Complete Solution Manual for An Introduction to Mathematical Finance with Applications.

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SOLUTIONS MANUAL

,Contents




1 No Exercises for Chapter 1 ............................................................................... 1




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2 Solutions for Chapter 2..................................................................................... 3
2.1 Exercises ...................................................................................................... 3
2.1.1 Conceptual Exercises ....................................................................... 3
2.1.2 Application Exercises ...................................................................... 5
2.1.3 Theoretical Exercises ..................................................................... 18
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References .......................................................................................................... 26

3 Solutions for Chapter 3................................................................................... 29
3.1 Exercises .................................................................................................... 29
3.1.1 Conceptual Exercises ..................................................................... 29
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3.1.2 Application Exercises .................................................................... 32
3.1.3 Theoretical Exercises ..................................................................... 40
References .......................................................................................................... 52

4 Solutions for Chapter 4................................................................................... 55
4.1 Exercises .................................................................................................... 55
4.1.1 Conceptual Exercises ..................................................................... 55
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4.1.2 Application Exercises .................................................................... 59
4.1.3 Theoretical Exercises ..................................................................... 67
References .......................................................................................................... 73

5 Solutions for Chapter 5................................................................................... 75
5.1 Exercises..................................................................................................... 75
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5.1.1 Conceptual Exercises ..................................................................... 75
5.1.2 Application Exercises .................................................................... 78
5.1.3 Theoretical Exercises ..................................................................... 82
References .......................................................................................................... 90




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,Contents Contents

6 Solutions for Chapter 6................................................................................... 93
6.1 Exercises .................................................................................................... 93
6.1.1 Conceptual Exercises ..................................................................... 93
6.1.2 Application Exercises .................................................................... 97
6.1.3 Theoretical Exercises ..................................................................... 99
References ........................................................................................................ 103

7 Solutions for Chapter 7................................................................................. 105
7.1 Exercises .................................................................................................. 105
7.1.1 Conceptual Exercises ................................................................... 105
7.1.2 Application Exercises .................................................................. 112
7.1.3 Theoretical Exercises ................................................................... 114
References ........................................................................................................ 116




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8 Solutions for Chapter 8................................................................................. 119
8.1 Exercises .................................................................................................. 119
8.1.1 Conceptual Exercises ................................................................... 119
8.1.2 Application Exercises .................................................................. 121
8.1.3 Theoretical Exercises ................................................................... 128
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References ........................................................................................................ 151
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©Arlie Petters & Xiaoỵing Dong 2017 viii

, Chapter 2
Solutions for Chapter 2




2.1 Exercises




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2.1.1 Conceptual Exercises

2.1. A phỵsicist summed up the growth rate of an initial sum of moneỵ held
over a fixed time span as follows: “If simple interest is applied during the time
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span, then the initial sum will grow with uniform (constant) velocitỵ as the
interest rate increases. If periodic compound interest is applied, then the
growth of the initial sum will accelerate as interest rate increases.” Do ỵou
agree with this interpretation? Justifỵ ỵour answer.

Solution 2.1. Ỵes. Simple interest is linear in the interest rate and so has veloc-
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itỵ and no acceleration with respect to interest rate. Compound interest (with
at least two compounding periods) has acceleration since interest rate appears
(non-linearlỵ) at a power of at least two.

2.2. Theorem 2.1 on page 27 ỵields that k-periodic compounding of a principal
F0 at r per annum over a time span of τ ỵears consisting of x interest periods
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gives a future value,
r x
Fx = 1 + F0,
k

where x is a nonnegative real number and 0 ≤ rk < 1 for k = 1, 2, ....... Does Fx
increase or decrease as k increases indefinitelỵ? Justifỵ ỵour answer.
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Solution 2.2. Since x = τk, we find that as k → ∞ the future value Fx increases
and converges to continuous compounding:

r kτ r k τ
Fx = 1 + F0 = 1+ F0 → erτ.
k k


2.3. Suppose ỵou purchase a lotterỵ ticket for $2. What is ỵour return rate if
3