PRACTICE OF STATS - 1 TERM ACCESS CODE
4th Edition
ISBN: 9781319403348
Author: BALDI
Publisher: Macmillan Higher Education
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Question
Chapter 12, Problem 12.1AYK
To determine
To find: does X have a binomial distribution?
Expert Solution & Answer
Answer to Problem 12.1AYK
X has a binomial distribution.
Explanation of Solution
Given:
Random dialing machine make 15 calls and 20% of the calls reach a live person.
Calculation:
The four conditions for a binomial setting are: binary (success/failure), independent, trials, fixed number of trials and
Binary: Satisfied, a success is reaching a live person and a failure is not reaching a live person
Independent: Satisfied, because the telephone numbers are selected at random.
Fixed number of trials: Satisfied,
Probability of success: Satisfied,
Thus X has a binomial distribution.
Conclusion:
Probability of success: Satisfied,
Thus X has a binomial distribution.
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Students have asked these similar questions
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 12 Solutions
PRACTICE OF STATS - 1 TERM ACCESS CODE
Ch. 12 - Prob. 12.1AYKCh. 12 - Prob. 12.2AYKCh. 12 - Prob. 12.3AYKCh. 12 - Prob. 12.4AYKCh. 12 - Prob. 12.5AYKCh. 12 - Prob. 12.6AYKCh. 12 - Prob. 12.7AYKCh. 12 - Prob. 12.8AYKCh. 12 - Prob. 12.9AYKCh. 12 - Prob. 12.10AYK
Ch. 12 - Prob. 12.11AYKCh. 12 - Prob. 12.12AYKCh. 12 - Prob. 12.13AYKCh. 12 - Prob. 12.14AYKCh. 12 - Prob. 12.15AYKCh. 12 - Prob. 12.16AYKCh. 12 - Prob. 12.17AYKCh. 12 - Prob. 12.18AYKCh. 12 - Prob. 12.19CYSCh. 12 - Prob. 12.20CYSCh. 12 - Prob. 12.21CYSCh. 12 - Prob. 12.22CYSCh. 12 - Prob. 12.23CYSCh. 12 - Prob. 12.24CYSCh. 12 - Prob. 12.25CYSCh. 12 - Prob. 12.26CYSCh. 12 - Prob. 12.27CYSCh. 12 - Prob. 12.28CYSCh. 12 - Prob. 12.29ECh. 12 - Prob. 12.30ECh. 12 - Prob. 12.31ECh. 12 - Prob. 12.32ECh. 12 - Prob. 12.33ECh. 12 - Prob. 12.34ECh. 12 - Prob. 12.35ECh. 12 - Prob. 12.36ECh. 12 - Prob. 12.37ECh. 12 - Prob. 12.38ECh. 12 - Prob. 12.39ECh. 12 - Prob. 12.40ECh. 12 - Prob. 12.41ECh. 12 - Prob. 12.42ECh. 12 - Prob. 12.43ECh. 12 - Prob. 12.44ECh. 12 - Prob. 12.45ECh. 12 - Prob. 12.46ECh. 12 - Prob. 12.47ECh. 12 - Prob. 12.48ECh. 12 - Prob. 12.49ECh. 12 - Prob. 12.50ECh. 12 - Prob. 12.51ECh. 12 - Prob. 12.52ECh. 12 - Prob. 12.53E
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