Basic College Mathematics With Early Integers
3rd Edition
ISBN: 9780133864717
Author: Martin-Gay, K. Elayn
Publisher: Pearson,
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Chapter B.2, Problem 1P
To determine
The product of
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For each month of the year, Taylor collected the average high temperatures in Jackson, Mississippi. He used the data to create the histogram shown. Which set of data did he use to create the histogram?
A
55, 60, 64, 72, 73, 75, 77, 81, 83, 91, 91, 92\ 55,\ 60,\ 64,\ 72,\ 73,\ 75,\ 77,\ 81,\ 83,\ 91,\ 91,\ 92 55, 60, 64, 72, 73, 75, 77, 81, 83, 91, 91, 92
B
55, 57, 60, 65, 70, 71, 78, 79, 85, 86, 88, 91\ 55,\ 57,\ 60,\ 65,\ 70,\ 71,\ 78,\ 79,\ 85,\ 86,\ 88,\ 91 55, 57, 60, 65, 70, 71, 78, 79, 85, 86, 88, 91
C
55, 60, 63, 64, 65, 71, 83, 87, 88, 88, 89, 93\ 55,\ 60,\ 63,\ 64,\ 65,\ 71,\ 83,\ 87,\ 88,\ 88,\ 89,\ 93 55, 60, 63, 64, 65, 71, 83, 87, 88, 88, 89, 93
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55, 58, 60, 66, 68, 75, 77, 82, 86, 89, 91, 91\ 55,\ 58,\ 60,\ 66,\ 68,\ 75,\ 77,\ 82,\ 86,\ 89,\ 91,\ 91 55, 58, 60, 66, 68, 75, 77, 82, 86, 89, 91, 91
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?
Chapter B Solutions
Basic College Mathematics With Early Integers
Ch. B.1 - Prob. 1PCh. B.1 - Prob. 2PCh. B.1 - Prob. 3PCh. B.1 - Prob. 4PCh. B.1 - Prob. 5PCh. B.1 - Prob. 6PCh. B.1 - Prob. 7PCh. B.1 - Prob. 8PCh. B.1 - Prob. 9PCh. B.1 - Prob. 10P
Ch. B.1 - Prob. 11PCh. B.1 - Prob. 1ECh. B.1 - Prob. 2ECh. B.1 - Prob. 3ECh. B.1 - Prob. 4ECh. B.1 - Prob. 5ECh. B.1 - Prob. 6ECh. B.1 - Prob. 7ECh. B.1 - Prob. 8ECh. B.1 - Prob. 9ECh. B.1 - Prob. 10ECh. B.1 - Prob. 11ECh. B.1 - Prob. 12ECh. B.1 - Prob. 13ECh. B.1 - Prob. 14ECh. B.1 - Prob. 15ECh. B.1 - Prob. 16ECh. B.1 - Prob. 17ECh. B.1 - Prob. 18ECh. B.1 - Prob. 19ECh. B.1 - Prob. 20ECh. B.1 - Prob. 21ECh. B.1 - Prob. 22ECh. B.1 - Prob. 23ECh. B.1 - Prob. 24ECh. B.1 - Prob. 25ECh. B.1 - Prob. 26ECh. B.1 - Prob. 27ECh. B.1 - Prob. 28ECh. B.1 - Prob. 29ECh. B.1 - Prob. 30ECh. B.1 - Prob. 31ECh. B.1 - Perform each indicated operation.
(35x2 + x − 5) −...Ch. B.1 - Prob. 33ECh. B.1 - Prob. 34ECh. B.1 - Prob. 35ECh. B.1 - Prob. 36ECh. B.1 - Prob. 37ECh. B.1 - Prob. 38ECh. B.1 - Prob. 39ECh. B.1 - Prob. 40ECh. B.1 - Prob. 41ECh. B.1 - Prob. 42ECh. B.1 - Prob. 43ECh. B.1 - Prob. 44ECh. B.1 - Prob. 45ECh. B.1 - Prob. 46ECh. B.1 - Prob. 47ECh. B.1 - Prob. 48ECh. B.1 - Prob. 49ECh. B.1 - Prob. 50ECh. B.1 - Prob. 51ECh. B.1 - Prob. 52ECh. B.1 - Prob. 53ECh. B.1 - Prob. 54ECh. B.1 - Prob. 55ECh. B.1 - Prob. 56ECh. B.1 - Prob. 57ECh. B.1 - Prob. 58ECh. B.1 - Prob. 59ECh. B.1 - Prob. 60ECh. B.1 - Prob. 61ECh. B.1 - Prob. 62ECh. B.1 - Prob. 63ECh. B.1 - Prob. 64ECh. B.1 - Prob. 65ECh. B.2 - Prob. 1PCh. B.2 - Prob. 2PCh. B.2 - Prob. 3PCh. B.2 - Prob. 4PCh. B.2 - Prob. 5PCh. B.2 - Prob. 6PCh. B.2 - Prob. 7PCh. B.2 - Prob. 8PCh. B.2 - Prob. 9PCh. B.2 - Prob. 1ECh. B.2 - Prob. 2ECh. B.2 - Prob. 3ECh. B.2 - Prob. 4ECh. B.2 - Prob. 5ECh. B.2 - Prob. 6ECh. B.2 - Prob. 7ECh. B.2 - Prob. 8ECh. B.2 - Prob. 9ECh. B.2 - Prob. 10ECh. B.2 - Prob. 11ECh. B.2 - Prob. 12ECh. B.2 - Prob. 13ECh. B.2 - Prob. 14ECh. B.2 - Prob. 15ECh. B.2 - Prob. 16ECh. B.2 - Prob. 17ECh. B.2 - Prob. 18ECh. B.2 - Prob. 19ECh. B.2 - Prob. 20ECh. B.2 - Prob. 21ECh. B.2 - Prob. 22ECh. B.2 - Prob. 23ECh. B.2 - Prob. 24ECh. B.2 - Prob. 25ECh. B.2 - Prob. 26ECh. B.2 - Prob. 27ECh. B.2 - Prob. 28ECh. B.2 - Prob. 29ECh. B.2 - Prob. 30ECh. B.2 - Prob. 31ECh. B.2 - Prob. 32ECh. B.2 - Prob. 33ECh. B.2 - Prob. 34ECh. B.2 - Prob. 35ECh. B.2 - Prob. 36ECh. B.2 - Prob. 37ECh. B.2 - Prob. 38ECh. B.2 - Prob. 39ECh. B.2 - Prob. 40ECh. B.2 - Prob. 41ECh. B.2 - Prob. 42ECh. B.2 - Prob. 43ECh. B.3 - Prob. 1PCh. B.3 - Prob. 2PCh. B.3 - Prob. 3PCh. B.3 - Prob. 4PCh. B.3 - Prob. 5PCh. B.3 - Prob. 6PCh. B.3 - Prob. 7PCh. B.3 - Prob. 8PCh. B.3 - Prob. 9PCh. B.3 - Prob. 1ECh. B.3 - Prob. 2ECh. B.3 - Prob. 3ECh. B.3 - Prob. 4ECh. B.3 - Prob. 5ECh. B.3 - Prob. 6ECh. B.3 - Prob. 7ECh. B.3 - Prob. 8ECh. B.3 - Prob. 9ECh. B.3 - Prob. 10ECh. B.3 - Prob. 11ECh. B.3 - Prob. 12ECh. B.3 - Prob. 13ECh. B.3 - Prob. 14ECh. B.3 - Prob. 15ECh. B.3 - Prob. 16ECh. B.3 - Prob. 17ECh. B.3 - Prob. 18ECh. B.3 - Prob. 19ECh. B.3 - Prob. 20ECh. B.3 - Prob. 21ECh. B.3 - Prob. 22ECh. B.3 - Prob. 23ECh. B.3 - Prob. 24ECh. B.3 - Prob. 25ECh. B.3 - Prob. 26ECh. B.3 - Prob. 27ECh. B.3 - Prob. 28ECh. B.3 - Prob. 29ECh. B.3 - Prob. 30ECh. B.3 - Prob. 31ECh. B.3 - Prob. 32ECh. B.3 - Prob. 33ECh. B.3 - Prob. 34ECh. B.3 - Prob. 35ECh. B.3 - Prob. 36ECh. B.3 - Prob. 37ECh. B.3 - Prob. 38ECh. B.3 - Prob. 39ECh. B.3 - Prob. 40ECh. B.3 - Prob. 41ECh. B.3 - Prob. 42ECh. B.3 - Prob. 43ECh. B.3 - Prob. 44ECh. B.3 - Prob. 45ECh. B.3 - Prob. 46ECh. B.3 - Prob. 47E
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