prob. 42ECh. 3.D - Fan Cost Index. The cost of attending a Major...Ch. 3.D - Price of Gold. The price of gold (end-of-year...Ch. 3.D - 45. Economic Freedom Index. The Heritage...Ch. 3.D - Consumer Price Index. Find a recent news report...Ch. 3.D - Prob. 47ECh. 3.D - Prob. 48ECh. 3.D - Consumer Confidence Index. Use a search engine to...Ch. 3.D - Prob. 50ECh. 3.D - Prob. 51ECh. 3.D - Prob. 52ECh. 3.D - Inflation Calculator. Use the Bureau of Labor...Ch. 3.D - Prob. 54ECh. 3.D - 51-56: Inflation Calculator. Use the Bureau of...Ch. 3.D - 51-56: Inflation Calculator. Use the Bureau of...Ch. 3.E - Study Table 3.5. What does the number “8” in the...Ch. 3.E - Study Table 3.5. Which statement is not supported...Ch. 3.E - During their freshman year, Derek’s GPA was 3.4...Ch. 3.E - A false negative in a cancer screening test means...Ch. 3.E - A false positive in a test for steroids means that...Ch. 3.E - Study Table 3.7. The total number of women who did...Ch. 3.E - Study Table 3.7. The total number of women whose...Ch. 3.E - Suppose that a home pregnancy test is 99%...Ch. 3.E - Study the graph in Figure 3.5a. Which of the...Ch. 3.E - Study the graph in Figure 3.5b. Which of the...Ch. 3.E - Prob. 1ECh. 3.E - Briefly explain why a positive result on a...Ch. 3.E - Prob. 3ECh. 3.E - Prob. 4ECh. 3.E - Despite the fact that the new drug lowered blood...Ch. 3.E - Our total class score is based only on homework...Ch. 3.E - Baggage screening machines are 98% accurate in...Ch. 3.E - The polygraph test showed that the suspect was...Ch. 3.E - The Republications claim the tax cut benefits...Ch. 3.E - The agency suffered a real cut in its annual...Ch. 3.E - Batting Percentages. The table below shows the...Ch. 3.E - 12. Jeter and Justice. The following table shows...Ch. 3.E - Test Scores. The table below shows eighth-grade...Ch. 3.E - Test Scores. Consider the following table...Ch. 3.E - Prob. 15ECh. 3.E - Prob. 16ECh. 3.E - Prob. 17ECh. 3.E - Disease Test. Suppose a test for a disease is 90%...Ch. 3.E - Performance Enhancement. Suppose that a test for...Ch. 3.E - Prob. 20ECh. 3.E - Political Math. Government spending for a popular...Ch. 3.E - 29. A Tax Cut. According to an analysis of a...Ch. 3.E - Basketball Records. Consider the following...Ch. 3.E - 22. Better Drug. Two drugs, A and B, were tested...Ch. 3.E - Prob. 25ECh. 3.E - Prob. 26ECh. 3.E - Airline Arrivals. The following table shows real...Ch. 3.E - Prob. 28ECh. 3.E - Drug Testing. Explore the issue of drug testing...Ch. 3.E - Prob. 30ECh. 3.E - Prob. 31E
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- As discussed in Section 8.3, the Markowitz model uses the variance of the portfolio as the measure of risk. However, variance includes deviations both below and above the mean return. Semivariance includes only deviations below the mean and is considered by many to be a better measure of risk. (a) Develop a model that minimizes semivariance for the Hauck Financial data given in the file HauckData with a required return of 10%. Assume that the five planning scenarios in the Hauck Financial Services model are equally likely to occur. Hint: Modify model (8.10)–(8.19). Define a variable ds for each scenario and let ds ≥ R − Rs with ds ≥ 0. Then make the objective function: Min 1 5 5 s = 1 ds2. Let FS = proportion of portfolio invested in the foreign stock mutual fund IB = proportion of portfolio invested in the intermediate-term bond fund LG = proportion of portfolio invested in the large-cap growth fund LV = proportion of portfolio invested in the large-cap value fund…arrow_forwardCalculus lll May I please have the blank lines completed, and final statement defined as a result? Thank you for the support!arrow_forwardFor each month of the year, Taylor collected the average high temperatures in Jackson, Mississippi. He used the data to create the histogram shown. Which set of data did he use to create the histogram? A 55, 60, 64, 72, 73, 75, 77, 81, 83, 91, 91, 92\ 55,\ 60,\ 64,\ 72,\ 73,\ 75,\ 77,\ 81,\ 83,\ 91,\ 91,\ 92 55, 60, 64, 72, 73, 75, 77, 81, 83, 91, 91, 92 B 55, 57, 60, 65, 70, 71, 78, 79, 85, 86, 88, 91\ 55,\ 57,\ 60,\ 65,\ 70,\ 71,\ 78,\ 79,\ 85,\ 86,\ 88,\ 91 55, 57, 60, 65, 70, 71, 78, 79, 85, 86, 88, 91 C 55, 60, 63, 64, 65, 71, 83, 87, 88, 88, 89, 93\ 55,\ 60,\ 63,\ 64,\ 65,\ 71,\ 83,\ 87,\ 88,\ 88,\ 89,\ 93 55, 60, 63, 64, 65, 71, 83, 87, 88, 88, 89, 93 D 55, 58, 60, 66, 68, 75, 77, 82, 86, 89, 91, 91\ 55,\ 58,\ 60,\ 66,\ 68,\ 75,\ 77,\ 82,\ 86,\ 89,\ 91,\ 91 55, 58, 60, 66, 68, 75, 77, 82, 86, 89, 91, 91arrow_forward
- In this problem, we consider a Brownian motion (W+) t≥0. We consider a stock model (St)t>0 given (under the measure P) by d.St 0.03 St dt + 0.2 St dwt, with So 2. We assume that the interest rate is r = 0.06. The purpose of this problem is to price an option on this stock (which we name cubic put). This option is European-type, with maturity 3 months (i.e. T = 0.25 years), and payoff given by F = (8-5)+ (a) Write the Stochastic Differential Equation satisfied by (St) under the risk-neutral measure Q. (You don't need to prove it, simply give the answer.) (b) Give the price of a regular European put on (St) with maturity 3 months and strike K = 2. (c) Let X = S. Find the Stochastic Differential Equation satisfied by the process (Xt) under the measure Q. (d) Find an explicit expression for X₁ = S3 under measure Q. (e) Using the results above, find the price of the cubic put option mentioned above. (f) Is the price in (e) the same as in question (b)? (Explain why.)arrow_forwardProblem 4. Margrabe formula and the Greeks (20 pts) In the homework, we determined the Margrabe formula for the price of an option allowing you to swap an x-stock for a y-stock at time T. For stocks with initial values xo, yo, common volatility σ and correlation p, the formula was given by Fo=yo (d+)-x0Þ(d_), where In (±² Ꭲ d+ õ√T and σ = σ√√√2(1 - p). дго (a) We want to determine a "Greek" for ỡ on the option: find a formula for θα (b) Is дго θα positive or negative? (c) We consider a situation in which the correlation p between the two stocks increases: what can you say about the price Fo? (d) Assume that yo< xo and p = 1. What is the price of the option?arrow_forwardThe Course Name Real Analysis please Solve questions by Real Analysisarrow_forward
- We consider a 4-dimensional stock price model given (under P) by dẴ₁ = µ· Xt dt + йt · ΣdŴt where (W) is an n-dimensional Brownian motion, π = (0.02, 0.01, -0.02, 0.05), 0.2 0 0 0 0.3 0.4 0 0 Σ= -0.1 -4a За 0 0.2 0.4 -0.1 0.2) and a E R. We assume that ☑0 = (1, 1, 1, 1) and that the interest rate on the market is r = 0.02. (a) Give a condition on a that would make stock #3 be the one with largest volatility. (b) Find the diversification coefficient for this portfolio as a function of a. (c) Determine the maximum diversification coefficient d that you could reach by varying the value of a? 2arrow_forwardQuestion 1. Your manager asks you to explain why the Black-Scholes model may be inappro- priate for pricing options in practice. Give one reason that would substantiate this claim? Question 2. We consider stock #1 and stock #2 in the model of Problem 2. Your manager asks you to pick only one of them to invest in based on the model provided. Which one do you choose and why ? Question 3. Let (St) to be an asset modeled by the Black-Scholes SDE. Let Ft be the price at time t of a European put with maturity T and strike price K. Then, the discounted option price process (ert Ft) t20 is a martingale. True or False? (Explain your answer.) Question 4. You are considering pricing an American put option using a Black-Scholes model for the underlying stock. An explicit formula for the price doesn't exist. In just a few words (no more than 2 sentences), explain how you would proceed to price it. Question 5. We model a short rate with a Ho-Lee model drt = ln(1+t) dt +2dWt. Then the interest rate…arrow_forwardIn this problem, we consider a Brownian motion (W+) t≥0. We consider a stock model (St)t>0 given (under the measure P) by d.St 0.03 St dt + 0.2 St dwt, with So 2. We assume that the interest rate is r = 0.06. The purpose of this problem is to price an option on this stock (which we name cubic put). This option is European-type, with maturity 3 months (i.e. T = 0.25 years), and payoff given by F = (8-5)+ (a) Write the Stochastic Differential Equation satisfied by (St) under the risk-neutral measure Q. (You don't need to prove it, simply give the answer.) (b) Give the price of a regular European put on (St) with maturity 3 months and strike K = 2. (c) Let X = S. Find the Stochastic Differential Equation satisfied by the process (Xt) under the measure Q. (d) Find an explicit expression for X₁ = S3 under measure Q. (e) Using the results above, find the price of the cubic put option mentioned above. (f) Is the price in (e) the same as in question (b)? (Explain why.)arrow_forward
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