Business Analytics
3rd Edition
ISBN: 9780135231678
Author: Evans, James R. (james Robert)
Publisher: PEARSON EDUCATION (COLLEGE)
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Chapter 1, Problem 3.2CYU
Define prescriptive analytics and provide two examples.
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Question 1: Determine and interpret the correlation coefficient between the two variables. In your interpretation, discuss the direction of the relationship (positive, negative, or zero relationship). Also discuss the strength of the relationship.
Value of correlation coefficient:
Direction of the relationship (positive, negative, or zero relationship):
Strength of the relationship (strong/moderate/weak):
Question 2: Estimate the relationship between screen size and price using a simple linear regression model and interpret the estimated coefficients. In your interpretation, tell the dollar amount by which price will change for each unit of increase in screen size. (The answer for the…
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.)
Chapter 1 Solutions
Business Analytics
Ch. 1 - Explain why analytics is important in todays...Ch. 1 - Define business analytics.Ch. 1 - State three examples of how business analytics is...Ch. 1 - What are the key benefits of using business...Ch. 1 - What challenges do organizations face in using...Ch. 1 - Prob. 2.1CYUCh. 1 - How do statistical methods enhance business...Ch. 1 - What is operations research/management science?Ch. 1 - How does modern business analytics integrate...Ch. 1 - What are the components of a decision support...
Ch. 1 - Define prescriptive analytics and provide two...Ch. 1 - Define prescriptive analytics and provide two...Ch. 1 - Define prescriptive analytics and provide two...Ch. 1 - State three examples of how data are used in...Ch. 1 - How are data obtained from the Web used in...Ch. 1 - Define big data and list the four characteristics...Ch. 1 - Explain the concepts of data reliability and...Ch. 1 - Define a model and state three common forms of a...Ch. 1 - Prob. 5.2CYUCh. 1 - Prob. 5.3CYUCh. 1 - Define optimization and the characteristics of...Ch. 1 - Explain the importance of assumptions in building...Ch. 1 - What is the difference between uncertainty and...Ch. 1 - List the major phases of problem solving and...Ch. 1 - What lessons did Hewlett-Packard learn about using...Ch. 1 - For each of the following scenarios, state whether...Ch. 1 - Suppose that a manufacturer can produce a part for...Ch. 1 - Use the model developed in Example 1.5 to predict...Ch. 1 - A bank developed a model for predicting the...Ch. 1 - Four key marketing decision options are price (P),...Ch. 1 - Total marketing effort is a term used to describe...Ch. 1 - A manufacturer of headphones is preparing to set...Ch. 1 - PERFORMANCE LAWN EQUIPMENT In each chapter of this...Ch. 1 - Develop a spreadsheet for computing the demand for...Ch. 1 - The Excel file Science and Engineering Jobs shows...Ch. 1 - A new graduate has taken a job with an annual...Ch. 1 - Example 1.2 in the chapter described a scenario...Ch. 1 - Return on investment (ROI) is profit divided by...Ch. 1 - In the Accounting Professionals database, use...Ch. 1 - Prob. 7PEACh. 1 - Prob. 8PEACh. 1 - The worksheet Base Data in the Excel file Credit...Ch. 1 - The Excel file Store and Regional Sales Database...Ch. 1 - Define range names for all the data and model...Ch. 1 - Define range names for all the entities in the...Ch. 1 - Define range names for all the entities in the...
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- Problem 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_forwardWe 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_forward
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- The PDF of an amplitude X of a Gaussian signal x(t) is given by:arrow_forwardThe PDF of a random variable X is given by the equation in the picture.arrow_forwardFor a binary asymmetric channel with Py|X(0|1) = 0.1 and Py|X(1|0) = 0.2; PX(0) = 0.4 isthe probability of a bit of “0” being transmitted. X is the transmitted digit, and Y is the received digit.a. Find the values of Py(0) and Py(1).b. What is the probability that only 0s will be received for a sequence of 10 digits transmitted?c. What is the probability that 8 1s and 2 0s will be received for the same sequence of 10 digits?d. What is the probability that at least 5 0s will be received for the same sequence of 10 digits?arrow_forward
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