RISKMETRICS. Dr Philip Symes

Size: px
Start display at page:

Download "RISKMETRICS. Dr Philip Symes"

Transcription

1 1 RISKMETRICS Dr Philip Symes

2 1. Introduction 2 RiskMetrics is JP Morgan's risk management methodology. It was released in 1994 This was to standardise risk analysis in the industry. Scenarios are generated using: Historical simulation; Theoretical modelling; Stress testing scenarios. Metholodolgies are discussed in the short term limit Collateral is not modelled.

3 2. Contents 3 This presenation will focus on these topics. Risk Factors in the RiskMetrics approach. Methodologies for risk management. Products and pricing frameworks. Risk analysis and reporting.

4 3. Risk Factors 4 The main factors affecting portfolio value are modelled in RiskMetrics. Equities: Individual prices (absolute or relative to an index (β)); Index levels, e.g. FTSE 100; Affects equities and equity futures/options. FX rates: Affects cash positions, FX forwards/options and currency swaps. Commodity prices: Construct constant maturity curves; Affects spot and future prices.

5 4. Risk Factors (cont) 5 Interest rates are the fourth major factor. Yield curves are constructed from zero coupon and coupon bond prices; interest rate swap prices. Continuously compounded interest rate is used for simplicity other IR payments must be converted

6 5. Risk Factors (cont) 6 Coupon bonds are priced in terms of zero coupon bonds. Example: Bond maturing in 1 year; Semi-annual coupon of 10%: Same process is applied to swaps. IR are used for pricing swaps, options and fixed income.

7 6. Risk Factors (cont) 7 RiskMetrics also deals with less major factors that affect price. Credit spread: Construct yield curves with similar quality instruments; Calibrate: add a spread to each security. Implied volatility: Used for pricing options; Assume constant implied volatility if no historic data.

8 7. Empirical Models 8 Distribution of returns is given by past performance No theoretical models are used. The historical simulation method: Uses observations of actual changes in risk factors; Events are scaled with their frequency of occurrence; Models these changes to generate scenarios. Past observations must be scaled according to their volatility (Hull & White Model). Method includes extreme returns that occurred during the historical period.

9 8. Empirical Models (cont.) 9 Changes in asset prices are converted to risk factors. Formalise ideas in a matrix R of historical returns using of n risk factors with m daily returns: So each row of R corresponds to a specific scenario r.

10 9. Empirical Models (cont.) 10 Obtain a T-day P&L scenario from R: Take row/scenario r from R; This gives a vector of prices P (for each risk factor). Obtain price P of risk factor T days from now using Price each instrument using P 0 and scenario price P T. The portfolio P&L is given by

11 10. Theoretical Models 11 The multivariate normal model is used to predict returns: This model assumes lognormal returns; Geometric random walk; This is standard - see Hull or Wilmott for more details. Drifts are assumed to be zero (volatility dominates): No accurate predictions available for time horizons below 3 months; Zero assumption as good as any prediction.

12 11. Theoretical Models (cont.) 12 The return on the risk factor with these assumptions is: Volatility estimated from exponentially weighted moving average:

13 12. Theoretical Models (cont.) 13 An exponentially weighting moving average scheme is used to determine the decay factors: The optimal value was found by finding the minimum mean square difference between the variance estimate and the actual squared return on each day. Decay factors were set at: 0.94 (1-day) from 112 days of data; 0.97 (1-month) from 227 days of data. The number of days included comes from the fact that % of information is contained in the last ln10 ln λ days

14 13. Theoretical Models (cont.) 14 One day returns are: Conditioned on the current level of volatility; Independent across time; Normally distributed. RiskMetrics This does not preclude a heavy tailed unconditional distribution E.g. if volatilities dependent on the day of the week, then days could be dealt with separately.

15 14. Theoretical Models (cont.) 15 Multivariate method can be generalised to include multiple risk factors: these are correlated with a covariance matrix. In this case, the return for each asset i is now given by: And the covariance between i and j by:

16 15. Theoretical Models (cont.) 16 The covariance matrix is most easily written as: Where the mxn matrix of weighted returns is:

17 16. Theoretical Models (cont.) 17 Monte Carlo (MC) simulation: Generates scenarios from of random numbers; See MC in Finance presentation for more details. Generating random scenarios: Use Principle Component Analysis to derive formula.

18 17. Theoretical Models (cont.) 18 The c ij used in the formula are not unique: These coefficients satisfy certain requirements. They build up a vector C of units [c ij ]. The covariance matrix can then be written as: And the vector of returns as:

19 18. Theoretical Models (cont.) 19 Independent standard normal variables (ISNV) are used to generate random scenarios: L'Ecuyer method with 2x10 18 period; Will take years to repeat scenarios. Matrix decomposition by Cholesky or Single Value decomposition methods: See FIDES presentation for details on matrix decomposition; Note that Cholesky decomposition only works for positive definite matrices; But any negative terms are redundant anyway.

20 19. Theoretical Models (cont.) 20 The scheme to generate the MC variables is: 1) Generate a set z of ISNV; 2) Transform ISNV to set of returns r, correlated to each risk factor using matrix C from c ij so 3) Obtain the price of each risk factor (as for historical simulation); 4) Price each instrument at current price and 1-day price scenario; 5) Get portfolio P&L (as for historical simulation).

21 20. Theoretical Models (cont.) 21 Parametric methods (PM) are an alternative to MC. The method uses approximate pricing for every instrument to get analytic formulae: Assumes lognormality of returns. PM uses a δ-method : It models changes in asset values in a portfolio; This is based on a linear approximation. This makes PM faster than MC MC is still often preferred as it is more accurate.

22 21. Theoretical Models (cont.) 22 The present value V is given by a 1 st order Taylor expansion: There is a simple expression for P&L where δ are delta equivalents :

23 22. Theoretical Models (cont.) 23 Assume the lognormality of returns, because: Lognormal returns aggregate nicely across time (temporal additive); One period returns are independent; This implies that the volatility scales with root of time consistent with MC; Average P&L from this method is 0 since instrument prices and risk levels are linear. The alternative is percentage returns These aggregate across assets.

24 23. Stress Testing 24 Stress tests are needed to complement statistical models: Stress tests and models predict different types of scenarios; Stress tests need certain types of credible scenarios. Selection of stress events is important, and can be: Historical events E.g. Tequila crisis in 1995; User defined simple scenarios E.g. interest rate steepeners; User defined predictive models These take account of correlations, etc.

25 24. Stress Testing (cont.) 25 Using historical events is a useful way of creating meaningful scenarios What would happen to my portfolio if the events that caused x crash happened again? In general, between times t and T, the historical returns are given by: The P&L for the portfolio based on this is:

26 25. Stress Testing (cont.) 26 The portfolio must be revalued based on the events in the stress scenario. The RiskMetrics framework: Defines changes for a subset of core factors; Uses these to predict the effect on peripheral factors. Covariance matrices are used for multiple core factors Approach corresponds to multivariate regression (as before).

27 26. Stress Testing (cont.) 27 Example with 1 core factor: $1,000 in Indonesian JSE equity index; Scenario of 10% currency devaluation (IDR): With β=0.2, JSE index drops by an average 2%.

28 27. Pricing Framework: Basic Concepts 28 Cashflows are the building blocks for describing positions in RiskMetrics. Cashflows must always be mapped and discounted: The NPV of a cashflow is the product of cashflow amount and discount factor; Cashflow mapping means that principal and coupon payments are converted to their equivalent zero coupon rates at the payoff date. Yield curves are treated in RiskMetrics as piecewise linear. Points between vertices are joined with straight lines. RiskMetrics uses continuous compounding (see earlier).

29 28. Pricing Framework Examples 29 The first example is a fixed coupon bond: Duration 2 yr; Par value $100; Interest rate 5% p.a.; semi-annual coupons; first coupon 4.75% at 6 m: Interpolation of interest rates from term structure RiskMetrics sum of discounted cashflows: $98.03

30 29. Pricing Framework Examples (cont.) 30 E.g. a vanilla interest rate swap: Fixed for floating, with exchange of notionals; 1.25 y to maturity. Floating leg: Firm receives 6-mo LIBOR (next value 6.0%); Use cashflow mapping for 3, 9 & 15 months: Fixed leg: Firm pays 5% semi-annually on $100M notional: Value of swap:

31 30. Pricing Framework Examples (cont.) 31 Options can also be priced in this framework, e.g. a bond option. Black's Model is an extension of Black-Scholes: Assumes lognormal distribution of the value of the underlying at maturity; Can be used for Eu options, IR derivatives, caps & floors and swaptions.

32 31. Pricing Framework Examples (cont.) 32 The bond forward price, F, is given by: Consider a 10-month Eu bond option on: 9.75-year bond, $1,000 par value, r=10% semi-annual coupon; Dirty price $960 and clean price of X=$1,000; 3, 9 and 10 month risk free IR's are 9%, 9.5% and 10% p.a.; σ=9% annualised volatility of T=10 month bond price; $50 coupons in 3 months and 9 months; Bond forward price is: Option price is $9.49

33 32. Risk Measures 33 Value At Risk is the industry standard methodology: It states that, at a certain confidence limit (e.g. 99%) no more that x will be lost in a T day period; The current value of portfolio is used for predicting losses; VAR is the method specified in Basel 2. Marginal VAR (MVAR) is an extension to the VAR principle: It shows the amount of risk a particular position is adding to portfolio; It uses the parametric approach to separate out the risks and find correlations.

34 33. Risk Measures (cont.) 34 Incremental VAR (IVAR)is similar to MVAR: IVAR uses MVAR to adjust portfolio risk; It shows the sensitivity of VAR to portfolio changes. However, there are several drawbacks with VAR: There is no estimate of the size of losses once the VAR limit is exceeded; VAR is not a coherent measure of risk.

35 34. Risk Measures (cont.) 35 Coherent measures of risk have these properties: Translational invariance Adding cash to a portfolio decreases risk by the same amount; Subadditivity Risk of the sum of portfolios is smaller than the sum of their individual risks; Positive homogeneity of degree 1 If the size of the positions doubles, the risk will double; Monotonicity If portfolio A has higher losses than B for all risk factors, then A is riskier than B.

36 35. Risk Measures (cont.) 36 Expected shortfall (ES) provides more information than VAR on tail of the P&L distribution: It gives an average measure of how heavy the tail is; It is a convex function of portfolio weights useful for risk optimisation; The ES is always higher than the VAR. ES is a coherent risk measure. Combined with VAR, ES gives a measure of the cost of insuring portfolio losses These two methods are complementary.

37 36. Risk Reporting 37 At the simplest level, reporting is just a P&L histogram Shows VAR and expected shortfall MC shows lowest figures Historical simulation shows most conservative figures RiskMetrics

38 37. Risk Reporting (cont.) 38 Often need more detailed analysis to dissect risk and identify risk sources in a portfolio. Drilldowns slice-up portfolio risk to give more details. Drilldown dimensions are these sub-categories: Position; Portfolio; Asset type; Counterparty; Currency; Risk type (FX, IR, etc.); Yield curve maturity.

39 38. Risk Reporting (cont.) 39 Drilldown dimensions come in two main groups. Proper dimensions are groups of positions: Position assigned to one bucket so easy to calculate; E.g. region could assign VAR to different regions. Improper dimensions are groups of risk factors: Position might correspond to more than one bucket; E.g. an FX swap has IR risk, FX risk and two yield curves. Simulation or parametric methods must be used.

40 37. Summary 40 RiskMetrics is the industry standard risk analysis methodology: But does not include collateral. We have dealt only with non-collateralised trades in the short-term limit. RiskMetrics can handle trades in different asset classes Some examples have been shown. RiskMetrics handles risk by defining core risk factors, analyses the risk using 5 different methods and reports the risk using 2 metrics. RiskMetrics can be expanded to include non-normal distributions, copulas, etc.

Market Risk Analysis Volume IV. Value-at-Risk Models

Market Risk Analysis Volume IV. Value-at-Risk Models Market Risk Analysis Volume IV Value-at-Risk Models Carol Alexander John Wiley & Sons, Ltd List of Figures List of Tables List of Examples Foreword Preface to Volume IV xiii xvi xxi xxv xxix IV.l Value

More information

Credit Exposure Measurement Fixed Income & FX Derivatives

Credit Exposure Measurement Fixed Income & FX Derivatives 1 Credit Exposure Measurement Fixed Income & FX Derivatives Dr Philip Symes 1. Introduction 2 Fixed Income Derivatives Exposure Simulation. This methodology may be used for fixed income and FX derivatives.

More information

Calculating VaR. There are several approaches for calculating the Value at Risk figure. The most popular are the

Calculating VaR. There are several approaches for calculating the Value at Risk figure. The most popular are the VaR Pro and Contra Pro: Easy to calculate and to understand. It is a common language of communication within the organizations as well as outside (e.g. regulators, auditors, shareholders). It is not really

More information

HANDBOOK OF. Market Risk CHRISTIAN SZYLAR WILEY

HANDBOOK OF. Market Risk CHRISTIAN SZYLAR WILEY HANDBOOK OF Market Risk CHRISTIAN SZYLAR WILEY Contents FOREWORD ACKNOWLEDGMENTS ABOUT THE AUTHOR INTRODUCTION XV XVII XIX XXI 1 INTRODUCTION TO FINANCIAL MARKETS t 1.1 The Money Market 4 1.2 The Capital

More information

IEOR E4602: Quantitative Risk Management

IEOR E4602: Quantitative Risk Management IEOR E4602: Quantitative Risk Management Basic Concepts and Techniques of Risk Management Martin Haugh Department of Industrial Engineering and Operations Research Columbia University Email: martin.b.haugh@gmail.com

More information

Financial Risk Measurement/Management

Financial 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 information

Market 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. 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 information

Risk e-learning. Modules Overview.

Risk e-learning. Modules Overview. Risk e-learning Modules Overview Risk Sensitivities Market Risk Foundation (Banks) Understand delta risk sensitivity as an introduction to a broader set of risk sensitivities Explore the principles of

More information

Handbook of Financial Risk Management

Handbook of Financial Risk Management Handbook of Financial Risk Management Simulations and Case Studies N.H. Chan H.Y. Wong The Chinese University of Hong Kong WILEY Contents Preface xi 1 An Introduction to Excel VBA 1 1.1 How to Start Excel

More information

Statistical Models and Methods for Financial Markets

Statistical Models and Methods for Financial Markets Tze Leung Lai/ Haipeng Xing Statistical Models and Methods for Financial Markets B 374756 4Q Springer Preface \ vii Part I Basic Statistical Methods and Financial Applications 1 Linear Regression Models

More information

Value at Risk Risk Management in Practice. Nikolett Gyori (Morgan Stanley, Internal Audit) September 26, 2017

Value at Risk Risk Management in Practice. Nikolett Gyori (Morgan Stanley, Internal Audit) September 26, 2017 Value at Risk Risk Management in Practice Nikolett Gyori (Morgan Stanley, Internal Audit) September 26, 2017 Overview Value at Risk: the Wake of the Beast Stop-loss Limits Value at Risk: What is VaR? Value

More information

Bloomberg. Portfolio Value-at-Risk. Sridhar Gollamudi & Bryan Weber. September 22, Version 1.0

Bloomberg. 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 information

Alternative VaR Models

Alternative 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 information

Market Risk VaR: Model- Building Approach. Chapter 15

Market Risk VaR: Model- Building Approach. Chapter 15 Market Risk VaR: Model- Building Approach Chapter 15 Risk Management and Financial Institutions 3e, Chapter 15, Copyright John C. Hull 01 1 The Model-Building Approach The main alternative to historical

More information

Market Risk Analysis Volume II. Practical Financial Econometrics

Market 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 information

Executive Summary: A CVaR Scenario-based Framework For Minimizing Downside Risk In Multi-Asset Class Portfolios

Executive Summary: A CVaR Scenario-based Framework For Minimizing Downside Risk In Multi-Asset Class Portfolios Executive Summary: A CVaR Scenario-based Framework For Minimizing Downside Risk In Multi-Asset Class Portfolios Axioma, Inc. by Kartik Sivaramakrishnan, PhD, and Robert Stamicar, PhD August 2016 In this

More information

INTEREST RATES AND FX MODELS

INTEREST RATES AND FX MODELS INTEREST RATES AND FX MODELS 7. Risk Management Andrew Lesniewski Courant Institute of Mathematical Sciences New York University New York March 8, 2012 2 Interest Rates & FX Models Contents 1 Introduction

More information

Oracle Financial Services Market Risk User Guide

Oracle Financial Services Market Risk User Guide Oracle Financial Services User Guide Release 8.0.4.0.0 March 2017 Contents 1. INTRODUCTION... 1 PURPOSE... 1 SCOPE... 1 2. INSTALLING THE SOLUTION... 3 2.1 MODEL UPLOAD... 3 2.2 LOADING THE DATA... 3 3.

More information

Risk Management anil Financial Institullons^

Risk Management anil Financial Institullons^ Risk Management anil Financial Institullons^ Third Edition JOHN C. HULL WILEY John Wiley & Sons, Inc. Contents Preface ' xix CHAPTBM Introduction! 1 1.1 Risk vs. Return for Investors, 2 1.2 The Efficient

More information

Market risk measurement in practice

Market risk measurement in practice Lecture notes on risk management, public policy, and the financial system Allan M. Malz Columbia University 2018 Allan M. Malz Last updated: October 23, 2018 2/32 Outline Nonlinearity in market risk Market

More information

Market Risk Analysis Volume I

Market Risk Analysis Volume I Market Risk Analysis Volume I Quantitative Methods in Finance Carol Alexander John Wiley & Sons, Ltd List of Figures List of Tables List of Examples Foreword Preface to Volume I xiii xvi xvii xix xxiii

More information

Comparison of Estimation For Conditional Value at Risk

Comparison of Estimation For Conditional Value at Risk -1- University of Piraeus Department of Banking and Financial Management Postgraduate Program in Banking and Financial Management Comparison of Estimation For Conditional Value at Risk Georgantza Georgia

More information

Risk Management. Exercises

Risk Management. Exercises Risk Management Exercises Exercise Value at Risk calculations Problem Consider a stock S valued at $1 today, which after one period can be worth S T : $2 or $0.50. Consider also a convertible bond B, which

More information

MFM Practitioner Module: Quantitative Risk Management. John Dodson. September 6, 2017

MFM Practitioner Module: Quantitative Risk Management. John Dodson. September 6, 2017 MFM Practitioner Module: Quantitative September 6, 2017 Course Fall sequence modules quantitative risk management Gary Hatfield fixed income securities Jason Vinar mortgage securities introductions Chong

More information

Risk Modeling: Lecture outline and projects. (updated Mar5-2012)

Risk Modeling: Lecture outline and projects. (updated Mar5-2012) Risk Modeling: Lecture outline and projects (updated Mar5-2012) Lecture 1 outline Intro to risk measures economic and regulatory capital what risk measurement is done and how is it used concept and role

More information

Recent developments in. Portfolio Modelling

Recent developments in. Portfolio Modelling Recent developments in Portfolio Modelling Presentation RiskLab Madrid Agenda What is Portfolio Risk Tracker? Original Features Transparency Data Technical Specification 2 What is Portfolio Risk Tracker?

More information

Razor Risk Market Risk Overview

Razor Risk Market Risk Overview Razor Risk Market Risk Overview Version 1.0 (Final) Prepared by: Razor Risk Updated: 20 April 2012 Razor Risk 7 th Floor, Becket House 36 Old Jewry London EC2R 8DD Telephone: +44 20 3194 2564 e-mail: peter.walsh@razor-risk.com

More information

Overview. We will discuss the nature of market risk and appropriate measures

Overview. We will discuss the nature of market risk and appropriate measures Market Risk Overview We will discuss the nature of market risk and appropriate measures RiskMetrics Historic (back stimulation) approach Monte Carlo simulation approach Link between market risk and required

More information

IEOR E4602: Quantitative Risk Management

IEOR 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 information

Field Guide to Internal Models under the Basel Committee s Fundamental review of the trading book framework

Field Guide to Internal Models under the Basel Committee s Fundamental review of the trading book framework Field Guide to Internal Models under the Basel Committee s Fundamental review of the trading book framework Barry Pearce, Director, Skew Vega Limited A R T I C L E I N F O A B S T R A C T Article history:

More information

Master 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.  > 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 information

The 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. 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 information

INDIAN INSTITUTE OF QUANTITATIVE FINANCE

INDIAN INSTITUTE OF QUANTITATIVE FINANCE 2018 FRM EXAM TRAINING SYLLABUS PART I Introduction to Financial Mathematics 1. Introduction to Financial Calculus a. Variables Discrete and Continuous b. Univariate and Multivariate Functions Dependent

More information

Building a Zero Coupon Yield Curve

Building a Zero Coupon Yield Curve Building a Zero Coupon Yield Curve Clive Bastow, CFA, CAIA ABSTRACT Create and use a zero- coupon yield curve from quoted LIBOR, Eurodollar Futures, PAR Swap and OIS rates. www.elpitcafinancial.com Risk-

More information

Introduction Dickey-Fuller Test Option Pricing Bootstrapping. Simulation Methods. Chapter 13 of Chris Brook s Book.

Introduction Dickey-Fuller Test Option Pricing Bootstrapping. Simulation Methods. Chapter 13 of Chris Brook s Book. Simulation Methods Chapter 13 of Chris Brook s Book Christopher Ting http://www.mysmu.edu/faculty/christophert/ Christopher Ting : christopherting@smu.edu.sg : 6828 0364 : LKCSB 5036 April 26, 2017 Christopher

More information

A general approach to calculating VaR without volatilities and correlations

A general approach to calculating VaR without volatilities and correlations page 19 A general approach to calculating VaR without volatilities and correlations Peter Benson * Peter Zangari Morgan Guaranty rust Company Risk Management Research (1-212) 648-8641 zangari_peter@jpmorgan.com

More information

The Fundamental Review of the Trading Book: from VaR to ES

The Fundamental Review of the Trading Book: from VaR to ES The Fundamental Review of the Trading Book: from VaR to ES Chiara Benazzoli Simon Rabanser Francesco Cordoni Marcus Cordi Gennaro Cibelli University of Verona Ph. D. Modelling Week Finance Group (UniVr)

More information

Financial Risk Measurement/Management

Financial 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 information

Maturity as a factor for credit risk capital

Maturity as a factor for credit risk capital Maturity as a factor for credit risk capital Michael Kalkbrener Λ, Ludger Overbeck y Deutsche Bank AG, Corporate & Investment Bank, Credit Risk Management 1 Introduction 1.1 Quantification of maturity

More information

Oracle Financial Services Market Risk User Guide

Oracle Financial Services Market Risk User Guide Oracle Financial Services User Guide Release 8.0.1.0.0 August 2016 Contents 1. INTRODUCTION... 1 1.1 PURPOSE... 1 1.2 SCOPE... 1 2. INSTALLING THE SOLUTION... 3 2.1 MODEL UPLOAD... 3 2.2 LOADING THE DATA...

More information

A Hybrid Commodity and Interest Rate Market Model

A Hybrid Commodity and Interest Rate Market Model A Hybrid Commodity and Interest Rate Market Model University of Technology, Sydney June 1 Literature A Hybrid Market Model Recall: The basic LIBOR Market Model The cross currency LIBOR Market Model LIBOR

More information

Derivatives Options on Bonds and Interest Rates. Professor André Farber Solvay Business School Université Libre de Bruxelles

Derivatives Options on Bonds and Interest Rates. Professor André Farber Solvay Business School Université Libre de Bruxelles Derivatives Options on Bonds and Interest Rates Professor André Farber Solvay Business School Université Libre de Bruxelles Caps Floors Swaption Options on IR futures Options on Government bond futures

More information

The University of Chicago, Booth School of Business Business 41202, Spring Quarter 2012, Mr. Ruey S. Tsay. Solutions to Final Exam

The University of Chicago, Booth School of Business Business 41202, Spring Quarter 2012, Mr. Ruey S. Tsay. Solutions to Final Exam The University of Chicago, Booth School of Business Business 41202, Spring Quarter 2012, Mr. Ruey S. Tsay Solutions to Final Exam Problem A: (40 points) Answer briefly the following questions. 1. Consider

More information

Financial Risk Management

Financial Risk Management Financial Risk Management Professor: Thierry Roncalli Evry University Assistant: Enareta Kurtbegu Evry University Tutorial exercices #3 1 Maximum likelihood of the exponential distribution 1. We assume

More information

ORE Applied: Dynamic Initial Margin and MVA

ORE Applied: Dynamic Initial Margin and MVA ORE Applied: Dynamic Initial Margin and MVA Roland Lichters QuantLib User Meeting at IKB, Düsseldorf 8 December 2016 Agenda Open Source Risk Engine Dynamic Initial Margin and Margin Value Adjustment Conclusion

More information

Multi-Curve Pricing of Non-Standard Tenor Vanilla Options in QuantLib. Sebastian Schlenkrich QuantLib User Meeting, Düsseldorf, December 1, 2015

Multi-Curve Pricing of Non-Standard Tenor Vanilla Options in QuantLib. Sebastian Schlenkrich QuantLib User Meeting, Düsseldorf, December 1, 2015 Multi-Curve Pricing of Non-Standard Tenor Vanilla Options in QuantLib Sebastian Schlenkrich QuantLib User Meeting, Düsseldorf, December 1, 2015 d-fine d-fine All rights All rights reserved reserved 0 Swaption

More information

Structured Derivatives Valuation. Ľuboš Briatka. Praha, 7 June 2016

Structured Derivatives Valuation. Ľuboš Briatka. Praha, 7 June 2016 Structured Derivatives Valuation Ľuboš Briatka Praha, 7 June 2016 Global financial assets = 225 trillion USD Size of derivatives market = 710 trillion USD BIS Quarterly Review, September 2014 Size of derivatives

More information

Economic Scenario Generator: Applications in Enterprise Risk Management. Ping Sun Executive Director, Financial Engineering Numerix LLC

Economic Scenario Generator: Applications in Enterprise Risk Management. Ping Sun Executive Director, Financial Engineering Numerix LLC Economic Scenario Generator: Applications in Enterprise Risk Management Ping Sun Executive Director, Financial Engineering Numerix LLC Numerix makes no representation or warranties in relation to information

More information

Interest Rate Modeling

Interest Rate Modeling Chapman & Hall/CRC FINANCIAL MATHEMATICS SERIES Interest Rate Modeling Theory and Practice Lixin Wu CRC Press Taylor & Francis Group Boca Raton London New York CRC Press is an imprint of the Taylor & Francis

More information

Economic Capital. Implementing an Internal Model for. Economic Capital ACTUARIAL SERVICES

Economic 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 information

Market interest-rate models

Market interest-rate models Market interest-rate models Marco Marchioro www.marchioro.org November 24 th, 2012 Market interest-rate models 1 Lecture Summary No-arbitrage models Detailed example: Hull-White Monte Carlo simulations

More information

Risk Measurement in Credit Portfolio Models

Risk Measurement in Credit Portfolio Models 9 th DGVFM Scientific Day 30 April 2010 1 Risk Measurement in Credit Portfolio Models 9 th DGVFM Scientific Day 30 April 2010 9 th DGVFM Scientific Day 30 April 2010 2 Quantitative Risk Management Profit

More information

Financial Econometrics Notes. Kevin Sheppard University of Oxford

Financial Econometrics Notes. Kevin Sheppard University of Oxford Financial Econometrics Notes Kevin Sheppard University of Oxford Monday 15 th January, 2018 2 This version: 22:52, Monday 15 th January, 2018 2018 Kevin Sheppard ii Contents 1 Probability, Random Variables

More information

Financial Risk Management and Governance Beyond VaR. Prof. Hugues Pirotte

Financial Risk Management and Governance Beyond VaR. Prof. Hugues Pirotte Financial Risk Management and Governance Beyond VaR Prof. Hugues Pirotte 2 VaR Attempt to provide a single number that summarizes the total risk in a portfolio. What loss level is such that we are X% confident

More information

Risk Measuring of Chosen Stocks of the Prague Stock Exchange

Risk Measuring of Chosen Stocks of the Prague Stock Exchange Risk Measuring of Chosen Stocks of the Prague Stock Exchange Ing. Mgr. Radim Gottwald, Department of Finance, Faculty of Business and Economics, Mendelu University in Brno, radim.gottwald@mendelu.cz Abstract

More information

Modelling Counterparty Exposure and CVA An Integrated Approach

Modelling Counterparty Exposure and CVA An Integrated Approach Swissquote Conference Lausanne Modelling Counterparty Exposure and CVA An Integrated Approach Giovanni Cesari October 2010 1 Basic Concepts CVA Computation Underlying Models Modelling Framework: AMC CVA:

More information

Risk Measurement: An Introduction to Value at Risk

Risk Measurement: An Introduction to Value at Risk Risk Measurement: An Introduction to Value at Risk Thomas J. Linsmeier and Neil D. Pearson * University of Illinois at Urbana-Champaign July 1996 Abstract This paper is a self-contained introduction to

More information

Advanced Concepts in Capturing Market Risk: A Supervisory Perspective

Advanced Concepts in Capturing Market Risk: A Supervisory Perspective Advanced Concepts in Capturing Market Risk: A Supervisory Perspective Rodanthy Tzani Federal Reserve Bank of NY The views expressed in this presentation are strictly those of the presenter and do not necessarily

More information

UPDATED IAA EDUCATION SYLLABUS

UPDATED IAA EDUCATION SYLLABUS II. UPDATED IAA EDUCATION SYLLABUS A. Supporting Learning Areas 1. STATISTICS Aim: To enable students to apply core statistical techniques to actuarial applications in insurance, pensions and emerging

More information

Modern Derivatives. Pricing and Credit. Exposure Anatysis. Theory and Practice of CSA and XVA Pricing, Exposure Simulation and Backtest!

Modern Derivatives. Pricing and Credit. Exposure Anatysis. Theory and Practice of CSA and XVA Pricing, Exposure Simulation and Backtest! Modern Derivatives Pricing and Credit Exposure Anatysis Theory and Practice of CSA and XVA Pricing, Exposure Simulation and Backtest!ng Roland Lichters, Roland Stamm, Donal Gallagher Contents List of Figures

More information

Modeling credit risk in an in-house Monte Carlo simulation

Modeling credit risk in an in-house Monte Carlo simulation Modeling credit risk in an in-house Monte Carlo simulation Wolfgang Gehlen Head of Risk Methodology BIS Risk Control Beatenberg, 4 September 2003 Presentation overview I. Why model credit losses in a simulation?

More information

UCITS Financial Derivative Instruments and Efficient Portfolio Management. November 2015

UCITS Financial Derivative Instruments and Efficient Portfolio Management. November 2015 2015 UCITS Financial Derivative Instruments and Efficient Portfolio Management November 2015 3 Contents Relevant Legislation 5 Permitted FDI 5 Global Exposure 6 Commitment Approach 7 Commitment Approach-

More information

Asset Allocation in the 21 st Century

Asset Allocation in the 21 st Century Asset Allocation in the 21 st Century Paul D. Kaplan, Ph.D., CFA Quantitative Research Director, Morningstar Europe, Ltd. 2012 Morningstar Europe, Inc. All rights reserved. Harry Markowitz and Mean-Variance

More information

Jaime Frade Dr. Niu Interest rate modeling

Jaime Frade Dr. Niu Interest rate modeling Interest rate modeling Abstract In this paper, three models were used to forecast short term interest rates for the 3 month LIBOR. Each of the models, regression time series, GARCH, and Cox, Ingersoll,

More information

VaR vs CVaR in Risk Management and Optimization

VaR vs CVaR in Risk Management and Optimization VaR vs CVaR in Risk Management and Optimization Stan Uryasev Joint presentation with Sergey Sarykalin, Gaia Serraino and Konstantin Kalinchenko Risk Management and Financial Engineering Lab, University

More information

Calculating Counterparty Exposures for CVA

Calculating Counterparty Exposures for CVA Calculating Counterparty Exposures for CVA Jon Gregory Solum Financial (www.solum-financial.com) 19 th January 2011 Jon Gregory (jon@solum-financial.com) Calculating Counterparty Exposures for CVA, London,

More information

FINANCIAL DERIVATIVE. INVESTMENTS An Introduction to Structured Products. Richard D. Bateson. Imperial College Press. University College London, UK

FINANCIAL DERIVATIVE. INVESTMENTS An Introduction to Structured Products. Richard D. Bateson. Imperial College Press. University College London, UK FINANCIAL DERIVATIVE INVESTMENTS An Introduction to Structured Products Richard D. Bateson University College London, UK Imperial College Press Contents Preface Guide to Acronyms Glossary of Notations

More information

Oracle Financial Services Market Risk User Guide

Oracle Financial Services Market Risk User Guide Oracle Financial Services Market Risk User Guide Release 2.5.1 August 2015 Contents 1. INTRODUCTION... 1 1.1. PURPOSE... 1 1.2. SCOPE... 1 2. INSTALLING THE SOLUTION... 3 2.1. MODEL UPLOAD... 3 2.2. LOADING

More information

From Financial Risk Management. Full book available for purchase here.

From Financial Risk Management. Full book available for purchase here. From Financial Risk Management. Full book available for purchase here. Contents Preface Acknowledgments xi xvii CHAPTER 1 Introduction 1 Banks and Risk Management 1 Evolution of Bank Capital Regulation

More information

Impact of negative rates on pricing models. Veronica Malafaia ING Bank - FI/FM Quants, Credit & Trading Risk Amsterdam, 18 th November 2015

Impact of negative rates on pricing models. Veronica Malafaia ING Bank - FI/FM Quants, Credit & Trading Risk Amsterdam, 18 th November 2015 Impact of negative rates on pricing models Veronica Malafaia ING Bank - FI/FM Quants, Credit & Trading Risk Amsterdam, 18 th November 2015 Disclaimer: The views and opinions expressed in this presentation

More information

INTEREST RATES AND FX MODELS

INTEREST RATES AND FX MODELS INTEREST RATES AND FX MODELS 4. Convexity Andrew Lesniewski Courant Institute of Mathematics New York University New York February 24, 2011 2 Interest Rates & FX Models Contents 1 Convexity corrections

More information

The Statistical Mechanics of Financial Markets

The Statistical Mechanics of Financial Markets The Statistical Mechanics of Financial Markets Johannes Voit 2011 johannes.voit (at) ekit.com Overview 1. Why statistical physicists care about financial markets 2. The standard model - its achievements

More information

ESGs: Spoilt for choice or no alternatives?

ESGs: Spoilt for choice or no alternatives? ESGs: Spoilt for choice or no alternatives? FA L K T S C H I R S C H N I T Z ( F I N M A ) 1 0 3. M i t g l i e d e r v e r s a m m l u n g S AV A F I R, 3 1. A u g u s t 2 0 1 2 Agenda 1. Why do we need

More information

Week 7 Quantitative Analysis of Financial Markets Simulation Methods

Week 7 Quantitative Analysis of Financial Markets Simulation Methods Week 7 Quantitative Analysis of Financial Markets Simulation Methods Christopher Ting http://www.mysmu.edu/faculty/christophert/ Christopher Ting : christopherting@smu.edu.sg : 6828 0364 : LKCSB 5036 November

More information

Comparison of Capital Adequacy Requirements to Market Risks According Internal Models and Standardized Method

Comparison of Capital Adequacy Requirements to Market Risks According Internal Models and Standardized Method Charles University, Prague Faculty of Social Sciences Institute of Economic Studies Comparison of Capital Adequacy Requirements to Market Risks According Dissertation 2005 Jindra Klobásová Institute of

More information

Introduction to Algorithmic Trading Strategies Lecture 8

Introduction to Algorithmic Trading Strategies Lecture 8 Introduction to Algorithmic Trading Strategies Lecture 8 Risk Management Haksun Li haksun.li@numericalmethod.com www.numericalmethod.com Outline Value at Risk (VaR) Extreme Value Theory (EVT) References

More information

Introduction to Risk Management

Introduction to Risk Management Introduction to Risk Management ACPM Certified Portfolio Management Program c 2010 by Martin Haugh Introduction to Risk Management We introduce some of the basic concepts and techniques of risk management

More information

Statistical Methods in Financial Risk Management

Statistical Methods in Financial Risk Management Statistical Methods in Financial Risk Management Lecture 1: Mapping Risks to Risk Factors Alexander J. McNeil Maxwell Institute of Mathematical Sciences Heriot-Watt University Edinburgh 2nd Workshop on

More information

MATH FOR CREDIT. Purdue University, Feb 6 th, SHIKHAR RANJAN Credit Products Group, Morgan Stanley

MATH FOR CREDIT. Purdue University, Feb 6 th, SHIKHAR RANJAN Credit Products Group, Morgan Stanley MATH FOR CREDIT Purdue University, Feb 6 th, 2004 SHIKHAR RANJAN Credit Products Group, Morgan Stanley Outline The space of credit products Key drivers of value Mathematical models Pricing Trading strategies

More information

Operational Risk Aggregation

Operational Risk Aggregation Operational Risk Aggregation Professor Carol Alexander Chair of Risk Management and Director of Research, ISMA Centre, University of Reading, UK. Loss model approaches are currently a focus of operational

More information

Market Risk Management Framework. July 28, 2012

Market Risk Management Framework. July 28, 2012 Market Risk Management Framework July 28, 2012 Views or opinions in this presentation are solely those of the presenter and do not necessarily represent those of ICICI Bank Limited 2 Introduction Agenda

More information

FRTB: Standardised Approach

FRTB: Standardised Approach FRTB: Standardised Approach Tom Mills FinPricing http://www.finpricing.com Summary FRTB Definition FRTB vs Basel 2.5 FRTB Main Features FRTB Approaches FRTB Standardised Approach (SA) FRTB SA: Sensitivity

More information

Investment Performance, Analytics, and Risk Glossary of Terms

Investment Performance, Analytics, and Risk Glossary of Terms Investment Performance, Analytics, and Risk Glossary of Terms Investment Performance 4 Ex-Post Risk 12 Ex-Ante Risk 18 Equity Analytics 23 Fixed Income Analytics 26 3 ACCUMULATED BENEFIT OBLIGATION (ABO)

More information

Luis Seco University of Toronto

Luis Seco University of Toronto Luis Seco University of Toronto seco@math.utoronto.ca The case for credit risk: The Goodrich-Rabobank swap of 1983 Markov models A two-state model The S&P, Moody s model Basic concepts Exposure, recovery,

More information

Appendix A Financial Calculations

Appendix A Financial Calculations Derivatives Demystified: A Step-by-Step Guide to Forwards, Futures, Swaps and Options, Second Edition By Andrew M. Chisholm 010 John Wiley & Sons, Ltd. Appendix A Financial Calculations TIME VALUE OF MONEY

More information

Risk Management and Financial Institutions

Risk Management and Financial Institutions Risk Management and Financial Institutions Founded in 1807, John Wiley & Sons is the oldest independent publishing company in the United States. With offices in North America, Europe, Australia and Asia,

More information

VaR Introduction III: Monte Carlo VaR

VaR Introduction III: Monte Carlo VaR VaR Introduction III: Monte Carlo VaR Tom Mills FinPricing http://www.finpricing.com Summary VaR Definition VaR Roles VaR Pros and Cons VaR Approaches Monte Carlo VaR Monte Carlo VaR Methodology and Implementation

More information

INVESTMENT SERVICES RULES FOR RETAIL COLLECTIVE INVESTMENT SCHEMES

INVESTMENT SERVICES RULES FOR RETAIL COLLECTIVE INVESTMENT SCHEMES INVESTMENT SERVICES RULES FOR RETAIL COLLECTIVE INVESTMENT SCHEMES PART B: STANDARD LICENCE CONDITIONS Appendix VI Supplementary Licence Conditions on Risk Management, Counterparty Risk Exposure and Issuer

More information

INSTITUTE OF ACTUARIES OF INDIA

INSTITUTE OF ACTUARIES OF INDIA INSTITUTE OF ACTUARIES OF INDIA EXAMINATIONS 24 th March 2017 Subject ST6 Finance and Investment B Time allowed: Three Hours (10.15* 13.30 Hours) Total Marks: 100 INSTRUCTIONS TO THE CANDIDATES 1. Please

More information

SOLUTIONS 913,

SOLUTIONS 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 information

Financial Instruments Valuation and the Role of Quantitative Analysis in a Consulting Firm

Financial Instruments Valuation and the Role of Quantitative Analysis in a Consulting Firm Financial Instruments Valuation and the Role of Quantitative Analysis in a Consulting Firm Ľuboš Briatka Praha, May 29 th, 2012 Financial Instruments - definition A financial instrument is any contract

More information

Exhibit 2 The Two Types of Structures of Collateralized Debt Obligations (CDOs)

Exhibit 2 The Two Types of Structures of Collateralized Debt Obligations (CDOs) II. CDO and CDO-related Models 2. CDS and CDO Structure Credit default swaps (CDSs) and collateralized debt obligations (CDOs) provide protection against default in exchange for a fee. A typical contract

More information

Standardised Risk under Basel 3. Pardha Viswanadha, Product Management Calypso

Standardised Risk under Basel 3. Pardha Viswanadha, Product Management Calypso Standardised Risk under Basel 3 Pardha Viswanadha, Product Management Calypso Flow Regulatory risk landscape Trading book risk drivers Overview of SA-MR Issues & Challenges Overview of SA-CCR Issues &

More information

Comparison of market models for measuring and hedging synthetic CDO tranche spread risks

Comparison of market models for measuring and hedging synthetic CDO tranche spread risks Eur. Actuar. J. (2011) 1 (Suppl 2):S261 S281 DOI 10.1007/s13385-011-0025-1 ORIGINAL RESEARCH PAPER Comparison of market models for measuring and hedging synthetic CDO tranche spread risks Jack Jie Ding

More information

ROM SIMULATION Exact Moment Simulation using Random Orthogonal Matrices

ROM SIMULATION Exact Moment Simulation using Random Orthogonal Matrices ROM SIMULATION Exact Moment Simulation using Random Orthogonal Matrices Bachelier Finance Society Meeting Toronto 2010 Henley Business School at Reading Contact Author : d.ledermann@icmacentre.ac.uk Alexander

More information

The value of a bond changes in the opposite direction to the change in interest rates. 1 For a long bond position, the position s value will decline

The value of a bond changes in the opposite direction to the change in interest rates. 1 For a long bond position, the position s value will decline 1-Introduction Page 1 Friday, July 11, 2003 10:58 AM CHAPTER 1 Introduction T he goal of this book is to describe how to measure and control the interest rate and credit risk of a bond portfolio or trading

More information

AN ANALYTICALLY TRACTABLE UNCERTAIN VOLATILITY MODEL

AN ANALYTICALLY TRACTABLE UNCERTAIN VOLATILITY MODEL AN ANALYTICALLY TRACTABLE UNCERTAIN VOLATILITY MODEL FABIO MERCURIO BANCA IMI, MILAN http://www.fabiomercurio.it 1 Stylized facts Traders use the Black-Scholes formula to price plain-vanilla options. An

More information

Prudential sourcebook for Investment Firms. Chapter 6. Market risk

Prudential sourcebook for Investment Firms. Chapter 6. Market risk Prudential sourcebook for Investment Firms Chapter Market risk Section.1 : Market risk requirements.1 Market risk requirements.1.1 R IFPRU applies to an IFPRU investment firm, unless it is an exempt IFPRU

More information

Fixed Income and Risk Management

Fixed Income and Risk Management Fixed Income and Risk Management Fall 2003, Term 2 Michael W. Brandt, 2003 All rights reserved without exception Agenda and key issues Pricing with binomial trees Replication Risk-neutral pricing Interest

More information

From Financial Engineering to Risk Management. Radu Tunaru University of Kent, UK

From Financial Engineering to Risk Management. Radu Tunaru University of Kent, UK Model Risk in Financial Markets From Financial Engineering to Risk Management Radu Tunaru University of Kent, UK \Yp World Scientific NEW JERSEY LONDON SINGAPORE BEIJING SHANGHAI HONG KONG TAIPEI CHENNAI

More information