MATH48181/68181 ONLINE COURSE MATERIAL

Course Syllabus

Formulas to Remember for the In-Class Test on Friday 17 December 2021

Formulas to Remember for the Final Exam in January 2022

Handwritten Lecture Notes 2014/15 Academic Year

Handwritten Lecture Notes 2015/16 Academic Year

Handwritten Lecture Notes 2016/17 Academic Year

Handwritten Lecture Notes 2017/18 Academic Year

Handwritten Lecture Notes 2018/19 Academic Year

Handwritten Lecture Notes 2019/20 Academic Year

Podcasts for 2015/16 Academic Year

Podcasts for 2016/17 Academic Year

Podcasts for 2017/18 Academic Year

Podcasts for 2018/19 Academic Year

Podcasts for 2019/20 Academic Year

Week 3 Student Feedback 2014/2015 Academic Year

Week 3 Student Feedback 2015/2016 Academic Year

Week 3 Student Feedback 2016/2017 Academic Year

Week 3 Student Feedback 2017/2018 Academic Year

Week 3 Student Feedback 2018/2019 Academic Year

Week 3 Student Feedback 2019/2020 Academic Year

UEQ Results 2014/2015 Academic Year

UEQ Results 2015/2016 Academic Year

UEQ Results 2016/2017 Academic Year

UEQ Results 2017/2018 Academic Year

UEQ Results 2018/2019 Academic Year

UEQ Results 2019/2020 Academic Year

UEQ Results 2020/2021 Academic Year

UEQ Results 2021/2022 Academic Year

Some Financial Disasters

Biggest Financial Frauds

Some Extreme Events

Proof of Extremal Types Theorem

Formulas for VaR and ES

Financial Pareto Ratios

The Formula that Killed Wall Street

Extreme Values - Definition 1

Extreme Values - Definition 2

Extreme Values - Definition 3

VaR Picture 1

VaR Picture 2

VaR Picture 3

VaR Picture 4

VaR Picture 5

VaR Picture 6

VaR Picture 7

A Proof that VaR is Not Sub-Additive

Seven Proofs that ES is Sub-Additive

A Collection of Software for Analyzing Extreme Values

QR Student Survey Apps

PRELIMINARY MATERIAL

Gamma Function

• Video (YouTube Version)

• Handwritten Notes

Beta Function

• Video (YouTube Version)

• Handwritten Notes

A Differentiation Trick

• Video (YouTube Version)

• Handwritten Notes

Product Rules for Differentiation

• Video (YouTube Version)

• Handwritten Notes

L'Hopital's Rule

• Video (YouTube Version)

• Handwritten Notes

Properties of Sum

• Video (YouTube Version)

• Handwritten Notes

Properties of Product

• Video (YouTube Version)

• Handwritten Notes

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WEEK 1 (27 SEPTEMBER 2021 TO 1 OCTOBER 2021) MATERIAL

Welcome

• Video (YouTube Version)

• Handwritten Notes

Motivation

• Video (YouTube Version)

• Handwritten Notes

Three Definitions of Extreme Value

• Video (YouTube Version)

• Handwritten Notes

Distribution of Extreme Value under Definition 1

• Video (YouTube Version)

• Handwritten Notes

Review Session

• Handwritten Notes

• Podcast Video (YouTube Version)

• Zoom Video (YouTube Version)

Tutorial

• Sheet

• Typed Solutions for All Questions

• Handwritten Solutions for All Questions

• Zoom Video of Tutorial Session (YouTube Version)

• Video Solutions for All Questions (YouTube Version)

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WEEK 2 (4 OCTOBER 2021 TO 8 OCTOBER 2021) MATERIAL

Extremal Types Theorem

• Video (YouTube Version)

• Handwritten Notes

Conditions for Extremal Types Theorem

• Video (YouTube Version)

• Handwritten Notes

Alternative Conditions for Extremal Types Theorem

• Video (YouTube Version)

• Handwritten Notes

Formulas for Norming Constants

• Video (YouTube Version)

• Handwritten Notes

An Example Where Extremal Types Theorem Fails

• Video (YouTube Version)

• Handwritten Notes

Review Session

• Handwritten Notes

Tutorial

• Sheet

• Typed Solutions for All Questions

• Handwritten Solutions for All Questions

• Zoom Video of Tutorial Session (YouTube Version)

• Podcast Video of Tutorial Session (YouTube Version)

• Video Solutions for All Questions (YouTube Version)

Quiz

• Problem 1

• Solutions to Problem 1

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WEEK 3 (11 OCTOBER 2021 TO 15 OCTOBER 2021) MATERIAL

Condition to Check Extremal Types Theorem for Discrete Distributions

• Video (YouTube Version)

• Handwritten Notes

Generalized Extreme Value (GEV) Distribution and Properties

• Video (YouTube Version)

• Handwritten Notes

Definition 2, Generalized Pareto (GP) Distribution and Properties

• Video (YouTube Version)

• Handwritten Notes

Definition 3 and Distribution

• Video (YouTube Version)

• Handwritten Notes

Review Session

• Handwritten Notes

• Podcast Video (YouTube Version)

• Zoom Video (YouTube Version)

Tutorial

• Sheet

• Typed Solutions for All Questions

• Handwritten Solutions for All Questions

• Zoom Video of Tutorial Session (YouTube Version)

• Podcast Video of Tutorial Session (YouTube Version)

• Video Solutions for All Questions (YouTube Version)

Quiz

• Problem 2

• Solutions to Problem 2

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WEEK 4 (18 OCTOBER 2021 TO 22 OCTOBER 2021) MATERIAL

Introduction to Portfolio Theory

• Video (YouTube Version)

• Handwritten Notes

Case 1 of Portfolio Theory

• Video (YouTube Version)

• Handwritten Notes

Case 2 of Portfolio Theory

• Video (YouTube Version)

• Handwritten Notes

Case 3 of Portfolio Theory

• Video (YouTube Version)

• Handwritten Notes

Case 4 of Portfolio Theory

• Video (YouTube Version)

• Handwritten Notes

Review Session

• Handwritten Notes

• Podcast Video (YouTube Version)

• Zoom Video (YouTube Version)

Tutorial

• Sheet

• Typed Solutions for All Questions

• Handwritten Solutions for All Questions

• Zoom Video of Tutorial Session (YouTube Version)

• Podcast Video of Tutorial Session (YouTube Version)

• Video Solutions for All Questions (YouTube Version)

Quiz

• Problem 3

• Solutions to Problem 3

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WEEK 5 (25 OCTOBER 2021 TO 29 OCTOBER 2021) MATERIAL

Preliminaries for Cases 5 and 6

• Video (YouTube Version)

• Handwritten Notes

Case 5 of Portfolio Theory

• Video (YouTube Version)

• Handwritten Notes

Case 6 of Portfolio Theory

• Video (YouTube Version)

• Handwritten Notes

Review Session

• Handwritten Notes

• Podcast Video (YouTube Version)

• Zoom Video (YouTube Version)

Tutorial

• Sheet

• Typed Solutions for All Questions

• Handwritten Solutions for All Questions

• Zoom Video of Tutorial Session (YouTube Version)

• Podcast Video of Tutorial Session (YouTube Version)

• Video Solutions for All Questions (YouTube Version)

Quiz

• Problem 4

• Solutions to Problem 4

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WEEK 6 (8 NOVEMBER 2021 TO 12 NOVEMBER 2021) MATERIAL

Introduction to Financial Risk Measures

• Video (YouTube Version)

• Handwritten Notes

Two Most Popular Risk Measures

• Video (YouTube Version)

• Handwritten Notes

Simple Expressions for Value at Risk and Expected Shortfall

• Video (YouTube Version)

• Handwritten Notes

Proofs of Properties for Value at Risk and Expected Shortfall

• Video (YouTube Version)

• Handwritten Notes

Review Session

• Zoom Video (YouTube Version)

• Podcast Video (YouTube Version)

• Handwritten Notes

Tutorial

• Sheet

• Typed Solutions for All Questions

• Handwritten Solutions for All Questions

• Zoom Video of Tutorial Session (YouTube Version)

• Podcast Video of Tutorial Session (YouTube Version)

• Video Solutions for All Questions (YouTube Version)

Quiz

• Problem 5

• Solutions to Problem 5

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WEEK 7 (15 NOVEMBER 2021 TO 19 NOVEMBER 2021) MATERIAL

Parametric Estimation of Value at Risk

• Video (YouTube Version)

• Handwritten Notes

Nonparametric Estimation of Value at Risk

• Video (YouTube Version)

• Handwritten Notes

Semiparametric Estimation of Value at Risk

• Video (YouTube Version)

• Handwritten Notes

Review Session

• Zoom Video (YouTube Version)

• Podcast Video (YouTube Version)

• Handwritten Notes

Tutorial

• Sheet

• Typed Solutions for All Questions

• Handwritten Solutions for All Questions

• Zoom Video of Tutorial Session (YouTube Version)

• Podcast Video of Tutorial Session (YouTube Version)

• Video Solutions for All Questions (YouTube Version)

Quiz

• Problem 6

• Solutions to Problem 6

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WEEK 8 (22 NOVEMBER 2021 TO 26 NOVEMBER 2021) MATERIAL

Parametric Estimation of Expected Shortfall

• Video (YouTube Version)

• Handwritten Notes

Nonparametric Estimation of Expected Shortfall

• Video (YouTube Version)

• Handwritten Notes

Semiparametric Estimation of Expected Shortfall

• Video (YouTube Version)

• Handwritten Notes

Review Session

• Zoom Video (YouTube Version)

• Podcast Video (YouTube Version)

• Handwritten Notes

Tutorial

• Sheet

• Typed Solutions for All Questions

• Handwritten Solutions for All Questions

• Zoom Video of Tutorial Session (YouTube Version)

• Podcast Video of Tutorial Session (YouTube Version)

• Video Solutions for All Questions (YouTube Version)

Quiz

• Problem 7

• Solutions to Problem 7

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WEEK 9 (29 NOVEMBER 2021 TO 3 DECEMBER 2021) MATERIAL

Introduction to Copulas

• Video (YouTube Version)

• Handwritten Notes

Definition of A Copula

• Video (YouTube Version)

• Handwritten Notes

Two Most Popular Models for Copulas

• Video (YouTube Version)

• Handwritten Notes

Review Session

• Zoom Video (YouTube Version)

• Podcast Video (YouTube Version)

• Handwritten Notes

Tutorial

• Sheet

• Typed Solutions for All Questions

• Handwritten Solutions for All Questions

• Zoom Video of Tutorial Session (YouTube Version)

• Podcast Video of Tutorial Session (YouTube Version)

• Video Solutions for All Questions (YouTube Version)

Quiz

• Problem 8

• Solutions to Problem 8

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WEEK 10 (6 DECEMBER 2021 TO 10 DECEMBER 2021) MATERIAL

Introduction to Bivariate Extreme Value Theory

• Video (YouTube Version)

• Handwritten Notes

Definition of A Bivariate Extreme Value and Its Distribution

• Video (YouTube Version)

• Handwritten Notes

Procedure to Find Bivariate Extreme Value Distribution

• Video (YouTube Version)

• Handwritten Notes

Representations for Bivariate Extreme Value Distributions

• Video (YouTube Version)

• Handwritten Notes

Review Session

• Zoom Video (YouTube Version)

• Podcast Video (YouTube Version)

• Handwritten Notes

Tutorial

• Sheet

• Typed Solutions for All Questions

• Handwritten Solutions for All Questions

• Zoom Video of Tutorial Session (YouTube Version)

• Podcast Video of Tutorial Session (YouTube Version)

• Video Solutions for All Questions (YouTube Version)

Quiz

• Problem 9

• Solutions to Problem 9

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WEEK 11 (13 DECEMBER 2021 TO 17 DECEMBER 2021) MATERIAL

Revision

• Zoom Video (YouTube Version)

• Podcast Video (YouTube Version)

• Handwritten Notes

Tutorial

• Sheet

• Typed Solutions for All Questions

• Handwritten Solutions for All Questions

• Video of Tutorial Session

• Video Solutions for All Questions (YouTube Version)

Quiz

• Problem 10

• Solutions to Problem 10

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SUPPLEMENTARY NOTES

• Chapter 1

• Chapter 2

• Chapter 3

• Chapter 4

• Chapter 5

• Chapter 6

• Chapter 7

• Chapter 8

• Chapter 9

• Chapter 10

QUIZZES AND SOLUTIONS FOR 2018/2019 ACADEMIC YEAR

• Problem 1 due 12:00noon Tuesday 9 October 2018

• Solutions to Problem 1

• Problem 2 due 12:00noon Tuesday 23 October 2018

• Solutions to Problem 2

• Problem 3 due 12:00noon Tuesday 6 November 2018

• Solutions to Problem 3

• Problem 4 due 12:00noon Tuesday 20 November 2018

• Solutions to Problem 4

• Problem 5 due 12:00noon Tuesday 4 December 2018

• Solutions to Problem 5

QUIZZES AND SOLUTIONS FOR 2019/2020 ACADEMIC YEAR

• Problem 1 due 12:00noon Tuesday 8 October 2019

• Solutions to Problem 1

• Problem 2 due 12:00noon Tuesday 22 October 2019

• Solutions to Problem 2

• Problem 3 due 12:00noon Tuesday 5 November 2019

• Solutions to Problem 3

• Problem 4 due 12:00noon Tuesday 19 November 2019

• Solutions to Problem 4

• Problem 5 due 12:00noon Tuesday 3 December 2019

• Solutions to Problem 5

QUIZZES AND SOLUTIONS FOR 2020/2021 ACADEMIC YEAR

• Problem 1 due 12:00noon Tuesday 10 November 2020

• Solutions to Problem 1

• Problem 2 due 12:00noon Tuesday 17 November 2020

• Solutions to Problem 2

• Problem 3 due 12:00noon Tuesday 24 November 2020

• Solutions to Problem 3

• Problem 4 due 12:00noon Tuesday 1 December 2020

• Solutions to Problem 4

• Problem 5 due 12:00noon Tuesday 8 December 2020

• Solutions to Problem 5

• Problem 6 due 12:00noon Tuesday 15 December 2020

• Solutions to Problem 6

• Problem 7 due 12:00noon Tuesday 22 December 2020

• Solutions to Problem 7

• Problem 8 due 12:00noon Tuesday 5 January 2021

• Solutions to Problem 8

• Problem 9 due 12:00noon Tuesday 12 January 2021

• Solutions to Problem 9

• Problem 10 due 12:00noon Tuesday 19 January 2021

• Solutions to Problem 10

IN-CLASS TESTS AND SOLUTIONS

• 2014/15 Test for Math4/68181

• Solutions to the 2014/15 Test

• 2015/16 Test for Math4/68181

• Solutions to the 2015/16 Test

• 2016/17 Test for Math4/68181

• Solutions to the 2016/17 Test

• 2017/18 Test for Math4/68181

• Solutions to the 2017/18 Test

• 2018/19 Test for Math4/68181

• Solutions to the 2018/19 Test

• 2019/20 Test for Math4/68181

• Solutions to the 2019/20 Test

• 2020/21 Test for Math4/68181

• Solutions to the 2021/21 Test

• 2021/22 Test for Math4/68181

• Solutions to the 2021/22 Test

EXAM PAPERS AND SOLUTIONS

• 2012/13 Exam for Math4/68181

• Solutions

• 2013/14 Exam for Math4/68181

• Solutions

• 2014/15 Exam for Math4/68181

• 2015/16 Exam for Math4/68181

• Solutions

• 2016/17 Exam for Math4/68181

• Solutions

• 2017/18 Exam for Math4/68181

• Solutions

• 2018/19 Exam for Math4/68181

• Solutions

• 2019/20 Exam for Math4/68181

• Solutions

• 2020/21 Exam for Math4/68181

• Solutions

• 2021/22 Exam for Math4/68181

• Solutions

FREE BOOKS ON EXTREME VALUES

• Modelling Extremal Events: For Insurance and Finance

• Extremes and Related Properties of Random Sequences and Processes

• Extreme values, Regular Variation and Point Processes

• An Introduction to Statistical Modelling of Extreme Values

• Extreme Value Distributions: Theory and Applications

SOME RESEARCH PAPERS IN FINANCIAL STATISTICS

• Paper 1

• Paper 2

• Paper 3

• Paper 4