Elementary Statistics Using Excel (6th Edition)
6th Edition
ISBN: 9780134506623
Author: Mario F. Triola
Publisher: PEARSON
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Chapter 4.3, Problem 1BSC
To determine
To describe: 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?
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?
2
Question 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…
Chapter 4 Solutions
Elementary Statistics Using Excel (6th Edition)
Ch. 4.1 - 1. New Jersey Lottery Let A denote the event of...Ch. 4.1 - 2. Probability Rewrite the following statement so...Ch. 4.1 - 3. Interpreting Weather While this exercise was...Ch. 4.1 - 4. Subjective Probability Estimate the probability...Ch. 4.1 - 5. Identifying Probability Values Which of the...Ch. 4.1 - 6. Penicillin “Who discovered penicillin: Sean...Ch. 4.1 - 7. Avogadro Constant If you are asked on a quiz to...Ch. 4.1 - 8. Births Example 2 in this section includes the...Ch. 4.1 - In Exercises 9-12, assume that 50 births are...Ch. 4.1 - In Exercises 9-12, assume that 50 births are...
Ch. 4.1 - In Exercises 9-12, assume that 50 births are...Ch. 4.1 - In Exercises 9-12, assume that 50 births are...Ch. 4.1 - In Exercises 13-20, express the indicated degree...Ch. 4.1 - 14. SAT Test When making a random guess for an...Ch. 4.1 - In Exercises 13-20, express the indicated degree...Ch. 4.1 - In Exercises 13-20, express the indicated degree...Ch. 4.1 - 17. Randomness When using a computer to randomly...Ch. 4.1 - Prob. 18BSCCh. 4.1 - Prob. 19BSCCh. 4.1 - Prob. 20BSCCh. 4.1 - In Exercises 21-24, refer to the sample data in...Ch. 4.1 - In Exercises 21-24, refer to the sample data in...Ch. 4.1 - In Exercises 21-24, refer to the sample data in...Ch. 4.1 - In Exercises 21-24, refer to the sample data in...Ch. 4.1 - In Exercises 25-32, find the probability and...Ch. 4.1 - In Exercises 25-32, find the probability and...Ch. 4.1 - Prob. 27BSCCh. 4.1 - Prob. 28BSCCh. 4.1 - Prob. 29BSCCh. 4.1 - Prob. 30BSCCh. 4.1 - Prob. 31BSCCh. 4.1 - In Exercises 25-32, find the probability and...Ch. 4.1 - Prob. 33BSCCh. 4.1 - Prob. 34BSCCh. 4.1 - Prob. 35BSCCh. 4.1 - Prob. 36BSCCh. 4.1 - Prob. 37BSCCh. 4.1 - Prob. 38BSCCh. 4.1 - Prob. 39BSCCh. 4.1 - Prob. 40BSCCh. 4.1 - Prob. 41BBCh. 4.1 - Prob. 42BBCh. 4.1 - Prob. 43BBCh. 4.1 - Prob. 44BBCh. 4.2 - 1. Notation When randomly selecting an adult, A...Ch. 4.2 - 2. Notation When randomly selecting adults, let M...Ch. 4.2 - 3. Sample for a Poll There are 15,524,971 adults...Ch. 4.2 - Prob. 4BSCCh. 4.2 - Prob. 5BSCCh. 4.2 - Prob. 6BSCCh. 4.2 - Prob. 7BSCCh. 4.2 - Prob. 8BSCCh. 4.2 - In Exercises 9-20, use the data in the following...Ch. 4.2 - In Exercises 9-20, use the data in the following...Ch. 4.2 - In Exercises 9-20, use the data in the following...Ch. 4.2 - In Exercises 9-20, use the data in the following...Ch. 4.2 - In Exercises 9-20; use the data in the following...Ch. 4.2 - Prob. 14BSCCh. 4.2 - In Exercises 9-20, use the data in the following...Ch. 4.2 - In Exercises 9-20, use the data in the following...Ch. 4.2 - In Exercises 9-20, use the data in the following...Ch. 4.2 - In Exercises 9-20, use the data in the following...Ch. 4.2 - In Exercises 9-20, use the data in the following...Ch. 4.2 - In Exercises 9-20, use the data in the following...Ch. 4.2 - Prob. 21BSCCh. 4.2 - Prob. 22BSCCh. 4.2 - Prob. 23BSCCh. 4.2 - In Exercises 21-24, use these results from the...Ch. 4.2 - Prob. 25BSCCh. 4.2 - Prob. 26BSCCh. 4.2 - Prob. 27BSCCh. 4.2 - Prob. 28BSCCh. 4.2 - Prob. 29BSCCh. 4.2 - Prob. 30BSCCh. 4.2 - Prob. 31BBCh. 4.2 - 32. Same Birthdays If 25 people are randomly...Ch. 4.2 - Prob. 33BBCh. 4.2 - Prob. 34BBCh. 4.3 - 1. Language: Complement of “At Least One” Let A =...Ch. 4.3 - 2. Probability of At Least One Let A = the event...Ch. 4.3 - 3. Notation When selecting one of your Facebook...Ch. 4.3 - 3. Notation When selecting one of your Facebook...Ch. 4.3 - At Least One. In Exercises 5-12, find the...Ch. 4.3 - 6. Probability of a Girl Assuming that boys and...Ch. 4.3 - At Least One. In Exercises 5-12, find the...Ch. 4.3 - At Least One. In Exercises 5-12, find the...Ch. 4.3 - At Least One. In Exercises 5-12, find the...Ch. 4.3 - At Least One. In Exercises 5-12, find the...Ch. 4.3 - Prob. 11BSCCh. 4.3 - At Least One. In Exercises 5-12, find the...Ch. 4.3 - Denomination Effect. In Exercises 13-16, use the...Ch. 4.3 - Prob. 14BSCCh. 4.3 - Prob. 15BSCCh. 4.3 - Denomination Effect. In Exercises 13-16, use the...Ch. 4.3 - Prob. 17BSCCh. 4.3 - In Exercises 17-20, refer to the accompanying...Ch. 4.3 - Prob. 19BSCCh. 4.3 - Prob. 20BSCCh. 4.3 - Prob. 21BSCCh. 4.3 - Prob. 22BSCCh. 4.3 - Prob. 23BSCCh. 4.3 - 24. Composite Water Samples The Fairfield County...Ch. 4.3 - Prob. 25BBCh. 4.4 - 1. Notation What does the symbol ! represent? Six...Ch. 4.4 - Prob. 2BSCCh. 4.4 - Prob. 3BSCCh. 4.4 - Prob. 4BSCCh. 4.4 - In Exercises 5–36, express all probabilities as...Ch. 4.4 - 6. Social Security Numbers A Social Security...Ch. 4.4 - Prob. 7BSCCh. 4.4 - 8. Soccer Shootout In soccer, a tie at the end of...Ch. 4.4 - 9. Grading Exams Your professor has just collected...Ch. 4.4 - 10. Radio Station Call Letters If radio station...Ch. 4.4 - 11. Scheduling Routes A presidential candidate...Ch. 4.4 - 12. Survey Reliability A survey with 12 questions...Ch. 4.4 - Prob. 13BSCCh. 4.4 - Prob. 14BSCCh. 4.4 - Prob. 15BSCCh. 4.4 - Prob. 16BSCCh. 4.4 - Prob. 17BSCCh. 4.4 - Prob. 18BSCCh. 4.4 - 19. ZIP Code If you randomly select five digits,...Ch. 4.4 - Prob. 20BSCCh. 4.4 - Prob. 21BSCCh. 4.4 - Prob. 22BSCCh. 4.4 - Prob. 23BSCCh. 4.4 - Prob. 24BSCCh. 4.4 - Prob. 25BSCCh. 4.4 - Prob. 26BSCCh. 4.4 - Prob. 27BSCCh. 4.4 - Prob. 28BSCCh. 4.4 - 29. Mega Millions As of this writing, the Mega...Ch. 4.4 - Prob. 30BSCCh. 4.4 - Prob. 31BSCCh. 4.4 - Prob. 32BSCCh. 4.4 - Prob. 33BSCCh. 4.4 - Prob. 34BSCCh. 4.4 - Prob. 35BSCCh. 4.4 - Prob. 36BSCCh. 4.4 - Prob. 37BBCh. 4.4 - Prob. 38BBCh. 4.5 - Simulating Dice When two dice are rolled, the...Ch. 4.5 - Prob. 2BSCCh. 4.5 - Prob. 3BSCCh. 4.5 - Prob. 4BSCCh. 4.5 - Prob. 5BSCCh. 4.5 - Prob. 6BSCCh. 4.5 - Prob. 7BSCCh. 4.5 - Prob. 8BSCCh. 4.5 - Prob. 9BSCCh. 4.5 - Prob. 10BSCCh. 4.5 - Prob. 11BSCCh. 4.5 - Prob. 12BSCCh. 4.5 - Prob. 13BSCCh. 4.5 - Prob. 14BSCCh. 4.5 - Prob. 15BSCCh. 4.5 - Prob. 16BSCCh. 4.5 - Prob. 17BBCh. 4.5 - Prob. 18BBCh. 4 - Prob. 1CQQCh. 4 - Prob. 2CQQCh. 4 - Prob. 3CQQCh. 4 - Prob. 4CQQCh. 4 - Prob. 5CQQCh. 4 - Prob. 6CQQCh. 4 - Prob. 7CQQCh. 4 - Prob. 8CQQCh. 4 - Prob. 9CQQCh. 4 - Prob. 10CQQCh. 4 - Prob. 1RECh. 4 - In Exercises 1–10, use the data in the...Ch. 4 - In Exercises 1–10, use the data in the...Ch. 4 - Prob. 4RECh. 4 - Prob. 5RECh. 4 - Prob. 6RECh. 4 - Prob. 7RECh. 4 - Prob. 8RECh. 4 - Prob. 9RECh. 4 - Prob. 10RECh. 4 - Prob. 11RECh. 4 - Prob. 12RECh. 4 - Prob. 13RECh. 4 - Prob. 14RECh. 4 - Prob. 15RECh. 4 - Prob. 16RECh. 4 - Prob. 17RECh. 4 - Prob. 18RECh. 4 - Prob. 1CRECh. 4 - Prob. 2CRECh. 4 - Prob. 3CRECh. 4 - Prob. 4CRECh. 4 - Prob. 5CRECh. 4 - Prob. 6CRECh. 4 - Prob. 1EPCh. 4 - Prob. 1FDDCh. 4 - Prob. 2FDDCh. 4 - Prob. 3FDDCh. 4 - Prob. 4FDDCh. 4 - Prob. 5FDDCh. 4 - Prob. 6FDDCh. 4 - Prob. 7FDDCh. 4 - Prob. 8FDDCh. 4 - Prob. 9FDD
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