Fundamentals of Biostatistics
8th Edition
ISBN: 9781305268920
Author: Bernard Rosner
Publisher: Cengage Learning
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Chapter 7.3, Problem A.1RE
What is the difference between a type I and type II error?
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Problem 3. Pricing a multi-stock option the Margrabe formula
The purpose of this problem is to price a swap option in a 2-stock model, similarly as
what we did in the example in the lectures. We consider a two-dimensional Brownian
motion given by W₁ = (W(¹), W(2)) on a probability space (Q, F,P). Two stock prices
are modeled by the following equations:
dX
=
dY₁ =
X₁ (rdt+
rdt+0₁dW!)
(²)),
Y₁ (rdt+dW+0zdW!"),
with Xo
xo and Yo =yo. This corresponds to the multi-stock model studied in class,
but with notation (X+, Y₁) instead of (S(1), S(2)). Given the model above, the measure
P is already the risk-neutral measure (Both stocks have rate of return r). We write
σ = 0₁+0%. We consider a swap option, which gives you the right, at time T, to
exchange one share of X for one share of Y. That is, the option has payoff
F=(Yr-XT).
(a) We first assume that r = 0 (for questions (a)-(f)). Write an explicit expression for
the process Xt.
Reminder before proceeding to question (b): Girsanov's theorem…
Problem 1. Multi-stock model
We consider a 2-stock model similar to the one studied in class. Namely, we consider
=
S(1)
S(2)
=
S(¹) exp (σ1B(1) + (M1 - 0/1 )
S(²) exp (02B(2) + (H₂-
M2
where (B(¹) ) +20 and (B(2) ) +≥o are two Brownian motions, with
t≥0
Cov (B(¹), B(2)) = p min{t, s}.
"
The purpose of this problem is to prove that there indeed exists a 2-dimensional Brownian
motion (W+)+20 (W(1), W(2))+20 such that
=
S(1)
S(2)
=
=
S(¹) exp (011W(¹) + (μ₁ - 01/1) t)
롱)
S(²) exp (021W (1) + 022W(2) + (112 - 03/01/12) t).
where σ11, 21, 22 are constants to be determined (as functions of σ1, σ2, p).
Hint: The constants will follow the formulas developed in the lectures.
(a) To show existence of (Ŵ+), first write the expression for both W. (¹) and W (2)
functions of (B(1), B(²)).
as
(b) Using the formulas obtained in (a), show that the process (WA) is actually a 2-
dimensional standard Brownian motion (i.e. show that each component is normal,
with mean 0, variance t, and that their…
The scores of 8 students on the midterm exam and final exam were as follows.
Student
Midterm
Final
Anderson
98
89
Bailey
88
74
Cruz
87
97
DeSana
85
79
Erickson
85
94
Francis
83
71
Gray
74
98
Harris
70
91
Find the value of the (Spearman's) rank correlation coefficient test statistic that would be used to test the claim of no correlation between midterm score and final exam score. Round your answer to 3 places after the decimal point, if necessary.
Test statistic: rs =
Chapter 7 Solutions
Fundamentals of Biostatistics
Ch. 7.3 - What is the difference between a type I and type...Ch. 7.3 - What is the difference between the critical-value...Ch. 7.3 - Several studies have shown that women with many...Ch. 7.7 - In the BMD study referred to in Case Study 2 (p....Ch. 7.7 - Prob. B.2RECh. 7.7 - Prob. B.3RECh. 7.9 - Prob. C.1RECh. 7.9 - Prob. C.2RECh. 7.9 - How much power did the test in Review Question...Ch. 7 - The mean serum-creatinine level measured in 12...
Ch. 7 - The mean serum-creatinine level measured in 12...Ch. 7 - The mean serum-creatinine level measured in 12...Ch. 7 - The mean serum-creatinine level measured in 1 2...Ch. 7 - The mean serum-creatinine level measured in 12...Ch. 7 - The mean serum-creatinine level measured in 12...Ch. 7 - The mean serumcreatinine level measured in 12...Ch. 7 - The mean serumcreatinine level measured in 12...Ch. 7 - Plasma-glucose levels are used to determine the...Ch. 7 - Plasma-glucose levels are used to determine the...Ch. 7 - Plasma-glucose levels are used to determine the...Ch. 7 - Suppose the incidence rate of myocardial...Ch. 7 - Suppose the incidence rate of myocardial...Ch. 7 - Suppose the incidence rate of myocardial...Ch. 7 - Suppose the incidence rate of myocardial...Ch. 7 - Suppose the incidence rate of myocardial...Ch. 7 - Suppose the annual incidence of asthma in the...Ch. 7 - Prob. 18PCh. 7 - Suppose the annual incidence of asthma in the...Ch. 7 - Prob. 20PCh. 7 - Ribosomal 5S RNA can be represented as a sequence...Ch. 7 - Ribosomal 5S RNA can be represented as a sequence...Ch. 7 - Ribosomal 5S RNA can be represented as a sequence...Ch. 7 - Ribosomal 5S RNA can be represented as a sequence...Ch. 7 - Ribosomal 5S RNA can be represented as a sequence...Ch. 7 - Suppose we identify 50 women 50 to 54 years of age...Ch. 7 - The drug erythromycin has been proposed to...Ch. 7 - A pilot study of a new antihypertensive agent is...Ch. 7 - A pilot study of a new antihypertensive agent is...Ch. 7 - The proportion of deaths due to lung cancer in...Ch. 7 - The proportion of deaths due to lung cancer in...Ch. 7 - The proportion of deaths due to lung cancer in...Ch. 7 - The proportion of deaths due to lung cancer in...Ch. 7 - The proportion of deaths due to lung cancer in...Ch. 7 - Iron-deficiency anemia is an important nutritional...Ch. 7 - Iron-deficiency anemia is an important nutritional...Ch. 7 - Iron-deficiency anemia is an important nutritional...Ch. 7 - Iron-deficiency anemia is an important nutritional...Ch. 7 - Iron-deficiency anemia is an important nutritional...Ch. 7 - Iron-deficiency anemia is an important nutritional...Ch. 7 - Iron-deficiency anemia is an important nutritional...Ch. 7 - Iron-deficiency anemia is an important nutritional...Ch. 7 - Suppose a new test is proposed to identify...Ch. 7 - Suppose a new test is proposed to identify...Ch. 7 - Suppose a new test is proposed to identify...Ch. 7 - Suppose a new test is proposed to identify...Ch. 7 - Suppose a new test is proposed to identify...Ch. 7 - The mortality experience of 8146 male employees of...Ch. 7 - The mortality experience of 8146 male employees of...Ch. 7 - The mortality experience of 8146 male employees of...Ch. 7 - The mortality experience of 8146 male employees of...Ch. 7 - Researchers have reported that the incidence rate...Ch. 7 - Researchers have reported that the incidence rate...Ch. 7 - Researchers have reported that the incidence rate...Ch. 7 - Researchers have reported that the incidence rate...Ch. 7 - Left ventricular mass (LVM) is an important risk...Ch. 7 - Left ventricular mass (LVM) is an important risk...Ch. 7 - Left ventricular mass (LVM) is an important risk...Ch. 7 - Left ventricular mass (LVM) is an important risk...Ch. 7 - Prob. 60PCh. 7 - Previous studies have shown that supplementing the...Ch. 7 - Prob. 62PCh. 7 - Prob. 63PCh. 7 - Previous studies have shown that supplementing the...Ch. 7 - Prob. 65PCh. 7 - Prob. 66PCh. 7 - Refer to Data Set NIFED.DAT at...Ch. 7 - The combination of photochemotherapy with oral...Ch. 7 - The combination of photochemotherapy with oral...Ch. 7 - The combination of photochemotherapy with oral...Ch. 7 - Prob. 72PCh. 7 - Breast cancer is strongly influenced by a womans...Ch. 7 - Prob. 74PCh. 7 - An investigator wants to test a new eye drop that...Ch. 7 - Prob. 76PCh. 7 - Table 7.10 gives the itching scores reported by...Ch. 7 - Table 7.10 gives the itching scores reported by...Ch. 7 - Table 7.10 gives the itching scores reported by...Ch. 7 - Table 7.10 gives the itching scores reported by...Ch. 7 - Prob. 81PCh. 7 - Prob. 82PCh. 7 - Concurrent sexual partnerships are widely believed...Ch. 7 - Prob. 84PCh. 7 - Prob. 85PCh. 7 - Prob. 86PCh. 7 - Consider the birthweight data in Example 7.2. What...Ch. 7 - Consider the birthweight data in Example 7.2. Now...Ch. 7 - Prob. 89PCh. 7 - A screening program for neuroblastoma (a type of...Ch. 7 - A screening program for neuroblastoma (a type of...Ch. 7 - Prob. 92PCh. 7 - Prob. 93PCh. 7 - Prob. 94PCh. 7 - Prob. 95PCh. 7 - Prob. 96PCh. 7 - An experiment was performed to assess the efficacy...Ch. 7 - Medical errors are common in hospitals throughout...Ch. 7 - Prob. 99PCh. 7 - Prob. 100PCh. 7 - Prob. 101PCh. 7 - Prob. 102PCh. 7 - Prob. 103PCh. 7 - Prob. 104PCh. 7 - Osteoporosis is an important cause of morbidity in...Ch. 7 - Osteoporosis is an important cause of morbidity in...Ch. 7 - Osteoporosis is an important cause of morbidity in...Ch. 7 - Prob. 108PCh. 7 - Prob. 109PCh. 7 - Prob. 110PCh. 7 - Prob. 111PCh. 7 - Prob. 112PCh. 7 - Prob. 113PCh. 7 - A study was conducted in Sweden to relate the age...Ch. 7 - A study was conducted in Sweden to relate the age...Ch. 7 - A study was conducted in Sweden to relate the age...Ch. 7 - Prob. 117PCh. 7 - Prob. 118PCh. 7 - Prob. 119PCh. 7 - Prob. 120PCh. 7 - Prob. 121P
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