EBK BIOSTATISTICS FOR THE BIOLOGICAL AN
2nd Edition
ISBN: 9780134679228
Author: ROY
Publisher: PEARSON CUSTOM PUB.(CONSIGNMENT)
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Chapter 4, Problem 12RE
a.
To determine
To find: The
b.
To determine
To find: The probability that the birthday of the randomly selected person is in October
c.
To determine
To find: The subjective probability of getting someone who knows that in Japan 18th October is National Statistics day.
d.
To determine
To find: Whether the probability of getting someone who knows that in Japan 18th October is National Statistics day is unlikely or not
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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 4 Solutions
EBK BIOSTATISTICS FOR THE BIOLOGICAL AN
Ch. 4.1 - Prob. 1SLCTCh. 4.1 - Prob. 2SLCTCh. 4.1 - Prob. 3SLCTCh. 4.1 - Prob. 4SLCTCh. 4.1 - Prob. 5SLCTCh. 4.1 - Prob. 6SLCTCh. 4.1 - Prob. 7SLCTCh. 4.1 - Prob. 8SLCTCh. 4.1 - Prob. 9SLCTCh. 4.1 - Prob. 10SLCT
Ch. 4.1 - Prob. 11SLCTCh. 4.1 - Prob. 12SLCTCh. 4.1 - Prob. 13SLCTCh. 4.1 - Prob. 14SLCTCh. 4.1 - Prob. 15SLCTCh. 4.1 - Prob. 16SLCTCh. 4.1 - Prob. 17SLCTCh. 4.1 - Prob. 18SLCTCh. 4.1 - Prob. 19SLCTCh. 4.1 - Prob. 20SLCTCh. 4.1 - Prob. 21SLCTCh. 4.1 - Prob. 22SLCTCh. 4.1 - Prob. 23SLCTCh. 4.1 - Prob. 24SLCTCh. 4.1 - Prob. 25SLCTCh. 4.1 - Prob. 26SLCTCh. 4.1 - Prob. 27SLCTCh. 4.1 - Prob. 28SLCTCh. 4.1 - Prob. 29SLCTCh. 4.1 - Prob. 30SLCTCh. 4.1 - Prob. 31SLCTCh. 4.1 - Prob. 32SLCTCh. 4.1 - Prob. 33SLCTCh. 4.1 - Prob. 34SLCTCh. 4.1 - Prob. 35SLCTCh. 4.1 - Prob. 36SLCTCh. 4.1 - Prob. 37SLCTCh. 4.1 - Prob. 38SLCTCh. 4.1 - Prob. 39SLCTCh. 4.1 - Prob. 40SLCTCh. 4.2 - Prob. 1SLCTCh. 4.2 - Prob. 2SLCTCh. 4.2 - Prob. 3SLCTCh. 4.2 - Prob. 4SLCTCh. 4.2 - Prob. 5SLCTCh. 4.2 - Prob. 6SLCTCh. 4.2 - Prob. 7SLCTCh. 4.2 - Prob. 8SLCTCh. 4.2 - Prob. 9SLCTCh. 4.2 - Prob. 10SLCTCh. 4.2 - Prob. 11SLCTCh. 4.2 - Prob. 12SLCTCh. 4.2 - Prob. 13SLCTCh. 4.2 - Prob. 14SLCTCh. 4.2 - Prob. 15SLCTCh. 4.2 - Prob. 16SLCTCh. 4.2 - Prob. 17SLCTCh. 4.2 - Prob. 18SLCTCh. 4.2 - Prob. 19SLCTCh. 4.2 - Prob. 20SLCTCh. 4.2 - Prob. 21SLCTCh. 4.2 - Prob. 22SLCTCh. 4.2 - Prob. 23SLCTCh. 4.2 - Prob. 24SLCTCh. 4.2 - Prob. 25SLCTCh. 4.2 - Prob. 26SLCTCh. 4.2 - Prob. 27SLCTCh. 4.2 - Prob. 28SLCTCh. 4.2 - Prob. 29SLCTCh. 4.2 - Prob. 30SLCTCh. 4.2 - Prob. 31SLCTCh. 4.2 - Prob. 32SLCTCh. 4.2 - Prob. 33SLCTCh. 4.2 - Prob. 34SLCTCh. 4.3 - Prob. 1SLCTCh. 4.3 - Prob. 2SLCTCh. 4.3 - Prob. 3SLCTCh. 4.3 - Prob. 4SLCTCh. 4.3 - Prob. 5SLCTCh. 4.3 - Prob. 6SLCTCh. 4.3 - Prob. 7SLCTCh. 4.3 - Prob. 8SLCTCh. 4.3 - Prob. 9SLCTCh. 4.3 - Prob. 10SLCTCh. 4.3 - Prob. 11SLCTCh. 4.3 - Prob. 12SLCTCh. 4.3 - Prob. 13SLCTCh. 4.3 - Prob. 14SLCTCh. 4.3 - Prob. 15SLCTCh. 4.3 - Prob. 16SLCTCh. 4.3 - Prob. 17SLCTCh. 4.3 - Prob. 18SLCTCh. 4.3 - Prob. 19SLCTCh. 4.3 - Prob. 20SLCTCh. 4.3 - Prob. 21SLCTCh. 4.3 - Prob. 22SLCTCh. 4.3 - Prob. 23SLCTCh. 4.3 - Prob. 24SLCTCh. 4.3 - Prob. 25SLCTCh. 4.4 - Prob. 1SLCTCh. 4.4 - Prob. 2SLCTCh. 4.4 - Prob. 3SLCTCh. 4.4 - Prob. 4SLCTCh. 4.4 - Prob. 5SLCTCh. 4.4 - Prob. 6SLCTCh. 4.4 - Prob. 7SLCTCh. 4.4 - Prob. 8SLCTCh. 4.4 - Prob. 9SLCTCh. 4.4 - Prob. 10SLCTCh. 4.4 - Prob. 11SLCTCh. 4.4 - Prob. 12SLCTCh. 4.4 - Prob. 13SLCTCh. 4.4 - Prob. 14SLCTCh. 4.4 - Prob. 15SLCTCh. 4.4 - Prob. 16SLCTCh. 4.4 - Prob. 17SLCTCh. 4.4 - Prob. 18SLCTCh. 4.5 - Prob. 1SLCTCh. 4.5 - Prob. 2SLCTCh. 4.5 - Prob. 3SLCTCh. 4.5 - Prob. 4SLCTCh. 4.5 - Prob. 5SLCTCh. 4.5 - Prob. 6SLCTCh. 4.5 - Prob. 7SLCTCh. 4.5 - Prob. 8SLCTCh. 4.5 - Prob. 9SLCTCh. 4.5 - Prob. 10SLCTCh. 4.5 - Prob. 11SLCTCh. 4.5 - Prob. 12SLCTCh. 4.5 - Prob. 13SLCTCh. 4.5 - Prob. 14SLCTCh. 4.5 - Prob. 15SLCTCh. 4.5 - Prob. 16SLCTCh. 4.5 - Prob. 17SLCTCh. 4.5 - Prob. 18SLCTCh. 4.5 - Prob. 19SLCTCh. 4.5 - Prob. 20SLCTCh. 4.5 - Prob. 21SLCTCh. 4.6 - Prob. 1SLCTCh. 4.6 - Prob. 2SLCTCh. 4.6 - Prob. 3SLCTCh. 4.6 - Prob. 4SLCTCh. 4.6 - Prob. 5SLCTCh. 4.6 - Prob. 6SLCTCh. 4.6 - Prob. 7SLCTCh. 4.6 - Prob. 8SLCTCh. 4.6 - Prob. 9SLCTCh. 4.6 - Prob. 10SLCTCh. 4.6 - Prob. 11SLCTCh. 4.6 - Prob. 12SLCTCh. 4.6 - Prob. 13SLCTCh. 4.6 - Prob. 14SLCTCh. 4.6 - Prob. 15SLCTCh. 4.6 - Prob. 16SLCTCh. 4.6 - Prob. 17SLCTCh. 4.6 - Prob. 18SLCTCh. 4.6 - Prob. 19SLCTCh. 4.6 - Prob. 20SLCTCh. 4.6 - Prob. 21SLCTCh. 4.6 - Prob. 22SLCTCh. 4.6 - Prob. 23SLCTCh. 4.6 - Prob. 24SLCTCh. 4.6 - Prob. 25SLCTCh. 4.6 - Prob. 26SLCTCh. 4.6 - Prob. 27SLCTCh. 4.6 - Prob. 28SLCTCh. 4.6 - Prob. 29SLCTCh. 4.6 - Prob. 30SLCTCh. 4.6 - Prob. 31SLCTCh. 4.6 - Prob. 32SLCTCh. 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 - Prob. 2RECh. 4 - Prob. 3RECh. 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. 1CRECh. 4 - Prob. 2CRECh. 4 - Prob. 3CRECh. 4 - Prob. 4CRECh. 4 - Prob. 5CRE
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