STATS:DATA+MODELS-MY LAB ACC >CUSTOM<
21st Edition
ISBN: 9780137643127
Author: DeVeaux
Publisher: PEARSON
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Chapter 10, Problem 6E
To determine
Comment whether the sample selected by the company is a simple random sample or not.
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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 10 Solutions
STATS:DATA+MODELS-MY LAB ACC >CUSTOM<
Ch. 10.2 - 1. Various claims are often made for surveys. Why...Ch. 10.4 - 2. We need to survey a random sample of the 300...Ch. 10 - Prob. 1ECh. 10 - 2. Satisfied workers The managers of a large...Ch. 10 - Prob. 3ECh. 10 - Prob. 4ECh. 10 - Prob. 5ECh. 10 - 6. Sampling satisfaction A company hoping to...Ch. 10 - Prob. 7ECh. 10 - 8. Satisfactory satisfaction samples For each...
Ch. 10 - Prob. 9ECh. 10 - 10. Happy employees The company plans to have the...Ch. 10 - Prob. 11ECh. 10 - 12. Surveying employees The company of Exercise 2...Ch. 10 - Prob. 13ECh. 10 - 14. Student center survey For their class project,...Ch. 10 - Prob. 15ECh. 10 - Prob. 16ECh. 10 - Prob. 17ECh. 10 - In Exercises 17 to 23, for the reports about...Ch. 10 - Prob. 19ECh. 10 - Prob. 20ECh. 10 - Prob. 21ECh. 10 - In Exercises 17 to 23, for the reports about...Ch. 10 - Prob. 23ECh. 10 - 24. Mistaken poll A local TV station conducted a...Ch. 10 - Prob. 25ECh. 10 - 26. Parent opinion, part 1 In a large city school...Ch. 10 - Prob. 27ECh. 10 - 28. Churches For your political science class,...Ch. 10 - 29. Playground Some people have been complaining...Ch. 10 - 30. Roller coasters An amusement park has opened a...Ch. 10 - 31. Playground, act two The survey described in...Ch. 10 - 32. Wording the survey Two members of the PTA...Ch. 10 - 33. Banning ephedra An online poll on a website...Ch. 10 - 34. Survey questions Examine each of the following...Ch. 10 - Prob. 35ECh. 10 - 36. Phone surveys Any time we conduct a survey, we...Ch. 10 - 37. Cell phone survey What about drawing a random...Ch. 10 - 39. Fuel economy Occasionally, when I fill my car...Ch. 10 - 40. Accounting Between quarterly audits, a company...Ch. 10 - 41. Happy workers? A manufacturing company employs...Ch. 10 - 42. Quality control Sammy’s Salsa, a small local...Ch. 10 - 43. A fish story Concerned about reports of...Ch. 10 - 44. Another fish story In recent years, beaches...Ch. 10 - 45. Sampling methods Consider each of these...Ch. 10 - 46. More sampling methods Consider each of these...
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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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