Derivatives Algorithms - Volume 1: Bones

346 Pages·2016·2.49 MB·English

by  Thomas Hyer

Derivatives
Algorithms
Volume 1: Bones Second Edition
9686_9789814699518_tp.indd 1 1/9/15 1:59 pm
b1816 MR SIA: FLY PAST b1816_FM
TTTThhhhiiiissss ppppaaaaggggeeee iiiinnnntttteeeennnnttttiiiioooonnnnaaaallllllllyyyy lllleeeefffftttt bbbbllllaaaannnnkkkk
bb11881166__FFMM..iinndddd vvii 1100//1100//22001144 11::1122::3399 PPMM
Derivatives
Algorithms
Volume 1: Bones Second Edition
Tom Hyer
World Scientific
NEW JERSEY • LONDON • SINGAPORE • BEIJING • SHANGHAI • HONG KONG • TAIPEI • CHENNAI • TOKYO
9686_9789814699518_tp.indd 2 1/9/15 1:59 pm
Published by
World Scientific Publishing Co. Pte. Ltd.
5 Toh Tuck Link, Singapore 596224
USA office: 27 Warren Street, Suite 401-402, Hackensack, NJ 07601
UK office: 57 Shelton Street, Covent Garden, London WC2H 9HE
Library of Congress Cataloging-in-Publication Data
Hyer, Tom.
Derivatives algorithm : Volume 1: bones / Tom Hyer, UBS, UK. -- Second Edition.
pages cm
Includes bibliographical references and index.
ISBN 978-9814699518 (hardcover : alk. paper)
1. Derivative securities--Data processing. 2. Algorithms--Data processing. I. Title.
HG6024.A3H94 2015
332.64'57028551--dc23
2015024082
British Library Cataloguing-in-Publication Data
A catalogue record for this book is available from the British Library.
Copyright © 2016 by World Scientific Publishing Co. Pte. Ltd.
All rights reserved. This book, or parts thereof, may not be reproduced in any form or by any means,
electronic or mechanical, including photocopying, recording or any information storage and retrieval
system now known or to be invented, without written permission from the publisher.
For photocopying of material in this volume, please pay a copying fee through the Copyright Clearance
Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, USA. In this case permission to photocopy
is not required from the publisher.
In-house Editors: Rajni Gamage/Karimah
Typeset by Stallion Press
Email: [e-mail]
Printed in Singapore
Karimah - Derivatives Algorithms - Vol 1 - Bones.indd 1 2/9/2015 10:34:33 AM
September1,2015 10:14 DerivativesAlgorithms—Volume1: Bones... -9inx6in b2189-fm pagev
For Kath – first, last, and always
v
b1816 MR SIA: FLY PAST b1816_FM
TTTThhhhiiiissss ppppaaaaggggeeee iiiinnnntttteeeennnnttttiiiioooonnnnaaaallllllllyyyy lllleeeefffftttt bbbbllllaaaannnnkkkk
bb11881166__FFMM..iinndddd vvii 1100//1100//22001144 11::1122::3399 PPMM
September1,2015 10:14 DerivativesAlgorithms—Volume1: Bones... -9inx6in b2189-fm pagevii
Contents
1. Introduction 1
1.1 Note on the Second Edition . . . . . . . . . . . . . . . . . 2
2. Principles 5
2.1 Our Code . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.1.1 auto. . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.1.2 override and final. . . . . . . . . . . . . . . . . 6
2.1.3 Wishful Thinking . . . . . . . . . . . . . . . . . . 7
2.2 Functional Programming . . . . . . . . . . . . . . . . . . . 8
2.3 Type and State . . . . . . . . . . . . . . . . . . . . . . . . 8
2.4 Physical Code Structure . . . . . . . . . . . . . . . . . . . 9
2.4.1 Facts . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.5 Platform . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.6 Some Design Patterns . . . . . . . . . . . . . . . . . . . . 12
2.6.1 Factory Method . . . . . . . . . . . . . . . . . . . 12
2.6.2 Decorator . . . . . . . . . . . . . . . . . . . . . . . 12
2.6.3 Singleton . . . . . . . . . . . . . . . . . . . . . . . 13
2.6.4 Composites . . . . . . . . . . . . . . . . . . . . . . 13
2.7 Optimization . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.7.1 Calibration . . . . . . . . . . . . . . . . . . . . . . 14
2.7.2 map . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.8 Threads . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
3. Types and Interfaces 17
3.1 The User Base . . . . . . . . . . . . . . . . . . . . . . . . 17
3.2 A Public Example . . . . . . . . . . . . . . . . . . . . . . 18
vii
September1,2015 10:14 DerivativesAlgorithms—Volume1: Bones... -9inx6in b2189-fm pageviii
viii DerivativesAlgorithms
3.3 Interface Generation . . . . . . . . . . . . . . . . . . . . . 21
3.4 Interface Types . . . . . . . . . . . . . . . . . . . . . . . . 22
3.4.1 Tables and Cells . . . . . . . . . . . . . . . . . . . 22
3.4.2 Variety . . . . . . . . . . . . . . . . . . . . . . . . 23
3.4.3 Containers . . . . . . . . . . . . . . . . . . . . . . 25
3.5 Machinist . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
3.6 Exception Messaging . . . . . . . . . . . . . . . . . . . . . 29
3.6.1 Macro Hackery . . . . . . . . . . . . . . . . . . . . 32
3.7 Environment . . . . . . . . . . . . . . . . . . . . . . . . . 34
3.7.1 Fast-Path Optimization . . . . . . . . . . . . . . . 37
3.7.2 Repository Access . . . . . . . . . . . . . . . . . . 41
3.8 Enumerated Types . . . . . . . . . . . . . . . . . . . . . . 43
4. Vector and Matrix Computations 47
4.1 Customizing Vectors . . . . . . . . . . . . . . . . . . . . . 47
4.2 Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . 48
4.2.1 Join . . . . . . . . . . . . . . . . . . . . . . . . . . 51
4.3 Matrices and Square Matrices . . . . . . . . . . . . . . . . 52
4.3.1 Internal Layout . . . . . . . . . . . . . . . . . . . 52
4.3.2 Pasting and Formatting . . . . . . . . . . . . . . . 53
4.4 Matrix Multiplication . . . . . . . . . . . . . . . . . . . . 55
4.4.1 Inheritance and Substitutability . . . . . . . . . . 56
4.5 Decompositions (Square) . . . . . . . . . . . . . . . . . . . 57
4.6 Decompositions (Symmetric) . . . . . . . . . . . . . . . . 58
4.7 Decompositions (Sparse) . . . . . . . . . . . . . . . . . . . 60
4.7.1 Tridiagonal Matrices. . . . . . . . . . . . . . . . . 61
4.7.2 Band Diagonal Matrices. . . . . . . . . . . . . . . 62
4.7.3 SLAP Format . . . . . . . . . . . . . . . . . . . . 64
4.7.4 The Symmetric Case . . . . . . . . . . . . . . . . 67
4.8 Decompositions (Other) . . . . . . . . . . . . . . . . . . . 69
5. Persistence and Memory 71
5.1 Storage . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
5.2 Extraction . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
5.2.1 Example: Linear Interpolant . . . . . . . . . . . . 76
5.2.2 Reader Registry . . . . . . . . . . . . . . . . . . . 78
5.3 Code Generation . . . . . . . . . . . . . . . . . . . . . . . 78
5.4 A Display Interface . . . . . . . . . . . . . . . . . . . . . . 80
September1,2015 10:14 DerivativesAlgorithms—Volume1: Bones... -9inx6in b2189-fm pageix
Contents ix
5.4.1 Storage . . . . . . . . . . . . . . . . . . . . . . . . 80
5.4.2 Display Format . . . . . . . . . . . . . . . . . . . 82
5.4.3 Extraction . . . . . . . . . . . . . . . . . . . . . . 83
5.4.4 Refinements . . . . . . . . . . . . . . . . . . . . . 86
5.5 Auditing . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
5.5.1 Bag . . . . . . . . . . . . . . . . . . . . . . . . . . 87
5.5.2 Filling Up . . . . . . . . . . . . . . . . . . . . . . 88
5.5.3 Audit Types . . . . . . . . . . . . . . . . . . . . . 90
5.6 More on Repositories . . . . . . . . . . . . . . . . . . . . . 92
5.6.1 Naming . . . . . . . . . . . . . . . . . . . . . . . . 92
5.6.2 Matching . . . . . . . . . . . . . . . . . . . . . . . 93
5.6.3 Capturing State . . . . . . . . . . . . . . . . . . . 93
5.6.4 Unique Objects . . . . . . . . . . . . . . . . . . . 94
6. Testing Framework 97
6.1 Component Tests . . . . . . . . . . . . . . . . . . . . . . . 97
6.1.1 Physical Structure . . . . . . . . . . . . . . . . . . 99
6.1.2 Reuse . . . . . . . . . . . . . . . . . . . . . . . . . 99
6.2 Regression Tests . . . . . . . . . . . . . . . . . . . . . . . 100
6.2.1 Repository Instrumentation . . . . . . . . . . . . . 100
6.3 No Silver Bullet . . . . . . . . . . . . . . . . . . . . . . . . 101
7. Further Maths 103
7.1 Interpolation . . . . . . . . . . . . . . . . . . . . . . . . . 103
7.1.1 Functions of Time . . . . . . . . . . . . . . . . . . 105
7.2 Special Functions . . . . . . . . . . . . . . . . . . . . . . . 106
7.2.1 The Normal Distribution . . . . . . . . . . . . . . 106
7.3 Root Solvers . . . . . . . . . . . . . . . . . . . . . . . . . . 107
7.4 Underdetermined Search . . . . . . . . . . . . . . . . . . . 111
7.4.1 Function and Jacobian . . . . . . . . . . . . . . . 112
7.4.2 Weights and Smoothing . . . . . . . . . . . . . . . 114
7.4.3 Monitoring Progress . . . . . . . . . . . . . . . . . 115
7.5 Quadrature . . . . . . . . . . . . . . . . . . . . . . . . . . 117
7.5.1 Gaussian Quadrature . . . . . . . . . . . . . . . . 118
7.5.2 Adaptive Quadrature . . . . . . . . . . . . . . . . 120
7.6 Distributions . . . . . . . . . . . . . . . . . . . . . . . . . 120
7.6.1 Implied Vol . . . . . . . . . . . . . . . . . . . . . . 121
7.7 Baskets . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122