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

Size: px
Start display at page:

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

Transcription

1 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

2 Contents List of Figures ListofTables Preface Acknowledgements List ofabbreviations and Symbols xiv xxii xxv xxix xxx Parti Discounting 1 1 Discounting Before the Crisis The risk-free rate Pacing linear Instruments Forward rate agreements Interest rate swaps FXforwards Tenor basis swaps Cross-currency basis swaps Curve building Pricing non-linear instruments Caps and floors Swaptions 11 2 What Changed with the Crisis Basis products and spreads Tenor basis swaps Cross-currency basis swaps Collateralization 17 3 Clearing House Pricing Introduction of central counterparties Margin requirements Building the OIS curve USD specialities Building the forward protection curves More USD specialities Example: implying the par asset swap spread 27 vii

3 viii Contents 3.8 Interpolation Pricing non-linear instruments European swaptions Bermudan swaptions Not all currencies are equal 33 4 Global Discounting Collateralization in a foreign currency Non-rebalancing cross-currency swaps Rebalancing cross-currency swaps Examples: approximations of basis spreads Tenor basis spreads Fiat cross-currency swaps OIS cross-currency basis spread LIBOR cross-currency basis spread 43 5 CSA Discounting ISDA agreements and CSA complexities Currency options Negative overnight rates Other assets as collateral Thresholds and asymmetries Some thoughts on initial margin 51 6 Fair Value Hedge Accounting in a Multi-Curve World Introduction Hedge effectiveness Single-curve valuation Multi-curve valuation 59 Part II Credit and Debit Value Adjustment 67 7 Introduction 69 8 Fundamentals Unilateral CVA Bilateral CVA 76 9 Single Trade CVA Interest rate swap Exercise within interest periods Amortizing swap A simple swap CVA model Cash-settled European options FX forward Cross-currency swap Rebalancing cross-currency swap 101

4 Contents j ix Part III Risk Factor Evolution 10 Introduction - A Monte Carlo Framework 11 Interest Rates 11.1 Linear Gauss Markov model Multiple curves Invariances Relation to the Hull-White model in T-forward measure 11.2 Products Zero bond option European swaption Bermudan swaption with deterministic basis Stochastic basis 11.3 CSA discounting revisited 11.4 Exposure evolution examples 12 Foreign Exchange 12.1 Cross-currency LGM 12.2 Multi-currency LGM 12.3 Calibration Interest rate processes FX processes Correlations 12.4 Cross-currency basis 12.5 Exposure evolution examples 13 Inflation 13.1 Products 13.2 Jarrow-Yildirim model Calibration Foreign currency inflation 13.3 Dodgson-Kainth model Calibration Foreign currency inflation 13.4 Seasonality 13.5 Exposure evolution examples 14 Equity and Commodity 14.1 Equity 14.2 Commodity 15 Credit 15.1 Market 15.2 Gaussian model Conclusion

5 x Contents 15.3 Cox-Ingersoll-Ross model CIR without jumps Relaxed feller constraint CDS spread distribution CIRwith jumps: JCIR JCIR extension Examples: CDS CVA and wrong-way risk Conclusion Black-Karasinski model Peng-Kou model Review CDS and CDS option Compound Poisson process Compound Polya process Examples Conclusion 233 Part IV XVA Cross-Asset Scenario Generation Expectations and covariances Path generation Pseudo-random vs low discrepancy sequences Long-term interest rate Simulation Netting and Collateral Netting Non-netted counterparty exposures Netting set exposures Generalized counterparty exposures Collateralization Collateralized netting set exposure CSAmargining Margin settlement Interest accrual FXrisk Collateral choice Early Exercise and American Monte Carlo American Monte Carlo Utilizing American Monte Carlo for CVA CVA Risk and Algorithmic Differentiation Algorithmic differentiation AD basics 276

6 Contents j xi 19.3 AD examples Vanilla swap and interest rate sensitivities European swaptions with deltas and vega cube Further applications of AD FVA A simple definition of FVA DVA = FBA? The role of the spreads The expectation approach The semi-replication approach CSA pricing revisited MVA Outlook KVA KVA by semi-replication Calculation of KVA Risk-warehousing and TVA 308 Part V Credit Risk Introduction Fundamentals Portfolio credit models Independent defaults Static default correlation modelling Dynamic default correlation modelling Industry portfolio credit models Pricing Portfolio Credit Products Introduction Synthetic portfolio credit derivatives Nth-to-default basket Synthetic collateralized debt Obligation Synthetic CDO Cashflow structures Introduction Cashflow CDO structures Overall pricing framework Pricing formulas Example results Test deal 347

7 xii [ Contents Testresults Discussion ofresults Credit Risk and Basel Capital for Derivatives Introduction Potential future exposure Real-world measure Traditional approach Adjusted risk-neutral approach Joint measure model approach Standardized approach, CEM and SA-CCR Current standardized approach: CEM New standardized approach: SA-CCR Basel internal model approach Capital requirements for centrally cleared derivatives CVA capital charge The Standard approach The IMM approach Mitigation of the CVA capital charge Exemptions Backtesting Introduction Backtest model framework Example: Anderson-Darling test REE backtesting Creating the sample distance and sampling distribution Example I: Risk-neutral LGM Example II: Risk-neutral LGM with drift adjustment Portfolio backtesting Outlook 390 Part VI Appendix 393 A The Change ofnumeraire Toolkit 395 B The Feynman-Kac Connection 398 C The Black76 Formula 400 C.l The Standard Black76 formula 400 C.2 The normal Black76 formula 401 D Hull-White Model 403 D.l Summary 403 D.2 Bank account and forward measure 407 D.3 Cross-currency Hull-White model 410

8 Contents J xiii E Linear Gauss Markov Model 423 E.l One Factor 423 E.2 Two factors 426 E.3 Cross-currency LGM 430 F Dodgson-Kainth Model 433 F.l Domestic currency inflation 433 F.2 Foreign currency inflation 435 G CIR Model with Jumps 441 H CDS and CDS Option: Filtration Switching and the PK Model 446 Bibliography 450 Index 457

Institute of Actuaries of India. Subject. ST6 Finance and Investment B. For 2018 Examinationspecialist Technical B. Syllabus

Institute of Actuaries of India. Subject. ST6 Finance and Investment B. For 2018 Examinationspecialist Technical B. Syllabus Institute of Actuaries of India Subject ST6 Finance and Investment B For 2018 Examinationspecialist Technical B Syllabus Aim The aim of the second finance and investment technical subject is to instil

More information

Cross Asset CVA Application

Cross Asset CVA Application Cross Asset CVA Application Roland Lichters Quaternion Risk Management IKB QuantLib User Meeting IKB Deutsche Industriebank AG, 13-14 November 2013 1 About Quaternion Specialist risk consulting and solutions,

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

Fixed Income Modelling

Fixed Income Modelling Fixed Income Modelling CLAUS MUNK OXPORD UNIVERSITY PRESS Contents List of Figures List of Tables xiii xv 1 Introduction and Overview 1 1.1 What is fixed income analysis? 1 1.2 Basic bond market terminology

More information

The Next Steps in the xva Journey. Jon Gregory, Global Derivatives, Barcelona, 11 th May 2017 Copyright Jon Gregory 2017 page 1

The Next Steps in the xva Journey. Jon Gregory, Global Derivatives, Barcelona, 11 th May 2017 Copyright Jon Gregory 2017 page 1 The Next Steps in the xva Journey Jon Gregory, Global Derivatives, Barcelona, 11 th May 2017 Copyright Jon Gregory 2017 page 1 The Role and Development of xva CVA and Wrong-Way Risk FVA and MVA framework

More information

With Examples Implemented in Python

With Examples Implemented in Python SABR and SABR LIBOR Market Models in Practice With Examples Implemented in Python Christian Crispoldi Gerald Wigger Peter Larkin palgrave macmillan Contents List of Figures ListofTables Acknowledgments

More information

Advances in Valuation Adjustments. Topquants Autumn 2015

Advances in Valuation Adjustments. Topquants Autumn 2015 Advances in Valuation Adjustments Topquants Autumn 2015 Quantitative Advisory Services EY QAS team Modelling methodology design and model build Methodology and model validation Methodology and model optimisation

More information

Fuel Hedging. Management. Strategien for Airlines, Shippers, VISHNU N. GAJJALA

Fuel Hedging. Management. Strategien for Airlines, Shippers, VISHNU N. GAJJALA Fuel Hedging andrisk Management Strategien for Airlines, Shippers, and Other Consumers S. MOHAMED DAFIR VISHNU N. GAJJALA WlLEY Contents Preface Acknovuledgments Almut the Aiithors xiii xix xxi CHAPTER

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

FIXED INCOME SECURITIES

FIXED INCOME SECURITIES FIXED INCOME SECURITIES Valuation, Risk, and Risk Management Pietro Veronesi University of Chicago WILEY JOHN WILEY & SONS, INC. CONTENTS Preface Acknowledgments PART I BASICS xix xxxiii AN INTRODUCTION

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

Credit Risk Modelling This course can also be presented in-house for your company or via live on-line webinar

Credit Risk Modelling This course can also be presented in-house for your company or via live on-line webinar Credit Risk Modelling This course can also be presented in-house for your company or via live on-line webinar The Banking and Corporate Finance Training Specialist Course Overview For banks and financial

More information

Credit Risk Modelling This in-house course can also be presented face to face in-house for your company or via live in-house webinar

Credit Risk Modelling This in-house course can also be presented face to face in-house for your company or via live in-house webinar Credit Risk Modelling This in-house course can also be presented face to face in-house for your company or via live in-house webinar The Banking and Corporate Finance Training Specialist Course Content

More information

Martingale Methods in Financial Modelling

Martingale Methods in Financial Modelling Marek Musiela Marek Rutkowski Martingale Methods in Financial Modelling Second Edition Springer Table of Contents Preface to the First Edition Preface to the Second Edition V VII Part I. Spot and Futures

More information

Implementing Models in Quantitative Finance: Methods and Cases

Implementing Models in Quantitative Finance: Methods and Cases Gianluca Fusai Andrea Roncoroni Implementing Models in Quantitative Finance: Methods and Cases vl Springer Contents Introduction xv Parti Methods 1 Static Monte Carlo 3 1.1 Motivation and Issues 3 1.1.1

More information

CVA in Energy Trading

CVA in Energy Trading CVA in Energy Trading Arthur Rabatin Credit Risk in Energy Trading London, November 2016 Disclaimer The document author is Arthur Rabatin and all views expressed in this document are his own. All errors

More information

Modern Derivatives Pricing and Credit Exposure Analysis

Modern Derivatives Pricing and Credit Exposure Analysis Modern Derivatives Pricing and Credit Exposure Analysis This page intentionally left blank Modern Derivatives Pricing and Credit Exposure Analysis Theory and Practice of CSA and XVA Pricing, Exposure Simulation

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

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

Counterparty Credit Risk, Collateral and Funding With Pricing Cases for all Asset Classes

Counterparty Credit Risk, Collateral and Funding With Pricing Cases for all Asset Classes Counterparty Credit Risk, Collateral and Funding With Pricing Cases for all Asset Classes Damiano Brigo, Massimo Morini and Andrea Pallavicini Order now, and save!! The book s content is focused on rigorous

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

Callability Features

Callability Features 2 Callability Features 2.1 Introduction and Objectives In this chapter, we introduce callability which gives one party in a transaction the right (but not the obligation) to terminate the transaction early.

More information

XVA S, CSA S & OTC CLEARING

XVA S, CSA S & OTC CLEARING XVA S, CSA S & OTC CLEARING Plus the impact of regulation on OTC Derivatives Date November 2016 Author Darren Hooton, Business and Corporate Sales - FICC DEMYSTIFYING SOME OF THE DERIVATIVE MARKET TLA

More information

Martingale Methods in Financial Modelling

Martingale Methods in Financial Modelling Marek Musiela Marek Rutkowski Martingale Methods in Financial Modelling Second Edition \ 42 Springer - . Preface to the First Edition... V Preface to the Second Edition... VII I Part I. Spot and Futures

More information

Funding Value Adjustments and Discount Rates in the Valuation of Derivatives

Funding Value Adjustments and Discount Rates in the Valuation of Derivatives Funding Value Adjustments and Discount Rates in the Valuation of Derivatives John Hull Marie Curie Conference, Konstanz April 11, 2013 1 Question to be Considered Should funding costs be taken into account

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

Interest Rate Bermudan Swaption Valuation and Risk

Interest Rate Bermudan Swaption Valuation and Risk Interest Rate Bermudan Swaption Valuation and Risk Dmitry Popov FinPricing http://www.finpricing.com Summary Bermudan Swaption Definition Bermudan Swaption Payoffs Valuation Model Selection Criteria LGM

More information

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

2nd Order Sensis: PnL and Hedging

2nd Order Sensis: PnL and Hedging 2nd Order Sensis: PnL and Hedging Chris Kenyon 19.10.2017 Acknowledgements & Disclaimers Joint work with Jacques du Toit. The views expressed in this presentation are the personal views of the speaker

More information

Interest Rate Cancelable Swap Valuation and Risk

Interest Rate Cancelable Swap Valuation and Risk Interest Rate Cancelable Swap Valuation and Risk Dmitry Popov FinPricing http://www.finpricing.com Summary Cancelable Swap Definition Bermudan Swaption Payoffs Valuation Model Selection Criteria LGM Model

More information

INTRODUCTION TO THE ECONOMICS AND MATHEMATICS OF FINANCIAL MARKETS. Jakša Cvitanić and Fernando Zapatero

INTRODUCTION TO THE ECONOMICS AND MATHEMATICS OF FINANCIAL MARKETS. Jakša Cvitanić and Fernando Zapatero INTRODUCTION TO THE ECONOMICS AND MATHEMATICS OF FINANCIAL MARKETS Jakša Cvitanić and Fernando Zapatero INTRODUCTION TO THE ECONOMICS AND MATHEMATICS OF FINANCIAL MARKETS Table of Contents PREFACE...1

More information

Computational Methods in Finance

Computational Methods in Finance Chapman & Hall/CRC FINANCIAL MATHEMATICS SERIES Computational Methods in Finance AM Hirsa Ltfi) CRC Press VV^ J Taylor & Francis Group Boca Raton London New York CRC Press is an imprint of the Taylor &

More information

Hedging CVA. Jon Gregory ICBI Global Derivatives. Paris. 12 th April 2011

Hedging CVA. Jon Gregory ICBI Global Derivatives. Paris. 12 th April 2011 Hedging CVA Jon Gregory (jon@solum-financial.com) ICBI Global Derivatives Paris 12 th April 2011 CVA is very complex CVA is very hard to calculate (even for vanilla OTC derivatives) Exposure at default

More information

OIS and Its Impact on Modeling, Calibration and Funding of OTC Derivatives. May 31, 2012 Satyam Kancharla SVP, Client Solutions Group Numerix LLC

OIS and Its Impact on Modeling, Calibration and Funding of OTC Derivatives. May 31, 2012 Satyam Kancharla SVP, Client Solutions Group Numerix LLC OIS and Its Impact on Modeling, Calibration and Funding of OTC Derivatives May 31, 2012 Satyam Kancharla SVP, Client Solutions Group Numerix LLC Agenda Changes in Interest Rate market dynamics after the

More information

Counterparty Credit Risk

Counterparty Credit Risk Counterparty Credit Risk The New Challenge for Global Financial Markets Jon Gregory ) WILEY A John Wiley and Sons, Ltd, Publication Acknowledgements List of Spreadsheets List of Abbreviations Introduction

More information

Counterparty Credit Risk under Basel III

Counterparty Credit Risk under Basel III Counterparty Credit Risk under Basel III Application on simple portfolios Mabelle SAYAH European Actuarial Journal Conference September 8 th, 2016 Recent crisis and Basel III After recent crisis, and the

More information

palgrave Shipping Derivatives and Risk Management macmiuan Amir H. Alizadeh & Nikos K. Nomikos

palgrave Shipping Derivatives and Risk Management macmiuan Amir H. Alizadeh & Nikos K. Nomikos Shipping Derivatives and Risk Management Amir H. Alizadeh & Nikos K. Nomikos Faculty of Finance, Cass Business School, City University, London palgrave macmiuan Contents About the Authors. xv Preface and

More information

Efficient Lifetime Portfolio Sensitivities: AAD Versus Longstaff-Schwartz Compression Chris Kenyon

Efficient Lifetime Portfolio Sensitivities: AAD Versus Longstaff-Schwartz Compression Chris Kenyon Efficient Lifetime Portfolio Sensitivities: AAD Versus Longstaff-Schwartz Compression Chris Kenyon 26.03.2014 Contact: Chris.Kenyon@lloydsbanking.com Acknowledgments & Disclaimers Joint work with Andrew

More information

How Best To Incorporate The Leverage Ratio, LCR and NSFR into XVA?

How Best To Incorporate The Leverage Ratio, LCR and NSFR into XVA? How Best To Incorporate The Leverage Ratio, LCR and NSFR into XVA? Risk Minds 2015, Amsterdam Andrew Green Contents 1 Introduction 2 Leverage Ratio 3 LCR 4 5 Conclusion 6 Bibliography Disclaimer Joint

More information

PART II FRM 2018 CURRICULUM UPDATES

PART II FRM 2018 CURRICULUM UPDATES PART II FRM 2018 CURRICULUM UPDATES GARP updates the program curriculum every year to ensure study materials and exams reflect the most up-to-date knowledge and skills required to be successful as a risk

More information

IFRS 13 - CVA, DVA AND THE IMPLICATIONS FOR HEDGE ACCOUNTING

IFRS 13 - CVA, DVA AND THE IMPLICATIONS FOR HEDGE ACCOUNTING WHITEPAPER IFRS 13 - CVA, DVA AND THE IMPLICATIONS FOR HEDGE ACCOUNTING By Dmitry Pugachevsky, Rohan Douglas (Quantifi) Searle Silverman, Philip Van den Berg (Deloitte) IFRS 13 ACCOUNTING FOR CVA & DVA

More information

Credit Valuation Adjustment and Funding Valuation Adjustment

Credit Valuation Adjustment and Funding Valuation Adjustment Credit Valuation Adjustment and Funding Valuation Adjustment Alex Yang FinPricing http://www.finpricing.com Summary Credit Valuation Adjustment (CVA) Definition Funding Valuation Adjustment (FVA) Definition

More information

SYLLABUS. IEOR E4728 Topics in Quantitative Finance: Inflation Derivatives

SYLLABUS. IEOR E4728 Topics in Quantitative Finance: Inflation Derivatives SYLLABUS IEOR E4728 Topics in Quantitative Finance: Inflation Derivatives Term: Summer 2007 Department: Industrial Engineering and Operations Research (IEOR) Instructor: Iraj Kani TA: Wayne Lu References:

More information

Quantitative Finance Investment Advanced Exam

Quantitative Finance Investment Advanced Exam Quantitative Finance Investment Advanced Exam Important Exam Information: Exam Registration Order Study Notes Introductory Study Note Case Study Past Exams Updates Formula Package Table Candidates may

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

PART II FRM 2019 CURRICULUM UPDATES

PART II FRM 2019 CURRICULUM UPDATES PART II FRM 2019 CURRICULUM UPDATES GARP updates the program curriculum every year to ensure study materials and exams reflect the most up-to-date knowledge and skills required to be successful as a risk

More information

RISKMETRICS. Dr Philip Symes

RISKMETRICS. Dr Philip Symes 1 RISKMETRICS Dr Philip Symes 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

More information

Strategies For Managing CVA Exposures

Strategies For Managing CVA Exposures Strategies For Managing CVA Exposures Sebastien BOUCARD Global Head of CVA Trading www.ca-cib.com Contact Details Sebastien.boucard@ca-cib.com IMPORTANT NOTICE 2013 CRÉDIT AGRICOLE CORPORATE AND INVESTMENT

More information

Contents. Part I Introduction to Option Pricing

Contents. Part I Introduction to Option Pricing Part I Introduction to Option Pricing 1 Asset Pricing Basics... 3 1.1 Fundamental Concepts.................................. 3 1.2 State Prices in a One-Period Binomial Model.............. 11 1.3 Probabilities

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

Modeling Fixed-Income Securities and Interest Rate Options

Modeling Fixed-Income Securities and Interest Rate Options jarr_fm.qxd 5/16/02 4:49 PM Page iii Modeling Fixed-Income Securities and Interest Rate Options SECOND EDITION Robert A. Jarrow Stanford Economics and Finance An Imprint of Stanford University Press Stanford,

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

FUNDAMENTALS OF FUTURES AND OPTIONS MARKETS

FUNDAMENTALS OF FUTURES AND OPTIONS MARKETS SEVENTH EDITION FUNDAMENTALS OF FUTURES AND OPTIONS MARKETS GLOBAL EDITION John C. Hull / Maple Financial Group Professor of Derivatives and Risk Management Joseph L. Rotman School of Management University

More information

Discounting. Jeroen Kerkhof. 22 September c Copyright VAR Strategies BVBA 1 / 53

Discounting. Jeroen Kerkhof. 22 September c Copyright VAR Strategies BVBA 1 / 53 Discounting Jeroen Kerkhof 22 September 2010 c Copyright VAR Strategies BVBA 1 / 53 Overview c Copyright VAR Strategies BVBA 2 / 53 Time Value of Money c Copyright VAR Strategies BVBA 3 / 53 Time Value

More information

Callable Bond and Vaulation

Callable Bond and Vaulation and Vaulation Dmitry Popov FinPricing http://www.finpricing.com Summary Callable Bond Definition The Advantages of Callable Bonds Callable Bond Payoffs Valuation Model Selection Criteria LGM Model LGM

More information

FINCAD s Flexible Valuation Adjustment Solution

FINCAD s Flexible Valuation Adjustment Solution FINCAD s Flexible Valuation Adjustment Solution Counterparty credit risk measurement and valuation adjustment (CVA, DVA, FVA) computation are business-critical issues for a wide number of financial institutions.

More information

Bank of Japan Workshop - Credit Value Adjustment Trends. 14 th June 2010

Bank of Japan Workshop - Credit Value Adjustment Trends. 14 th June 2010 Bank of Japan Workshop - Credit Value Adjustment Trends 14 th June 2010 Senior Director Theodoros Stampoulis Agenda 1. History 2. Why now Survey; background 2-1 Highlight 2-2 Key findings 3. Updated! CVA

More information

Puttable Bond and Vaulation

Puttable Bond and Vaulation and Vaulation Dmitry Popov FinPricing http://www.finpricing.com Summary Puttable Bond Definition The Advantages of Puttable Bonds Puttable Bond Payoffs Valuation Model Selection Criteria LGM Model LGM

More information

NINTH EDITION FUNDAMENTALS OF. John C. Hüll

NINTH EDITION FUNDAMENTALS OF. John C. Hüll NINTH EDITION FUNDAMENTALS OF FUTURES AND OPTIONS MARKETS John C. Hüll Maple Financial Group Professor of Derivatives and Risk Management Joseph L. Rotman School of Management University of Toronto PEARSON

More information

Economic Scenario Generators

Economic Scenario Generators Economic Scenario Generators A regulator s perspective Falk Tschirschnitz, FINMA Bahnhofskolloquium Motivation FINMA has observed: Calibrating the interest rate model of choice has become increasingly

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

Learning takes you the extra mile. Rabobank Global Learning

Learning takes you the extra mile. Rabobank Global Learning Learning takes you the extra mile Rabobank Global Learning Release 38: 2016 FINANCIAL MARKETS COURSES Introduction to Financial Markets Financial Markets - An Introduction Money Markets - An Introduction

More information

(J)CIR(++) Hazard Rate Model

(J)CIR(++) Hazard Rate Model (J)CIR(++) Hazard Rate Model Henning Segger - Quaternion Risk Management c 2013 Quaternion Risk Management Ltd. All Rights Reserved. 1 1 2 3 4 5 6 c 2013 Quaternion Risk Management Ltd. All Rights Reserved.

More information

Introduction to Bonds The Bond Instrument p. 3 The Time Value of Money p. 4 Basic Features and Definitions p. 5 Present Value and Discounting p.

Introduction to Bonds The Bond Instrument p. 3 The Time Value of Money p. 4 Basic Features and Definitions p. 5 Present Value and Discounting p. Foreword p. xv Preface p. xvii Introduction to Bonds The Bond Instrument p. 3 The Time Value of Money p. 4 Basic Features and Definitions p. 5 Present Value and Discounting p. 6 Discount Factors p. 12

More information

WHITE PAPER THINKING FORWARD ABOUT PRICING AND HEDGING VARIABLE ANNUITIES

WHITE PAPER THINKING FORWARD ABOUT PRICING AND HEDGING VARIABLE ANNUITIES WHITE PAPER THINKING FORWARD ABOUT PRICING AND HEDGING VARIABLE ANNUITIES We can t solve problems by using the same kind of thinking we used when we created them. Albert Einstein As difficult as the recent

More information

Counterparty Risk - wrong way risk and liquidity issues. Antonio Castagna -

Counterparty Risk - wrong way risk and liquidity issues. Antonio Castagna - Counterparty Risk - wrong way risk and liquidity issues Antonio Castagna antonio.castagna@iasonltd.com - www.iasonltd.com 2011 Index Counterparty Wrong-Way Risk 1 Counterparty Wrong-Way Risk 2 Liquidity

More information

Stochastic Interest Rates

Stochastic Interest Rates Stochastic Interest Rates This volume in the Mastering Mathematical Finance series strikes just the right balance between mathematical rigour and practical application. Existing books on the challenging

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

Credit Risk in Derivatives Products

Credit Risk in Derivatives Products Credit Risk in Derivatives Products Understand how derivatives work, how they are used and the inherent credit risk experienced by both banks and their customers This in-house course can be presented in-house

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

Managing the Newest Derivatives Risks

Managing the Newest Derivatives Risks Managing the Newest Derivatives Risks Michel Crouhy IXIS Corporate and Investment Bank / A subsidiary of NATIXIS Derivatives 2007: New Ideas, New Instruments, New markets NYU Stern School of Business,

More information

Dynamic Copula Methods in Finance

Dynamic 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 information

Credit Risk Modeling Using Excel and VBA with DVD O. Gunter Loffler Peter N. Posch. WILEY A John Wiley and Sons, Ltd., Publication

Credit Risk Modeling Using Excel and VBA with DVD O. Gunter Loffler Peter N. Posch. WILEY A John Wiley and Sons, Ltd., Publication Credit Risk Modeling Using Excel and VBA with DVD O Gunter Loffler Peter N. Posch WILEY A John Wiley and Sons, Ltd., Publication Preface to the 2nd edition Preface to the 1st edition Some Hints for Troubleshooting

More information

Credit Risk: Modeling, Valuation and Hedging

Credit Risk: Modeling, Valuation and Hedging Tomasz R. Bielecki Marek Rutkowski Credit Risk: Modeling, Valuation and Hedging Springer Table of Contents Preface V Part I. Structural Approach 1. Introduction to Credit Risk 3 1.1 Corporate Bonds 4 1.1.1

More information

Package xva. November 26, 2016

Package xva. November 26, 2016 Type Package Package xva November 26, 2016 Title Calculates Credit Risk Valuation Adjustments Version 0.8.1 Date 2016-11-19 Author Tasos Grivas Maintainer Calculates a number of valuation adjustments including

More information

An Introduction to Modern Pricing of Interest Rate Derivatives

An Introduction to Modern Pricing of Interest Rate Derivatives School of Education, Culture and Communication Division of Applied Mathematics MASTER THESIS IN MATHEMATICS / APPLIED MATHEMATICS An Introduction to Modern Pricing of Interest Rate Derivatives by Hossein

More information

CVA. What Does it Achieve?

CVA. What Does it Achieve? CVA What Does it Achieve? Jon Gregory (jon@oftraining.com) page 1 Motivation for using CVA The uncertainty of CVA Credit curve mapping Challenging in hedging CVA The impact of Basel III rules page 2 Motivation

More information

AMSTERDAM BOSTON HEIDELBERG LONDON NEW YORK OXFORD PARIS SAN DIEGO SAN FRANCISCO SINGAPORE SYDNEY TOKYO Academic Press is an Imprint of Elsevier

AMSTERDAM BOSTON HEIDELBERG LONDON NEW YORK OXFORD PARIS SAN DIEGO SAN FRANCISCO SINGAPORE SYDNEY TOKYO Academic Press is an Imprint of Elsevier Computational Finance Using C and C# Derivatives and Valuation SECOND EDITION George Levy ELSEVIER AMSTERDAM BOSTON HEIDELBERG LONDON NEW YORK OXFORD PARIS SAN DIEGO SAN FRANCISCO SINGAPORE SYDNEY TOKYO

More information

Financial Risk Management

Financial Risk Management r r Financial Risk Management A Practitioner's Guide to Managing Market and Credit Risk Second Edition STEVEN ALLEN WILEY John Wiley & Sons, Inc. Contents Foreword Preface Acknowledgments About the Author

More information

Strategic Integration of xva, Margining and Regulatory Risk Platforms

Strategic Integration of xva, Margining and Regulatory Risk Platforms Strategic Integration of xva, Margining and Regulatory Risk Platforms Arthur Rabatin Head of Counterparty and Funding Risk Technology, Deutsche Bank AG 2 nd Annual Credit Risk Forum 19 th /20 th May 2016,

More information

Discrete-time Asset Pricing Models in Applied Stochastic Finance

Discrete-time Asset Pricing Models in Applied Stochastic Finance Discrete-time Asset Pricing Models in Applied Stochastic Finance P.C.G. Vassiliou ) WILEY Table of Contents Preface xi Chapter ^Probability and Random Variables 1 1.1. Introductory notes 1 1.2. Probability

More information

On Credit Valuation Adjustment (CVA) under Article 456(2) of Regulation (EU) No 575/2013 (Capital Requirements Regulation CRR)

On Credit Valuation Adjustment (CVA) under Article 456(2) of Regulation (EU) No 575/2013 (Capital Requirements Regulation CRR) EBA Report on CVA 25 February 2015 EBA Report On Credit Valuation Adjustment (CVA) under Article 456(2) of Regulation (EU) No 575/2013 (Capital Requirements Regulation CRR) and EBA Review On the application

More information

we def ine co nsulti n g MoCA Valuation out of the box

we def ine co nsulti n g MoCA Valuation out of the box we def ine co nsulti n g MoCA Valuation out of the box Easy and flexible to use Compact valuation of structured financial derivatives Structured financial derivatives are important tools when applying

More information

Introduction. Practitioner Course: Interest Rate Models. John Dodson. February 18, 2009

Introduction. Practitioner Course: Interest Rate Models. John Dodson. February 18, 2009 Practitioner Course: Interest Rate Models February 18, 2009 syllabus text sessions office hours date subject reading 18 Feb introduction BM 1 25 Feb affine models BM 3 4 Mar Gaussian models BM 4 11 Mar

More information

Implementing a cross asset class CVA and xva Framework

Implementing a cross asset class CVA and xva Framework Implementing a cross asset class CVA and xva Framework Head of CB&S Counterparty and Funding Risk Technology, AG CREDIT RISK Management Forum, May 7 th 8 th 2015 Vienna, Austria Global Universal Bank with

More information

Counterparty Credit Risk Simulation

Counterparty Credit Risk Simulation Counterparty Credit Risk Simulation Alex Yang FinPricing http://www.finpricing.com Summary Counterparty Credit Risk Definition Counterparty Credit Risk Measures Monte Carlo Simulation Interest Rate Curve

More information

Knockout cliquet, 233, 235

Knockout cliquet, 233, 235 Index A ABS. See Asset-backed securities (ABS) Adjustable-rate mortgages (ARMs), 14 Alternative beta, 335 Asset-backed securities (ABS), 48 Asset classes commodities, 2 equities, 2 fixed-income assets,

More information

The role of the Model Validation function to manage and mitigate model risk

The role of the Model Validation function to manage and mitigate model risk arxiv:1211.0225v1 [q-fin.rm] 21 Oct 2012 The role of the Model Validation function to manage and mitigate model risk Alberto Elices November 2, 2012 Abstract This paper describes the current taxonomy of

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

Monte Carlo Methods in Finance

Monte Carlo Methods in Finance Monte Carlo Methods in Finance Peter Jackel JOHN WILEY & SONS, LTD Preface Acknowledgements Mathematical Notation xi xiii xv 1 Introduction 1 2 The Mathematics Behind Monte Carlo Methods 5 2.1 A Few Basic

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

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

Calibration and Simulation of Interest Rate Models in MATLAB Kevin Shea, CFA Principal Software Engineer MathWorks

Calibration and Simulation of Interest Rate Models in MATLAB Kevin Shea, CFA Principal Software Engineer MathWorks Calibration and Simulation of Interest Rate Models in MATLAB Kevin Shea, CFA Principal Software Engineer MathWorks 2014 The MathWorks, Inc. 1 Outline Calibration to Market Data Calibration to Historical

More information

Negative Rates: The Challenges from a Quant Perspective

Negative Rates: The Challenges from a Quant Perspective Negative Rates: The Challenges from a Quant Perspective 1 Introduction Fabio Mercurio Global head of Quantitative Analytics Bloomberg There are many instances in the past and recent history where Treasury

More information

Traded Risk & Regulation

Traded Risk & Regulation DRAFT Traded Risk & Regulation University of Essex Expert Lecture 14 March 2014 Dr Paula Haynes Managing Partner Traded Risk Associates 2014 www.tradedrisk.com Traded Risk Associates Ltd Contents Introduction

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

FOR TRANSFER PRICING

FOR TRANSFER PRICING KAMAKURA RISK MANAGER FOR TRANSFER PRICING KRM VERSION 7.0 SEPTEMBER 2008 www.kamakuraco.com Telephone: 1-808-791-9888 Facsimile: 1-808-791-9898 2222 Kalakaua Avenue, 14th Floor, Honolulu, Hawaii 96815,

More information

Challenges in Counterparty Credit Risk Modelling

Challenges in Counterparty Credit Risk Modelling Challenges in Counterparty Credit Risk Modelling Alexander SUBBOTIN Head of Counterparty Credit Risk Models & Measures, Nordea November 23 th, 2015 Disclaimer This document has been prepared for the purposes

More information

Monte Carlo Methods in Financial Engineering

Monte Carlo Methods in Financial Engineering Paul Glassennan Monte Carlo Methods in Financial Engineering With 99 Figures

More information

Credit Risk in Derivatives Products

Credit Risk in Derivatives Products Credit Risk in Derivatives Products Understand how derivatives work, how they are used and the inherent credit risk experienced by both banks and their customers This in-house course can be presented in-house

More information