ERM (Part 1) Measurement and Modeling of Depedencies in Economic Capital. PAK Study Manual
|
|
- Maximilian Stewart
- 5 years ago
- Views:
Transcription
1 ERM (Part 1) Measurement and Modeling of Depedencies in Economic Capital
2 Related Learning Objectives 2b) Evaluate how risks are correlated, and give examples of risks that are positively correlated and risks that are negatively correlated 2c) Analyze and evaluate risk aggregation techniques, including use of correlation, integrated risk distributions and copulas 2f) Analyze the importance of tails of distributions, tail correlations, and low frequency / high severity events 2h) Construct approaches to managing various risks and evaluate how an entity makes decisions about techniques to model, measure and aggregate risks including but not limited to stochastic processes 5b) Define the basic elements and explain the uses of economic capital 5c) Explain the challenges and limits of economic capital calculations and explain how economic capital may differ from external requirements of rating agencies and regulators Key Points of This Reading 1) Understand different correlations (e.g. Pearson correlation, Spearman correlation, and Kendall Tau correlation) 2) Understand different risk aggregation methodologies (e.g. Variance- Covariance matrix, Copulas, and Causal modeling)
3 Economic Capital Prob. Expected Reserve VaR(95%) Economic Capital Mean 95 th Percentile It is the amount of capital needed to cover losses at a certain risk tolerance level (e.g. VaR(95%))
4 Risk Aggregation EC (Individual Risks) EC (Total Company) Prob. Expected Reserve VaR(95%) Economic Capital Prob. Expected Reserve Mean VaR(95%) Economic Capital 95 th Percentile Aggregation Method Prob. Expected Reserve VaR(95%) Economic Capital Mean 95 th Percentile Mean 95 th Percentile Prob. Expected Reserve VaR(95%) Economic Capital Mean 95 th Percentile
5 Solvency II Three Pillars Approach 1. Quantitative requirements 2. Qualitative requirements 3. Supervisory reporting and disclosure 1. Solvency Capital Requirement (SCR) 2. Minimum Capital Requirement (MCR) 1. European Standard Formula 2. Internal Model
6 Dependency vs. Correlation Dependency There is some link between two random variables, but it does NOT need to follow a linear pattern Correlation There is some link between two random variables, but it does follow a linear pattern Y Y X X
7 Deficiencies of Using Correlation 1. Correlation is a scalar measure of dependency 2. Possible values of correlation depend on the marginal distribution of the risks 3. Perfectly positively (negatively) dependent risks do not necessarily have a correlation of 1 (-1) 4. A correlation of zero does not imply independence between risks 5. Correlation is not invariant under monotonic transformations 6. Correlation is only defined when the variances of the risks are finite
8 Three Measures of Correlation Pearson's Rho Spearman's Rho Kendall's Tau ρ ( XY, ) = Cov[ X, Y ] Var( X ) Var( Y ) ρ ( XY, ) = rank Cov[ r( X ), r( Y )] Var( r( X )) Var( r( Y )) τ = S 0.5 nn ( 1) Value Correlation Rank Correlation Rank Correlation It is calculated directly from two data series Changing the value of an individual observation will change the value of Pearson s rho Pearson s rho is attractive as it is widely used and easy to calculate It is calculated from the position (rank) of the variables Changing the value of an individual observation (but not the position of the observation) will not change a rank correlation coefficient Because rank correlation coefficients to not depend on the underlying shape of data series, only the relative position of observations, their results are always valid However, it is only a valid measure of association when the data series on which it is being calculated are jointly elliptical However, whereas Pearson s rho can be used directly in some common multivariate distributions such as the normal and t, the rank correlation coefficients are more usually combined with copulas
9 Pearson s Rho X and Y are values RN X Y X 2 Y 2 XY (X-x) 2 (Y-y) 2 (X-x)(Y-y) Sum Cov[ X, Y ] 600 ρ ( XY, ) = = = 0.56 Var( X ) Var( Y ) (4600)(250) r XY n XY i i Xi Yi 5(4600) (200)(100) 2 2 5(12600) ( ) ( ) ( 200) 5(2250) ( 100 ) i i i i = = = n X X n Y Y
10 Ranks RN X Y Rank(X) Rank(Y) Sum Ascending Order
11 Spearman s Rho X and Y are ranks RN X Y X 2 Y 2 XY (X-x) 2 (Y-y) 2 (X-x)(Y-y) (X-Y) Sum ρ ( XY, ) = Cov[ X, Y ] 6 = = 0.60 Var( X ) Var( Y ) (10)(10) s r T 2 ( X 1 t Y ) t= t 8 XY, 2 2 = 1 6 = 1 6 = 0.6 TT ( 1) 5 (5 1)
12 Kendall's Tau Concordant Pair Discordant Pair (X 2,Y 2 ) (X 1,Y 1 ) (X 1,Y 1 ) (X 2,Y 2 ) (X 2 X 1 ) and (Y 2 Y 1 ) Same Sign (X 2 X 1 ) and (Y 2 Y 1 ) Opposite Sign Kendall's Tau = τ = C D 1 nn ( 1) 2
13 Kendall's Tau RN X Y C (+,+) D(+,-) C (-,-) D(+,-) C (-,-) C (+,+) C (+,+) D(-,+) C (+,+) C (+,+) (X 2 X 1 ) = 5 1 = +4 (Y 2 Y 1 ) = 4 3 = +1 C(+,+) (X 3 X 1 ) = 2 1 = +1 (Y 3 Y 1 ) = 1 3 = -2 D(+,-) Kendall's Tau = C D 7 3 τ = = = 0.5 nn ( 1) 0.5 (5 (5 1)) C D 7 3 τ = = = 0.4 C + D
Measuring Risk Dependencies in the Solvency II-Framework. Robert Danilo Molinari Tristan Nguyen WHL Graduate School of Business and Economics
Measuring Risk Dependencies in the Solvency II-Framework Robert Danilo Molinari Tristan Nguyen WHL Graduate School of Business and Economics 1 Overview 1. Introduction 2. Dependency ratios 3. Copulas 4.
More informationCorrelation and Diversification in Integrated Risk Models
Correlation and Diversification in Integrated Risk Models Alexander J. McNeil Department of Actuarial Mathematics and Statistics Heriot-Watt University, Edinburgh A.J.McNeil@hw.ac.uk www.ma.hw.ac.uk/ mcneil
More informationMaster s in Financial Engineering Foundations of Buy-Side Finance: Quantitative Risk and Portfolio Management. > Teaching > Courses
Master s in Financial Engineering Foundations of Buy-Side Finance: Quantitative Risk and Portfolio Management www.symmys.com > Teaching > Courses Spring 2008, Monday 7:10 pm 9:30 pm, Room 303 Attilio Meucci
More informationINTERNATIONAL JOURNAL FOR INNOVATIVE RESEARCH IN MULTIDISCIPLINARY FIELD ISSN Volume - 3, Issue - 2, Feb
Copula Approach: Correlation Between Bond Market and Stock Market, Between Developed and Emerging Economies Shalini Agnihotri LaL Bahadur Shastri Institute of Management, Delhi, India. Email - agnihotri123shalini@gmail.com
More informationEconomic Capital. Implementing an Internal Model for. Economic Capital ACTUARIAL SERVICES
Economic Capital Implementing an Internal Model for Economic Capital ACTUARIAL SERVICES ABOUT THIS DOCUMENT THIS IS A WHITE PAPER This document belongs to the white paper series authored by Numerica. It
More informationOperational Risk Modeling
Operational Risk Modeling RMA Training (part 2) March 213 Presented by Nikolay Hovhannisyan Nikolay_hovhannisyan@mckinsey.com OH - 1 About the Speaker Senior Expert McKinsey & Co Implemented Operational
More informationPage 2 Vol. 10 Issue 7 (Ver 1.0) August 2010
Page 2 Vol. 1 Issue 7 (Ver 1.) August 21 GJMBR Classification FOR:1525,1523,2243 JEL:E58,E51,E44,G1,G24,G21 P a g e 4 Vol. 1 Issue 7 (Ver 1.) August 21 variables rather than financial marginal variables
More informationP2.T8. Risk Management & Investment Management. Jorion, Value at Risk: The New Benchmark for Managing Financial Risk, 3rd Edition.
P2.T8. Risk Management & Investment Management Jorion, Value at Risk: The New Benchmark for Managing Financial Risk, 3rd Edition. Bionic Turtle FRM Study Notes By David Harper, CFA FRM CIPM and Deepa Raju
More informationKey Words: emerging markets, copulas, tail dependence, Value-at-Risk JEL Classification: C51, C52, C14, G17
RISK MANAGEMENT WITH TAIL COPULAS FOR EMERGING MARKET PORTFOLIOS Svetlana Borovkova Vrije Universiteit Amsterdam Faculty of Economics and Business Administration De Boelelaan 1105, 1081 HV Amsterdam, The
More informationAn Introduction to Copulas with Applications
An Introduction to Copulas with Applications Svenska Aktuarieföreningen Stockholm 4-3- Boualem Djehiche, KTH & Skandia Liv Henrik Hult, University of Copenhagen I Introduction II Introduction to copulas
More informationContents Part I Descriptive Statistics 1 Introduction and Framework Population, Sample, and Observations Variables Quali
Part I Descriptive Statistics 1 Introduction and Framework... 3 1.1 Population, Sample, and Observations... 3 1.2 Variables.... 4 1.2.1 Qualitative and Quantitative Variables.... 5 1.2.2 Discrete and Continuous
More informationSome developments about a new nonparametric test based on Gini s mean difference
Some developments about a new nonparametric test based on Gini s mean difference Claudio Giovanni Borroni and Manuela Cazzaro Dipartimento di Metodi Quantitativi per le Scienze Economiche ed Aziendali
More informationRisk aggregation in Solvency II : How to converge the approaches of the internal models and those of the standard formula?
Risk aggregation in Solvency II : How to converge the approaches of the internal models and those of the standard formula? - Laurent DEVINEAU (Université Lyon 1, Laboratoire SAF, Milliman Paris) - Stéphane
More informationModelling Dependence between the Equity and. Foreign Exchange Markets Using Copulas
Applied Mathematical Sciences, Vol. 8, 2014, no. 117, 5813-5822 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/ams.2014.47560 Modelling Dependence between the Equity and Foreign Exchange Markets
More informationCONCORDANCE MEASURES AND SECOND ORDER STOCHASTIC DOMINANCE PORTFOLIO EFFICIENCY ANALYSIS
CONCORDANCE MEASURES AND SECOND ORDER STOCHASTIC DOMINANCE PORTFOLIO EFFICIENCY ANALYSIS Milo Kopa, Tomá Tich Introduction The portfolio selection problem is one of the most important issues of financial
More informationRandom Variables and Probability Distributions
Chapter 3 Random Variables and Probability Distributions Chapter Three Random Variables and Probability Distributions 3. Introduction An event is defined as the possible outcome of an experiment. In engineering
More informationFrom Solvency I to Solvency II: a new era for capital requirements in insurance?
Milan, 26 November 2015 From Solvency I to Solvency II: a new era for capital requirements in insurance? prof. Nino Savelli Full professor of Risk Theory Faculty of Banking, Financial and Insurance Sciences
More informationDynamic Copula Methods in Finance
Dynamic Copula Methods in Finance Umberto Cherubini Fabio Gofobi Sabriea Mulinacci Silvia Romageoli A John Wiley & Sons, Ltd., Publication Contents Preface ix 1 Correlation Risk in Finance 1 1.1 Correlation
More informationLecture 4 of 4-part series. Spring School on Risk Management, Insurance and Finance European University at St. Petersburg, Russia.
Principles and Lecture 4 of 4-part series Spring School on Risk, Insurance and Finance European University at St. Petersburg, Russia 2-4 April 2012 University of Connecticut, USA page 1 Outline 1 2 3 4
More informationFinancial Risk Management
Financial Risk Management Professor: Thierry Roncalli Evry University Assistant: Enareta Kurtbegu Evry University Tutorial exercices #4 1 Correlation and copulas 1. The bivariate Gaussian copula is given
More information2.4 STATISTICAL FOUNDATIONS
2.4 STATISTICAL FOUNDATIONS Characteristics of Return Distributions Moments of Return Distribution Correlation Standard Deviation & Variance Test for Normality of Distributions Time Series Return Volatility
More informationTable of Contents. New to the Second Edition... Chapter 1: Introduction : Social Research...
iii Table of Contents Preface... xiii Purpose... xiii Outline of Chapters... xiv New to the Second Edition... xvii Acknowledgements... xviii Chapter 1: Introduction... 1 1.1: Social Research... 1 Introduction...
More informationToday's Agenda Hour 1 Correlation vs association, Pearson s R, non-linearity, Spearman rank correlation,
Today's Agenda Hour 1 Correlation vs association, Pearson s R, non-linearity, Spearman rank correlation, Hour 2 Hypothesis testing for correlation (Pearson) Correlation and regression. Correlation vs association
More informationGGraph. Males Only. Premium. Experience. GGraph. Gender. 1 0: R 2 Linear = : R 2 Linear = Page 1
GGraph 9 Gender : R Linear =.43 : R Linear =.769 8 7 6 5 4 3 5 5 Males Only GGraph Page R Linear =.43 R Loess 9 8 7 6 5 4 5 5 Explore Case Processing Summary Cases Valid Missing Total N Percent N Percent
More informationSOLUTIONS 913,
Illinois State University, Mathematics 483, Fall 2014 Test No. 3, Tuesday, December 2, 2014 SOLUTIONS 1. Spring 2013 Casualty Actuarial Society Course 9 Examination, Problem No. 7 Given the following information
More informationMarket Risk Analysis Volume II. Practical Financial Econometrics
Market Risk Analysis Volume II Practical Financial Econometrics Carol Alexander John Wiley & Sons, Ltd List of Figures List of Tables List of Examples Foreword Preface to Volume II xiii xvii xx xxii xxvi
More informationRisk Measurement and Management of Operational Risk in Insurance Companies under Solvency II
Risk Measurement and Management of Operational Risk in Insurance Companies under Solvency II AFIR/ERM Colloquium 2012, Mexico City October 2 nd, 2012 Nadine Gatzert and Andreas Kolb Friedrich-Alexander-University
More informationLecture 1 of 4-part series. Spring School on Risk Management, Insurance and Finance European University at St. Petersburg, Russia.
Principles and Lecture 1 of 4-part series Spring School on Risk, Insurance and Finance European University at St. Petersburg, Russia 2-4 April 2012 s University of Connecticut, USA page 1 s Outline 1 2
More informationContents. An Overview of Statistical Applications CHAPTER 1. Contents (ix) Preface... (vii)
Contents (ix) Contents Preface... (vii) CHAPTER 1 An Overview of Statistical Applications 1.1 Introduction... 1 1. Probability Functions and Statistics... 1..1 Discrete versus Continuous Functions... 1..
More informationWeek 1 Quantitative Analysis of Financial Markets Basic Statistics A
Week 1 Quantitative Analysis of Financial Markets Basic Statistics A Christopher Ting http://www.mysmu.edu/faculty/christophert/ Christopher Ting : christopherting@smu.edu.sg : 6828 0364 : LKCSB 5036 October
More informationTail Risk, Systemic Risk and Copulas
Tail Risk, Systemic Risk and Copulas 2010 CAS Annual Meeting Andy Staudt 09 November 2010 2010 Towers Watson. All rights reserved. Outline Introduction Motivation flawed assumptions, not flawed models
More informationSubject: Psychopathy
Research Skills Problem Sheet 3 : Graham Hole, March 009: Page 1: Research Skills: Statistics Problem Sheet 3: (Correlation and Regression): 1. The following numbers represent data from 1 individuals.
More informationDepartment of Econometrics and Business Statistics
ISSN 1440-771X Australia Department of Econometrics and Business Statistics http://www.buseco.monash.edu.au/depts/ebs/pubs/wpapers/ Assessing Dependence Changes in the Asian Financial Market Returns Using
More informationE-322 Muhammad Rahman CHAPTER-3
CHAPTER-3 A. OBJECTIVE In this chapter, we will learn the following: 1. We will introduce some new set of macroeconomic definitions which will help us to develop our macroeconomic language 2. We will develop
More informationFV N = PV (1+ r) N. FV N = PVe rs * N 2011 ELAN GUIDES 3. The Future Value of a Single Cash Flow. The Present Value of a Single Cash Flow
QUANTITATIVE METHODS The Future Value of a Single Cash Flow FV N = PV (1+ r) N The Present Value of a Single Cash Flow PV = FV (1+ r) N PV Annuity Due = PVOrdinary Annuity (1 + r) FV Annuity Due = FVOrdinary
More informationLecture notes on risk management, public policy, and the financial system. Credit portfolios. Allan M. Malz. Columbia University
Lecture notes on risk management, public policy, and the financial system Allan M. Malz Columbia University 2018 Allan M. Malz Last updated: June 8, 2018 2 / 23 Outline Overview of credit portfolio risk
More informationMarket Risk: FROM VALUE AT RISK TO STRESS TESTING. Agenda. Agenda (Cont.) Traditional Measures of Market Risk
Market Risk: FROM VALUE AT RISK TO STRESS TESTING Agenda The Notional Amount Approach Price Sensitivity Measure for Derivatives Weakness of the Greek Measure Define Value at Risk 1 Day to VaR to 10 Day
More informationAdvanced Tools for Risk Management and Asset Pricing
MSc. Finance/CLEFIN 2014/2015 Edition Advanced Tools for Risk Management and Asset Pricing June 2015 Exam for Non-Attending Students Solutions Time Allowed: 120 minutes Family Name (Surname) First Name
More informationMean-Variance Portfolio Theory
Mean-Variance Portfolio Theory Lakehead University Winter 2005 Outline Measures of Location Risk of a Single Asset Risk and Return of Financial Securities Risk of a Portfolio The Capital Asset Pricing
More informationSubject ST9 Enterprise Risk Management Syllabus
Subject ST9 Enterprise Risk Management Syllabus for the 2018 exams 1 June 2017 Aim The aim of the Enterprise Risk Management (ERM) Specialist Technical subject is to instil in successful candidates the
More informationPORTFOLIO MODELLING USING THE THEORY OF COPULA IN LATVIAN AND AMERICAN EQUITY MARKET
PORTFOLIO MODELLING USING THE THEORY OF COPULA IN LATVIAN AND AMERICAN EQUITY MARKET Vladimirs Jansons Konstantins Kozlovskis Natala Lace Faculty of Engineering Economics Riga Technical University Kalku
More information2. Copula Methods Background
1. Introduction Stock futures markets provide a channel for stock holders potentially transfer risks. Effectiveness of such a hedging strategy relies heavily on the accuracy of hedge ratio estimation.
More informationThe University of Chicago, Booth School of Business Business 41202, Spring Quarter 2011, Mr. Ruey S. Tsay. Solutions to Final Exam.
The University of Chicago, Booth School of Business Business 41202, Spring Quarter 2011, Mr. Ruey S. Tsay Solutions to Final Exam Problem A: (32 pts) Answer briefly the following questions. 1. Suppose
More informationECONOMIC CAPITAL MODELING CARe Seminar JUNE 2016
ECONOMIC CAPITAL MODELING CARe Seminar JUNE 2016 Boston Catherine Eska The Hanover Insurance Group Paul Silberbush Guy Carpenter & Co. Ronald Wilkins - PartnerRe Economic Capital Modeling Safe Harbor Notice
More informationHomework. Due Monday 11/2/2009 at beginning of class Chapter 6: 2 Additional Homework: Download data for
Data Code Go to http://stonybrook.datacodeinc.com User: SUNYSB Password: STONYBROOK11794 Download software for WorldwatchInsight and Marketlink and corresponding manuals Login using your personal login
More informationB. Maddah INDE 504 Discrete-Event Simulation. Output Analysis (3)
B. Maddah INDE 504 Discrete-Event Simulation Output Analysis (3) Variance Reduction Variance reduction techniques (VRT) are methods to reduce the variance (i.e. increase precision) of simulation output
More informationIEOR E4602: Quantitative Risk Management
IEOR E4602: Quantitative Risk Management Risk Measures Martin Haugh Department of Industrial Engineering and Operations Research Columbia University Email: martin.b.haugh@gmail.com Reference: Chapter 8
More informationSolvency II Insights for North American Insurers. CAS Centennial Meeting Damon Paisley Bill VonSeggern November 10, 2014
Solvency II Insights for North American Insurers CAS Centennial Meeting Damon Paisley Bill VonSeggern November 10, 2014 Agenda 1 Introduction to Solvency II 2 Pillar I 3 Pillar II and Governance 4 North
More informationValue at Risk Ch.12. PAK Study Manual
Value at Risk Ch.12 Related Learning Objectives 3a) Apply and construct risk metrics to quantify major types of risk exposure such as market risk, credit risk, liquidity risk, regulatory risk etc., and
More informationSubject SP9 Enterprise Risk Management Specialist Principles Syllabus
Subject SP9 Enterprise Risk Management Specialist Principles Syllabus for the 2019 exams 1 June 2018 Enterprise Risk Management Specialist Principles Aim The aim of the Enterprise Risk Management (ERM)
More informationCopulas? What copulas? R. Chicheportiche & J.P. Bouchaud, CFM
Copulas? What copulas? R. Chicheportiche & J.P. Bouchaud, CFM Multivariate linear correlations Standard tool in risk management/portfolio optimisation: the covariance matrix R ij = r i r j Find the portfolio
More informationLecture 3: Factor models in modern portfolio choice
Lecture 3: Factor models in modern portfolio choice Prof. Massimo Guidolin Portfolio Management Spring 2016 Overview The inputs of portfolio problems Using the single index model Multi-index models Portfolio
More informationAN ABSTRACT OF THE THESIS OF
AN ABSTRACT OF THE THESIS OF Maryam Agahi for the degree of Master of Science in Industrial Engineering presented on August 9, 2013 Title: Rank and Linear Correlation Differences in Simulation and other
More informationSubject CS1 Actuarial Statistics 1 Core Principles. Syllabus. for the 2019 exams. 1 June 2018
` Subject CS1 Actuarial Statistics 1 Core Principles Syllabus for the 2019 exams 1 June 2018 Copyright in this Core Reading is the property of the Institute and Faculty of Actuaries who are the sole distributors.
More informationA New Test for Correlation on Bivariate Nonnormal Distributions
Journal of Modern Applied Statistical Methods Volume 5 Issue Article 8 --06 A New Test for Correlation on Bivariate Nonnormal Distributions Ping Wang Great Basin College, ping.wang@gbcnv.edu Ping Sa University
More informationGrowth-indexed bonds and Debt distribution: Theoretical benefits and Practical limits
Growth-indexed bonds and Debt distribution: Theoretical benefits and Practical limits Julien Acalin Johns Hopkins University January 17, 2018 European Commission Brussels 1 / 16 I. Introduction Introduction
More informationLife under Solvency II Be prepared!
Life under Solvency II Be prepared! Moderator: Hugh Rosenbaum, Towers Watson Speakers: Tomas Wittbjer, Global Head of Insurance, IKANO SA Lorraine Stack, Marsh Management Services Dublin Session Overview
More information34.S-[F] SU-02 June All Syllabus Science Faculty B.Sc. I Yr. Stat. [Opt.] [Sem.I & II] - 1 -
[Sem.I & II] - 1 - [Sem.I & II] - 2 - [Sem.I & II] - 3 - Syllabus of B.Sc. First Year Statistics [Optional ] Sem. I & II effect for the academic year 2014 2015 [Sem.I & II] - 4 - SYLLABUS OF F.Y.B.Sc.
More informationDependence Modeling and Credit Risk
Dependence Modeling and Credit Risk Paola Mosconi Banca IMI Bocconi University, 20/04/2015 Paola Mosconi Lecture 6 1 / 53 Disclaimer The opinion expressed here are solely those of the author and do not
More informationImplied Systemic Risk Index (work in progress, still at an early stage)
Implied Systemic Risk Index (work in progress, still at an early stage) Carole Bernard, joint work with O. Bondarenko and S. Vanduffel IPAM, March 23-27, 2015: Workshop I: Systemic risk and financial networks
More informationRisk aggregation in Solvency II: How to converge the approaches of the internal models and those of the standard formula?
Risk aggregation in Solvency II: How to converge the approaches of the internal models and those of the standard formula? Laurent Devineau, Stéphane Loisel To cite this version: Laurent Devineau, Stéphane
More informationBasics of Probability
Basics of Probability By A.V. Vedpuriswar October 2, 2016 2, 2016 Random variables and events A random variable is an uncertain quantity. A outcome is an observed value of a random variable. An event is
More informationBloomberg. Portfolio Value-at-Risk. Sridhar Gollamudi & Bryan Weber. September 22, Version 1.0
Portfolio Value-at-Risk Sridhar Gollamudi & Bryan Weber September 22, 2011 Version 1.0 Table of Contents 1 Portfolio Value-at-Risk 2 2 Fundamental Factor Models 3 3 Valuation methodology 5 3.1 Linear factor
More informationPAK Study Manual Enterprise Risk Management (ERM) Exam Spring 2015 Edition
Enterprise Risk Management (ERM) Exam Spring 2015 Edition CTE VaR Solvency II Reinsurance Risk Aggregation Coherence Risk Measure Tail Dependency Strategic Risk Management Operational Risk Principles-Based
More informationLoss Simulation Model Testing and Enhancement
Loss Simulation Model Testing and Enhancement Casualty Loss Reserve Seminar By Kailan Shang Sept. 2011 Agenda Research Overview Model Testing Real Data Model Enhancement Further Development Enterprise
More information32.S [F] SU 02 June All Syllabus Science Faculty B.A. I Yr. Stat. [Opt.] [Sem.I & II] 1
32.S [F] SU 02 June 2014 2015 All Syllabus Science Faculty B.A. I Yr. Stat. [Opt.] [Sem.I & II] 1 32.S [F] SU 02 June 2014 2015 All Syllabus Science Faculty B.A. I Yr. Stat. [Opt.] [Sem.I & II] 2 32.S
More informationThe Experts In Actuarial Career Advancement. Product Preview. For More Information: or call 1(800)
P U B L I C A T I O N S The Experts In Actuarial Career Advancement Product Preview For More Information: email Support@ActexMadRiver.com or call 1(800) 282-2839 PL-1 Eric Brosius Loss Development Using
More informationPractical methods of modelling operational risk
Practical methods of modelling operational risk Andries Groenewald The final frontier for actuaries? Agenda 1. Why model operational risk? 2. Data. 3. Methods available for modelling operational risk.
More informationThe mean-variance portfolio choice framework and its generalizations
The mean-variance portfolio choice framework and its generalizations Prof. Massimo Guidolin 20135 Theory of Finance, Part I (Sept. October) Fall 2014 Outline and objectives The backward, three-step solution
More informationAre Market Neutral Hedge Funds Really Market Neutral?
Are Market Neutral Hedge Funds Really Market Neutral? Andrew Patton London School of Economics June 2005 1 Background The hedge fund industry has grown from about $50 billion in 1990 to $1 trillion in
More informationABSTRACT. RAMSEY, AUSTIN FORD. Empirical Studies in Policy, Prices, and Risk. (Under the direction of Barry Goodwin and Sujit Ghosh.
ABSTRACT RAMSEY, AUSTIN FORD. Empirical Studies in Policy, Prices, and Risk. (Under the direction of Barry Goodwin and Sujit Ghosh.) This dissertation is composed of essays that explore aspects of agricultural
More informationBROWNIAN MOTION Antonella Basso, Martina Nardon
BROWNIAN MOTION Antonella Basso, Martina Nardon basso@unive.it, mnardon@unive.it Department of Applied Mathematics University Ca Foscari Venice Brownian motion p. 1 Brownian motion Brownian motion plays
More informationAdvanced Quantitative Methods for Asset Pricing and Structuring
MSc. Finance/CLEFIN 2017/2018 Edition Advanced Quantitative Methods for Asset Pricing and Structuring May 2017 Exam for Non Attending Students Time Allowed: 95 minutes Family Name (Surname) First Name
More informationAli Burak Kurtulan Correlations in Economic Capital Models for Pension Fund Pooling
Ali Burak Kurtulan Correlations in Economic Capital Models for Pension Fund Pooling MSc Thesis 2009 Master Thesis Quantitative Finance and Actuarial Sciences Correlations in Economic Capital Models for
More informationby Aurélie Reacfin s.a. March 2016
Non-Life Deferred Taxes ORSA: under Solvency The II forward-looking challenge by Aurélie Miller* @ Reacfin s.a. March 2016 The Own Risk and Solvency Assessment (ORSA) is one of the most talked about requirements
More informationOpen Access Asymmetric Dependence Analysis of International Crude Oil Spot and Futures Based on the Time Varying Copula-GARCH
Send Orders for Reprints to reprints@benthamscience.ae The Open Petroleum Engineering Journal, 2015, 8, 463-467 463 Open Access Asymmetric Dependence Analysis of International Crude Oil Spot and Futures
More informationAspects on calculating the Solvency Capital Requirement with the use of internal models. Berglund Raoul, Koskinen Lasse, and Ronkainen Vesa
Aspects on calculating the Solvency Capital Requirement with the use of internal models Berglund Raoul, Koskinen Lasse, and Ronkainen Vesa Insurance Supervisory Authority of Finland 1 Mikonkatu 8, P.O.Box
More informationCHAPTER 2 Describing Data: Numerical
CHAPTER Multiple-Choice Questions 1. A scatter plot can illustrate all of the following except: A) the median of each of the two variables B) the range of each of the two variables C) an indication of
More informationRisk and Return and Portfolio Theory
Risk and Return and Portfolio Theory Intro: Last week we learned how to calculate cash flows, now we want to learn how to discount these cash flows. This will take the next several weeks. We know discount
More informationSOCIETY OF ACTUARIES QFI Investment Risk Management Exam Exam QFIIRM
SOCIETY OF ACTUARIES Exam QFIIRM Date: Friday, April 27, 2018 Time: 2:00 p.m. 4:15 p.m. INSTRUCTIONS TO CANDIDATES General Instructions 1. This examination has a total of 40 points. This exam consists
More informationStatistics for Managers Using Microsoft Excel 7 th Edition
Statistics for Managers Using Microsoft Excel 7 th Edition Chapter 5 Discrete Probability Distributions Statistics for Managers Using Microsoft Excel 7e Copyright 014 Pearson Education, Inc. Chap 5-1 Learning
More informationFinancial Risk Measurement/Management
550.446 Financial Risk Measurement/Management Week of September 23, 2013 Interest Rate Risk & Value at Risk (VaR) 3.1 Where we are Last week: Introduction continued; Insurance company and Investment company
More informationPricing multi-asset financial products with tail dependence using copulas
Pricing multi-asset financial products with tail dependence using copulas Master s Thesis J.P. de Kort Delft University of Technology Delft Institute for Applied Mathematics and ABN AMRO Bank N.V. Product
More informationBusiness Statistics: A First Course
Business Statistics: A First Course Fifth Edition Chapter 12 Correlation and Simple Linear Regression Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc. Chap 12-1 Learning Objectives In this
More informationThe University of Chicago, Booth School of Business Business 41202, Spring Quarter 2017, Mr. Ruey S. Tsay. Solutions to Final Exam
The University of Chicago, Booth School of Business Business 41202, Spring Quarter 2017, Mr. Ruey S. Tsay Solutions to Final Exam Problem A: (40 points) Answer briefly the following questions. 1. Describe
More informationAP Statistics Chapter 6 - Random Variables
AP Statistics Chapter 6 - Random 6.1 Discrete and Continuous Random Objective: Recognize and define discrete random variables, and construct a probability distribution table and a probability histogram
More informationSolvency, Capital Allocation and Fair Rate of Return in Insurance
Solvency, Capital Allocation and Fair Rate of Return in Insurance Michael Sherris Actuarial Studies Faculty of Commerce and Economics UNSW, Sydney, AUSTRALIA Telephone: + 6 2 9385 2333 Fax: + 6 2 9385
More informationA Method for Calculating Cost Correlation among Construction Projects in a Portfolio
International Journal of Architecture, Engineering and Construction Vol 1, No 3, September 2012, 134-141 A Method for Calculating Cost Correlation among Construction Projects in a Portfolio Payam Bakhshi
More informationDesirable properties for a good model of portfolio credit risk modelling
3.3 Default correlation binomial models Desirable properties for a good model of portfolio credit risk modelling Default dependence produce default correlations of a realistic magnitude. Estimation number
More informationCopulas and credit risk models: some potential developments
Copulas and credit risk models: some potential developments Fernando Moreira CRC Credit Risk Models 1-Day Conference 15 December 2014 Objectives of this presentation To point out some limitations in some
More information3.4 Copula approach for modeling default dependency. Two aspects of modeling the default times of several obligors
3.4 Copula approach for modeling default dependency Two aspects of modeling the default times of several obligors 1. Default dynamics of a single obligor. 2. Model the dependence structure of defaults
More informationFormulating SP\ Stochastic Programming\ Scenario Planning Models in What sbest!
Formulating SP\ Stochastic Programming\ Scenario Planning Models in What sbest! www.lindo.com December 2011 Modeling Uncertainty in General Optimization Problems Is there a general way of incorporating
More informationThe rth moment of a real-valued random variable X with density f(x) is. x r f(x) dx
1 Cumulants 1.1 Definition The rth moment of a real-valued random variable X with density f(x) is µ r = E(X r ) = x r f(x) dx for integer r = 0, 1,.... The value is assumed to be finite. Provided that
More informationNumerical Descriptions of Data
Numerical Descriptions of Data Measures of Center Mean x = x i n Excel: = average ( ) Weighted mean x = (x i w i ) w i x = data values x i = i th data value w i = weight of the i th data value Median =
More informationAlternative VaR Models
Alternative VaR Models Neil Roeth, Senior Risk Developer, TFG Financial Systems. 15 th July 2015 Abstract We describe a variety of VaR models in terms of their key attributes and differences, e.g., parametric
More informationAnalysis of the Influence of the Annualized Rate of Rentability on the Unit Value of the Net Assets of the Private Administered Pension Fund NN
Year XVIII No. 20/2018 175 Analysis of the Influence of the Annualized Rate of Rentability on the Unit Value of the Net Assets of the Private Administered Pension Fund NN Constantin DURAC 1 1 University
More informationBase SAS 9.2 Procedures Guide. Statistical Procedures Second Edition
Base SAS 9.2 Procedures Guide Statistical Procedures Second Edition The correct bibliographic citation for this manual is as follows: SAS Institute Inc. 2009. Base SAS 9.2 Procedures Guide: Statistical
More information29th India Fellowship Seminar
29th India Fellowship Seminar Is Risk Based Capital way forward? Adaptability to Indian Context & Comparison of various market consistent measures Guide: Sunil Sharma Presented by: Rakesh Kumar Niraj Kumar
More informationMeasures of Contribution for Portfolio Risk
X Workshop on Quantitative Finance Milan, January 29-30, 2009 Agenda Coherent Measures of Risk Spectral Measures of Risk Capital Allocation Euler Principle Application Risk Measurement Risk Attribution
More informationFINC 430 TA Session 7 Risk and Return Solutions. Marco Sammon
FINC 430 TA Session 7 Risk and Return Solutions Marco Sammon Formulas for return and risk The expected return of a portfolio of two risky assets, i and j, is Expected return of asset - the percentage of
More information