Solutions Manual to
accompany
An Introduction to
Financial Markets: A
Quantitative Approach
Paolo Brandimarte
A Wiley-Interscience Publication
JOHN WILEY & SONS, INC.
New York / Chichester / Weinheim / Brisbane / Singapore / Toronto
, Contents
Preface vii
1 Financial Markets: Functions, Institutions, and Traded Assets 1
1.1 Solutions 1
2 Basic Problems in Quantitative Finance 3
2.1 Solutions 3
2.2 Additional problems 8
3 Elementary Theory of Interest Rates 11
3.1 Solutions 11
4 Forward Rate Agreements, Interest Rate Futures, and Vanilla Swaps 17
4.1 Solutions 17
5 Fixed-Income Markets 19
5.1 Solutions 19
6 Interest Rate Risk Management 21
6.1 Solutions 21
7 Decision-Making under Uncertainty: The Static Case 29
7.1 Solutions 29
v
vi CONTENTS
8 Mean–Variance Efficient Portfolios 35
8.1 Solutions 35
9 Factor Models 43
10 Equilibrium Models: CAPM and APT 49
11 Modeling Dynamic Uncertainty 53
, 11.1 Solutions 53
12 Forward and Futures Contracts 59
12.1 Solutions 59
13 Option Pricing: Complete Markets 63
13.1 Solutions 63
14 Option Pricing: Incomplete Markets 81
15 Optimization Model Building 83
15.1 Solutions 83
16 Optimization Model Solving 91
16.1 Solutions 91
, Preface
This solutions manual contains worked-out solutions to end-of-chapter problems in the
book. Over time, I plan to add additional solved problems.
When useful, I will include hints about how software tools like R or MATLAB can be used.
In fact, these tools have been used to carry out the required calculations, and there may be
numerical differences in the results, if you use these environments, keeping the best
numerical precision, rather than using paper and a pocket calculator, possibly introducing
some rounding. Needless to say, the important point of these problems is conceptual, as they
should support the understanding of the underlying financial concepts. Therefore, do not
bother about small inconsistencies (which would be important in real life, where you have to
stick with market conventions in rounding things!).
The manual is work-in-progress, so be sure to check back every now and then, to see
whether a new version has been posted.
This version is dated December 12, 2018.
As usual, for comments, suggestions, and criticisms, my e-mail address is given below.
PAOLO BRANDIMARTE
vii
accompany
An Introduction to
Financial Markets: A
Quantitative Approach
Paolo Brandimarte
A Wiley-Interscience Publication
JOHN WILEY & SONS, INC.
New York / Chichester / Weinheim / Brisbane / Singapore / Toronto
, Contents
Preface vii
1 Financial Markets: Functions, Institutions, and Traded Assets 1
1.1 Solutions 1
2 Basic Problems in Quantitative Finance 3
2.1 Solutions 3
2.2 Additional problems 8
3 Elementary Theory of Interest Rates 11
3.1 Solutions 11
4 Forward Rate Agreements, Interest Rate Futures, and Vanilla Swaps 17
4.1 Solutions 17
5 Fixed-Income Markets 19
5.1 Solutions 19
6 Interest Rate Risk Management 21
6.1 Solutions 21
7 Decision-Making under Uncertainty: The Static Case 29
7.1 Solutions 29
v
vi CONTENTS
8 Mean–Variance Efficient Portfolios 35
8.1 Solutions 35
9 Factor Models 43
10 Equilibrium Models: CAPM and APT 49
11 Modeling Dynamic Uncertainty 53
, 11.1 Solutions 53
12 Forward and Futures Contracts 59
12.1 Solutions 59
13 Option Pricing: Complete Markets 63
13.1 Solutions 63
14 Option Pricing: Incomplete Markets 81
15 Optimization Model Building 83
15.1 Solutions 83
16 Optimization Model Solving 91
16.1 Solutions 91
, Preface
This solutions manual contains worked-out solutions to end-of-chapter problems in the
book. Over time, I plan to add additional solved problems.
When useful, I will include hints about how software tools like R or MATLAB can be used.
In fact, these tools have been used to carry out the required calculations, and there may be
numerical differences in the results, if you use these environments, keeping the best
numerical precision, rather than using paper and a pocket calculator, possibly introducing
some rounding. Needless to say, the important point of these problems is conceptual, as they
should support the understanding of the underlying financial concepts. Therefore, do not
bother about small inconsistencies (which would be important in real life, where you have to
stick with market conventions in rounding things!).
The manual is work-in-progress, so be sure to check back every now and then, to see
whether a new version has been posted.
This version is dated December 12, 2018.
As usual, for comments, suggestions, and criticisms, my e-mail address is given below.
PAOLO BRANDIMARTE
vii
