Understandable Statistics: Concepts and Methods
12th Edition
ISBN: 9781337119917
Author: Charles Henry Brase, Corrinne Pellillo Brase
Publisher: Cengage Learning
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Chapter 7.2, Problem 9P
To determine
Explain whether the confidence interval is longer or shorter for the
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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.)
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
Chapter 7 Solutions
Understandable Statistics: Concepts and Methods
Ch. 7.1 - In Problems 18, answer true or false. Explain your...Ch. 7.1 - In Problems 18, answer true or false. Explain your...Ch. 7.1 - In Problems 18, answer true or false. Explain your...Ch. 7.1 - In Problems 18, answer true or false. Explain your...Ch. 7.1 - In Problems 18, answer true or false. Explain your...Ch. 7.1 - In Problems 18, answer true or false. Explain your...Ch. 7.1 - In Problems 18, answer true or false. Explain your...Ch. 7.1 - In Problems 18, answer true or false. Explain your...Ch. 7.1 - Critical Thinking Sam computed a 95% confidence...Ch. 7.1 - Critical Thinking Sam computed a 90% confidence...
Ch. 7.1 - Basic Computation: Confidence Interval Suppose x...Ch. 7.1 - Basic Computation: Confidence Interval Suppose x...Ch. 7.1 - Basic Computation: Sample Size Suppose x has a...Ch. 7.1 - Basic Computation: Sample Size Suppose x has a...Ch. 7.1 - Zoology: Hummingbirds Allens hummingbird...Ch. 7.1 - Diagnostic Tests: Uric Acid Overproduction of uric...Ch. 7.1 - Diagnostic Tests: Plasma Volume Total plasma...Ch. 7.1 - Agriculture: Watermelon What price do farmers get...Ch. 7.1 - Prob. 19PCh. 7.1 - Confidence Intervals: Values of A random sample...Ch. 7.1 - Confidence Intervals: Sample Size A random sample...Ch. 7.1 - Ecology: Sand Dunes At wind speeds above 1000...Ch. 7.1 - Prob. 23PCh. 7.1 - Prob. 24PCh. 7.1 - Prob. 25PCh. 7.2 - Use Table 6 of Appendix II to find tc for a 0.95...Ch. 7.2 - Prob. 2PCh. 7.2 - Prob. 3PCh. 7.2 - Prob. 4PCh. 7.2 - Prob. 5PCh. 7.2 - Prob. 6PCh. 7.2 - Prob. 7PCh. 7.2 - Prob. 8PCh. 7.2 - Prob. 9PCh. 7.2 - Prob. 10PCh. 7.2 - Basic Computation: Confidence Interval Suppose x...Ch. 7.2 - Basic Computation: Confidence Interval A random...Ch. 7.2 - In Problems 1319, assume that the population of x...Ch. 7.2 - In Problems 1319, assume that the population of x...Ch. 7.2 - In Problems 1319, assume that the population of x...Ch. 7.2 - In Problems 1319, assume that the population of x...Ch. 7.2 - In Problems 1319, assume that the population of x...Ch. 7.2 - Prob. 18PCh. 7.2 - Prob. 19PCh. 7.2 - Prob. 20PCh. 7.2 - Prob. 21PCh. 7.2 - Prob. 22PCh. 7.2 - Prob. 23PCh. 7.3 - For all these problems, carry at least four digits...Ch. 7.3 - Prob. 2PCh. 7.3 - Prob. 3PCh. 7.3 - Prob. 4PCh. 7.3 - For all these problems, carry at least four digits...Ch. 7.3 - Prob. 6PCh. 7.3 - Prob. 7PCh. 7.3 - Prob. 8PCh. 7.3 - Prob. 9PCh. 7.3 - For all these problems, carry at least four digits...Ch. 7.3 - Prob. 11PCh. 7.3 - Prob. 12PCh. 7.3 - Prob. 13PCh. 7.3 - For all these problems, carry at least four digits...Ch. 7.3 - Prob. 15PCh. 7.3 - Prob. 16PCh. 7.3 - Prob. 17PCh. 7.3 - Prob. 18PCh. 7.3 - Prob. 19PCh. 7.3 - Prob. 20PCh. 7.3 - Prob. 21PCh. 7.3 - Prob. 22PCh. 7.3 - Prob. 23PCh. 7.3 - Prob. 24PCh. 7.3 - Prob. 25PCh. 7.3 - Prob. 26PCh. 7.3 - Prob. 27PCh. 7.3 - Prob. 28PCh. 7.4 - Prob. 1PCh. 7.4 - Prob. 2PCh. 7.4 - Prob. 3PCh. 7.4 - Prob. 4PCh. 7.4 - Prob. 5PCh. 7.4 - Prob. 6PCh. 7.4 - Prob. 7PCh. 7.4 - Prob. 8PCh. 7.4 - Prob. 9PCh. 7.4 - Prob. 10PCh. 7.4 - Prob. 11PCh. 7.4 - Prob. 12PCh. 7.4 - Prob. 13PCh. 7.4 - Prob. 14PCh. 7.4 - Prob. 15PCh. 7.4 - Prob. 16PCh. 7.4 - Answers may vary slightly due to rounding....Ch. 7.4 - Prob. 18PCh. 7.4 - Prob. 19PCh. 7.4 - Prob. 20PCh. 7.4 - Prob. 21PCh. 7.4 - Prob. 22PCh. 7.4 - Prob. 23PCh. 7.4 - Prob. 24PCh. 7.4 - Prob. 25PCh. 7.4 - Prob. 26PCh. 7.4 - Prob. 27PCh. 7.4 - Prob. 28PCh. 7.4 - Prob. 29PCh. 7.4 - Prob. 30PCh. 7.4 - Prob. 31PCh. 7 - Prob. 1CRPCh. 7 - Critical Thinking Suppose you are told that a 95%...Ch. 7 - Prob. 3CRPCh. 7 - Prob. 4CRPCh. 7 - Prob. 5CRPCh. 7 - For Problems 419, categorize each problem...Ch. 7 - Prob. 7CRPCh. 7 - For Problems 419, categorize each problem...Ch. 7 - Prob. 9CRPCh. 7 - For Problems 419, categorize each problem...Ch. 7 - For Problems 419, categorize each problem...Ch. 7 - For Problems 419, categorize each problem...Ch. 7 - Prob. 13CRPCh. 7 - Prob. 14CRPCh. 7 - Prob. 15CRPCh. 7 - For Problems 419, categorize each problem...Ch. 7 - Prob. 17CRPCh. 7 - Prob. 18CRPCh. 7 - Prob. 19CRPCh. 7 - Prob. 1DHCh. 7 - Prob. 2DHCh. 7 - Prob. 3DHCh. 7 - Prob. 1LCCh. 7 - Prob. 2LCCh. 7 - Prob. 3LCCh. 7 - Prob. 1UT
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