Fixed Income Modelling

Size: px
Start display at page:

Download "Fixed Income Modelling"

Transcription

1 Fixed Income Modelling CLAUS MUNK OXPORD UNIVERSITY PRESS

2 Contents List of Figures List of Tables xiii xv 1 Introduction and Overview What is fixed income analysis? Basic bond market terminology Bond markets and money markets Fixed income derivatives An overview of the book Exercises 23 2 Extracting Yield Curves from Bond Prices Introduction Bootstrapping Cubic splines The Nelson-Siegel parametrization Additional remarks on yield curve estimation Exercises 37 3 Stochastic Processes and Stochastic Calculus Introduction What is a stochastic process? Brownian motions Diffusion processes Ito processes Stochastic integrals Ito's Lemma Important diffusion processes Multi-dimensional processes Change of probability measure Exercises 80 4 A Review of General Asset Pricing Theory Introduction Assets, trading strategies, and arbitrage State-price deflators, risk-neutral probabilities, and market prices of risk Other useful probability measures Complete vs. incomplete markets Equilibrium and representative agents in complete markets Extension to intermediate dividends Diffusion models and the fundamental partial differential equation Concluding remarks Exercises 115

3 c Contents 5 The Economics of the Term Structure of Interest Rates Introduction Real interest rates and aggregate consumption Real interest rates and aggregate production Equilibrium term structure models Real and nominal interest rates and term structures The expectation hypothesis Liquidity preference, market segmentation, and preferred habitats Concluding remarks Exercises Fixed Income Securities Introduction Forwards and futures European options Caps, floors, and collars Swaps and swaptions American-style derivatives An overview of term structure models Exercises One-Factor Diffusion Models Introduction Affine models Merton's model Vasicek's model The Cox-Ingersoll-Ross model Generalized affine models Non-affine models Parameter estimation and empirical tests Concluding remarks Exercises Multi-Factor Diffusion Models Introduction The general multi-factor setting Affine multi-factor models Two-factor affine diffusion models Three-factor affine models Generalized affine models Other multi-factor diffusion models Final remarks Exercises Calibration of Diffusion Models Introduction Time-inhomogeneous affine models The Ho-Lee model (extended Merton) The Hull-White model (extended Vasicek) 269

4 Contents xi 9.5 The extended CIR model Calibration to other market data Initial and future term structures in calibrated models Calibrated non-affine models Is a calibrated one-factor model just as good as a multi-factor model? Final remarks Exercises Heath-Jarrow-Morton Models Introduction Basic assumptions Bond price dynamics and the drift restriction Three well-known special cases Gaussian HJM models Diffusion representations of HJM models HJM models with forward-rate dependent volatilities HJM models with unspanned stochastic volatility Concluding remarks Exercises Market Models Introduction General LIBOR market models The lognormal LIBOR market model Alternative LIBOR market models Swap market models Further remarks Exercises The Measurement and Management of Interest Rate Risk Introduction Traditional measures of interest rate risk Risk measures in one-factor diffusion models Immunization Risk measures in multi-factor diffusion models Duration-based pricing of options on bonds Alternative measures of interest rate risk Exercises Defaultable Bonds and Credit Derivatives Introduction Some basic concepts, relations, and practical issues Structural models Reduced-form models Hybrid models Copulas Markets for credit derivatives Credit default swaps (CDSs) Collateralized debt obligations (CDOs) 415

5 xii Contents Concluding remarks Exercises Mortgages and Mortgage-backed Securities Introduction Mortgages Mortgage-backed bonds The prepayment option Rational prepayment models Empirical prepayment models Risk measures for mortgage-backed bonds Other mortgage-backed securities The subprime crisis Concluding remarks Exercises Stock and Currency Derivatives When Interest Rates are Stochastic Introduction Stock options Options on forwards and futures Currency derivatives Final remarks Exercises 16 Numerical Techniques 16.1 Introduction 16.2 Numerical solution of PDEs 16.3 Monte Carlo simulation 16.4 Approximating trees 16.5 Concluding remarks 16.6 Exercises Appendix A: Results on the Lognormal Distribution References Index

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

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

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

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

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

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

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

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

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

Risk-Neutral Valuation

Risk-Neutral Valuation N.H. Bingham and Rüdiger Kiesel Risk-Neutral Valuation Pricing and Hedging of Financial Derivatives W) Springer Contents 1. Derivative Background 1 1.1 Financial Markets and Instruments 2 1.1.1 Derivative

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

Subject CT8 Financial Economics Core Technical Syllabus

Subject CT8 Financial Economics Core Technical Syllabus Subject CT8 Financial Economics Core Technical Syllabus for the 2018 exams 1 June 2017 Aim The aim of the Financial Economics subject is to develop the necessary skills to construct asset liability models

More information

Fixed Income Analysis

Fixed Income Analysis ICEF, Higher School of Economics, Moscow Master Program, Fall 2017 Fixed Income Analysis Course Syllabus Lecturer: Dr. Vladimir Sokolov (e-mail: vsokolov@hse.ru) 1. Course Objective and Format Fixed income

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

The Fixed Income Valuation Course. Sanjay K. Nawalkha Natalia A. Beliaeva Gloria M. Soto

The Fixed Income Valuation Course. Sanjay K. Nawalkha Natalia A. Beliaeva Gloria M. Soto Dynamic Term Structure Modeling The Fixed Income Valuation Course Sanjay K. Nawalkha Natalia A. Beliaeva Gloria M. Soto Dynamic Term Structure Modeling. The Fixed Income Valuation Course. Sanjay K. Nawalkha,

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

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

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

University of Washington at Seattle School of Business and Administration. Asset Pricing - FIN 592

University of Washington at Seattle School of Business and Administration. Asset Pricing - FIN 592 1 University of Washington at Seattle School of Business and Administration Asset Pricing - FIN 592 Office: MKZ 267 Phone: (206) 543 1843 Fax: (206) 221 6856 E-mail: jduarte@u.washington.edu http://faculty.washington.edu/jduarte/

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

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

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

25. Interest rates models. MA6622, Ernesto Mordecki, CityU, HK, References for this Lecture:

25. Interest rates models. MA6622, Ernesto Mordecki, CityU, HK, References for this Lecture: 25. Interest rates models MA6622, Ernesto Mordecki, CityU, HK, 2006. References for this Lecture: John C. Hull, Options, Futures & other Derivatives (Fourth Edition), Prentice Hall (2000) 1 Plan of Lecture

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

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

Quantitative Finance and Investment Core Exam

Quantitative Finance and Investment Core Exam Spring/Fall 2018 Important Exam Information: Exam Registration Candidates may register online or with an application. Order Study Notes Study notes are part of the required syllabus and are not available

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

Curriculum. Written by Administrator Sunday, 03 February :33 - Last Updated Friday, 28 June :10 1 / 10

Curriculum. Written by Administrator Sunday, 03 February :33 - Last Updated Friday, 28 June :10 1 / 10 1 / 10 Ph.D. in Applied Mathematics with Specialization in the Mathematical Finance and Actuarial Mathematics Professor Dr. Pairote Sattayatham School of Mathematics, Institute of Science, email: pairote@sut.ac.th

More information

ADVANCED ASSET PRICING THEORY

ADVANCED ASSET PRICING THEORY Series in Quantitative Finance -Vol. 2 ADVANCED ASSET PRICING THEORY Chenghu Ma Fudan University, China Imperial College Press Contents List of Figures Preface Background Organization and Content Readership

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

Introduction to Financial Mathematics

Introduction to Financial Mathematics Department of Mathematics University of Michigan November 7, 2008 My Information E-mail address: marymorj (at) umich.edu Financial work experience includes 2 years in public finance investment banking

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

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

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

Lecture 5: Review of interest rate models

Lecture 5: Review of interest rate models Lecture 5: Review of interest rate models Xiaoguang Wang STAT 598W January 30th, 2014 (STAT 598W) Lecture 5 1 / 46 Outline 1 Bonds and Interest Rates 2 Short Rate Models 3 Forward Rate Models 4 LIBOR and

More information

Faculty of Science. 2013, School of Mathematics and Statistics, UNSW

Faculty of Science. 2013, School of Mathematics and Statistics, UNSW Faculty of Science School of Mathematics and Statistics MATH5985 TERM STRUCTURE MODELLING Semester 2 2013 CRICOS Provider No: 00098G 2013, School of Mathematics and Statistics, UNSW MATH5985 Course Outline

More information

Master of Science in Finance (MSF) Curriculum

Master of Science in Finance (MSF) Curriculum Master of Science in Finance (MSF) Curriculum Courses By Semester Foundations Course Work During August (assigned as needed; these are in addition to required credits) FIN 510 Introduction to Finance (2)

More information

European call option with inflation-linked strike

European call option with inflation-linked strike Mathematical Statistics Stockholm University European call option with inflation-linked strike Ola Hammarlid Research Report 2010:2 ISSN 1650-0377 Postal address: Mathematical Statistics Dept. of Mathematics

More information

In this appendix, we look at how to measure and forecast yield volatility.

In this appendix, we look at how to measure and forecast yield volatility. Institutional Investment Management: Equity and Bond Portfolio Strategies and Applications by Frank J. Fabozzi Copyright 2009 John Wiley & Sons, Inc. APPENDIX Measuring and Forecasting Yield Volatility

More information

MFE Course Details. Financial Mathematics & Statistics

MFE Course Details. Financial Mathematics & Statistics MFE Course Details Financial Mathematics & Statistics Calculus & Linear Algebra This course covers mathematical tools and concepts for solving problems in financial engineering. It will also help to satisfy

More information

Preface Objectives and Audience

Preface Objectives and Audience Objectives and Audience In the past three decades, we have witnessed the phenomenal growth in the trading of financial derivatives and structured products in the financial markets around the globe and

More information

One-Factor Models { 1 Key features of one-factor (equilibrium) models: { All bond prices are a function of a single state variable, the short rate. {

One-Factor Models { 1 Key features of one-factor (equilibrium) models: { All bond prices are a function of a single state variable, the short rate. { Fixed Income Analysis Term-Structure Models in Continuous Time Multi-factor equilibrium models (general theory) The Brennan and Schwartz model Exponential-ane models Jesper Lund April 14, 1998 1 Outline

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

Table of Contents. Part I. Deterministic Models... 1

Table of Contents. Part I. Deterministic Models... 1 Preface...xvii Part I. Deterministic Models... 1 Chapter 1. Introductory Elements to Financial Mathematics.... 3 1.1. The object of traditional financial mathematics... 3 1.2. Financial supplies. Preference

More information

Changes to Exams FM/2, M and C/4 for the May 2007 Administration

Changes to Exams FM/2, M and C/4 for the May 2007 Administration Changes to Exams FM/2, M and C/4 for the May 2007 Administration Listed below is a summary of the changes, transition rules, and the complete exam listings as they will appear in the Spring 2007 Basic

More information

THE USE OF NUMERAIRES IN MULTI-DIMENSIONAL BLACK- SCHOLES PARTIAL DIFFERENTIAL EQUATIONS. Hyong-chol O *, Yong-hwa Ro **, Ning Wan*** 1.

THE USE OF NUMERAIRES IN MULTI-DIMENSIONAL BLACK- SCHOLES PARTIAL DIFFERENTIAL EQUATIONS. Hyong-chol O *, Yong-hwa Ro **, Ning Wan*** 1. THE USE OF NUMERAIRES IN MULTI-DIMENSIONAL BLACK- SCHOLES PARTIAL DIFFERENTIAL EQUATIONS Hyong-chol O *, Yong-hwa Ro **, Ning Wan*** Abstract The change of numeraire gives very important computational

More information

MFE Course Details. Financial Mathematics & Statistics

MFE Course Details. Financial Mathematics & Statistics MFE Course Details Financial Mathematics & Statistics FE8506 Calculus & Linear Algebra This course covers mathematical tools and concepts for solving problems in financial engineering. It will also help

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

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

Interest rate models in continuous time

Interest rate models in continuous time slides for the course Interest rate theory, University of Ljubljana, 2012-13/I, part IV József Gáll University of Debrecen Nov. 2012 Jan. 2013, Ljubljana Continuous time markets General assumptions, notations

More information

Bond Evaluation, Selection, and Management

Bond Evaluation, Selection, and Management Bond Evaluation, Selection, and Management Second Edition R. STAFFORD JOHNSON WILEY John Wiley &c Sons, Inc. Contents Preface Acknowledgments xvii xxi PART OWE Bond Evaluation 1 CHAPTER 1 Overview of the

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

On the Essential Role of Finance Science in Finance Practice in Asset Management

On the Essential Role of Finance Science in Finance Practice in Asset Management On the Essential Role of Finance Science in Finance Practice in Asset Management Robert C. Merton School of Management Distinguished Professor of Finance Massachusetts Institute of Technology Nobel Laureate

More information

National University of Singapore Dept. of Finance and Accounting. FIN 3120A: Topics in Finance: Fixed Income Securities Lecturer: Anand Srinivasan

National University of Singapore Dept. of Finance and Accounting. FIN 3120A: Topics in Finance: Fixed Income Securities Lecturer: Anand Srinivasan National University of Singapore Dept. of Finance and Accounting FIN 3120A: Topics in Finance: Fixed Income Securities Lecturer: Anand Srinivasan Course Description: This course covers major topics in

More information

ONE NUMERICAL PROCEDURE FOR TWO RISK FACTORS MODELING

ONE NUMERICAL PROCEDURE FOR TWO RISK FACTORS MODELING ONE NUMERICAL PROCEDURE FOR TWO RISK FACTORS MODELING Rosa Cocozza and Antonio De Simone, University of Napoli Federico II, Italy Email: rosa.cocozza@unina.it, a.desimone@unina.it, www.docenti.unina.it/rosa.cocozza

More information

MATL481: INTEREST RATE THEORY N. H. BINGHAM. University of Liverpool, London Campus, Seminar Room 7. Wednesday 31 January 2018

MATL481: INTEREST RATE THEORY N. H. BINGHAM. University of Liverpool, London Campus, Seminar Room 7. Wednesday 31 January 2018 ullint0.tex am Wed 31.1.018 MATL481: INTEREST RATE THEORY N. H. BINGHAM University of Liverpool, London Campus, Seminar Room 7 n.bingham@ic.ac.uk; 00-7594-085 Wednesday 31 January 018 Course website My

More information

LIBOR models, multi-curve extensions, and the pricing of callable structured derivatives

LIBOR models, multi-curve extensions, and the pricing of callable structured derivatives Weierstrass Institute for Applied Analysis and Stochastics LIBOR models, multi-curve extensions, and the pricing of callable structured derivatives John Schoenmakers 9th Summer School in Mathematical Finance

More information

FIXED INCOME ASSET PRICING

FIXED INCOME ASSET PRICING BUS 35130 Autumn 2017 Pietro Veronesi Office: HPC409 (773) 702-6348 pietro.veronesi@ Course Objectives and Overview FIXED INCOME ASSET PRICING The universe of fixed income instruments is large and ever

More information

Empirical Dynamic Asset Pricing

Empirical Dynamic Asset Pricing Empirical Dynamic Asset Pricing Model Specification and Econometric Assessment Kenneth J. Singleton Princeton University Press Princeton and Oxford Preface Acknowledgments xi xiii 1 Introduction 1 1.1.

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

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

STOCHASTIC MODELLING OF ELECTRICITY AND RELATED MARKETS

STOCHASTIC MODELLING OF ELECTRICITY AND RELATED MARKETS Advanced Series on Statistical Science & Applied Probability Vol. I I STOCHASTIC MODELLING OF ELECTRICITY AND RELATED MARKETS Fred Espen Benth JGrate Saltyte Benth University of Oslo, Norway Steen Koekebakker

More information

DEPARTMENT OF FINANCE. Undergraduate Courses Postgraduate Courses

DEPARTMENT OF FINANCE. Undergraduate Courses Postgraduate Courses DEPARTMENT OF FINANCE Undergraduate Courses Postgraduate Courses Undergraduate Courses: FINA 110 Fundamentals of Business Finance [3-0-0:3] For non-sb&m students. Introductory business finance. Topics

More information

MSc Financial Mathematics

MSc Financial Mathematics MSc Financial Mathematics Programme Structure Week Zero Induction Week MA9010 Fundamental Tools TERM 1 Weeks 1-1 0 ST9080 MA9070 IB9110 ST9570 Probability & Numerical Asset Pricing Financial Stoch. Processes

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

Option Models for Bonds and Interest Rate Claims

Option Models for Bonds and Interest Rate Claims Option Models for Bonds and Interest Rate Claims Peter Ritchken 1 Learning Objectives We want to be able to price any fixed income derivative product using a binomial lattice. When we use the lattice to

More information

MFE/3F Questions Answer Key

MFE/3F Questions Answer Key MFE/3F Questions Download free full solutions from www.actuarialbrew.com, or purchase a hard copy from www.actexmadriver.com, or www.actuarialbookstore.com. Chapter 1 Put-Call Parity and Replication 1.01

More information

Introduction to Stochastic Calculus With Applications

Introduction to Stochastic Calculus With Applications Introduction to Stochastic Calculus With Applications Fima C Klebaner University of Melbourne \ Imperial College Press Contents Preliminaries From Calculus 1 1.1 Continuous and Differentiable Functions.

More information

MSc Financial Mathematics

MSc Financial Mathematics MSc Financial Mathematics The following information is applicable for academic year 2018-19 Programme Structure Week Zero Induction Week MA9010 Fundamental Tools TERM 1 Weeks 1-1 0 ST9080 MA9070 IB9110

More information

The Term Structure and Interest Rate Dynamics Cross-Reference to CFA Institute Assigned Topic Review #35

The Term Structure and Interest Rate Dynamics Cross-Reference to CFA Institute Assigned Topic Review #35 Study Sessions 12 & 13 Topic Weight on Exam 10 20% SchweserNotes TM Reference Book 4, Pages 1 105 The Term Structure and Interest Rate Dynamics Cross-Reference to CFA Institute Assigned Topic Review #35

More information

How to Implement Market Models Using VBA

How to Implement Market Models Using VBA How to Implement Market Models Using VBA How to Implement Market Models Using VBA FRANÇOIS GOOSSENS This edition first published 2015 2015 François Goossens Registered office John Wiley & Sons Ltd, The

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

CONTENTS. Introduction. Acknowledgments. What Is New in the Second Edition? Option Pricing Formulas Overview. Glossary of Notations

CONTENTS. Introduction. Acknowledgments. What Is New in the Second Edition? Option Pricing Formulas Overview. Glossary of Notations Introduction Acknowledgments What Is New in the Second Edition? Option Pricing Formulas Overview Glossary of Notations xvii xix xxi xxiii xxxv 1 Black-Scholes-Merton 1 1.1 Black-Scholes-Merton 2 1.1.1

More information

An Equilibrium Model of the Term Structure of Interest Rates

An Equilibrium Model of the Term Structure of Interest Rates Finance 400 A. Penati - G. Pennacchi An Equilibrium Model of the Term Structure of Interest Rates When bond prices are assumed to be driven by continuous-time stochastic processes, noarbitrage restrictions

More information

Lahore University of Management Sciences. FINN 422 Quantitative Finance Fall Semester 2015

Lahore University of Management Sciences. FINN 422 Quantitative Finance Fall Semester 2015 FINN 422 Quantitative Finance Fall Semester 2015 Instructors Room No. Office Hours Email Telephone Secretary/TA TA Office Hours Course URL (if any) Ferhana Ahmad 314 SDSB TBD ferhana.ahmad@lums.edu.pk

More information

Financial Modeling, Actuarial Valuation and Solvency in Insurance

Financial Modeling, Actuarial Valuation and Solvency in Insurance Mario V. Wiithrich Michael Merz Financial Modeling, Actuarial Valuation and Solvency in Insurance 4y Springer Contents 1 Introduction 1 1.1 Full Balance Sheet Approach 3 1.2 -Solvency Considerations 4

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

Term Structure Lattice Models

Term Structure Lattice Models IEOR E4706: Foundations of Financial Engineering c 2016 by Martin Haugh Term Structure Lattice Models These lecture notes introduce fixed income derivative securities and the modeling philosophy used to

More information

MFE/3F Questions Answer Key

MFE/3F Questions Answer Key MFE/3F Questions Download free full solutions from www.actuarialbrew.com, or purchase a hard copy from www.actexmadriver.com, or www.actuarialbookstore.com. Chapter 1 Put-Call Parity and Replication 1.01

More information

FINN 422 Quantitative Finance Fall Semester 2016

FINN 422 Quantitative Finance Fall Semester 2016 FINN 422 Quantitative Finance Fall Semester 2016 Instructors Ferhana Ahmad Room No. 314 SDSB Office Hours TBD Email ferhana.ahmad@lums.edu.pk, ferhanaahmad@gmail.com Telephone +92 42 3560 8044 (Ferhana)

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

Asset Pricing and Portfolio. Choice Theory SECOND EDITION. Kerry E. Back

Asset Pricing and Portfolio. Choice Theory SECOND EDITION. Kerry E. Back Asset Pricing and Portfolio Choice Theory SECOND EDITION Kerry E. Back Preface to the First Edition xv Preface to the Second Edition xvi Asset Pricing and Portfolio Puzzles xvii PART ONE Single-Period

More information

POSSIBILITY CGIA CURRICULUM

POSSIBILITY CGIA CURRICULUM LIMITLESSPOSSIBILITY CGIA CURRICULUM CANDIDATES BODY OF KNOWLEDGE FOR 2017 ABOUT CGIA The Chartered Global Investment Analyst (CGIA) is the world s largest and recognized professional body providing approved

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

Math 416/516: Stochastic Simulation

Math 416/516: Stochastic Simulation Math 416/516: Stochastic Simulation Haijun Li lih@math.wsu.edu Department of Mathematics Washington State University Week 13 Haijun Li Math 416/516: Stochastic Simulation Week 13 1 / 28 Outline 1 Simulation

More information

Lecture 18. More on option pricing. Lecture 18 1 / 21

Lecture 18. More on option pricing. Lecture 18 1 / 21 Lecture 18 More on option pricing Lecture 18 1 / 21 Introduction In this lecture we will see more applications of option pricing theory. Lecture 18 2 / 21 Greeks (1) The price f of a derivative depends

More information

The LIBOR Market Model and the volatility smile

The LIBOR Market Model and the volatility smile University of South Africa The LIBOR Market Model and the volatility smile Author: Michael Tavares Supervisor: Professor. B Swart Abstract The LIBOR Market Model (LLM) is a popular term structure interest

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

Practical example of an Economic Scenario Generator

Practical example of an Economic Scenario Generator Practical example of an Economic Scenario Generator Martin Schenk Actuarial & Insurance Solutions SAV 7 March 2014 Agenda Introduction Deterministic vs. stochastic approach Mathematical model Application

More information

M.I.T Financial Engineering

M.I.T Financial Engineering M.I.T. 15.460 Sloan School of Management Financial Engineering Kogan, Lo and Wang Fall 2016 Course Description Financial Engineering This course provides an introduction to financial engineering. The course

More information

From Discrete Time to Continuous Time Modeling

From Discrete Time to Continuous Time Modeling From Discrete Time to Continuous Time Modeling Prof. S. Jaimungal, Department of Statistics, University of Toronto 2004 Arrow-Debreu Securities 2004 Prof. S. Jaimungal 2 Consider a simple one-period economy

More information

Martingale Methods in Financial Modelling

Martingale Methods in Financial Modelling Stochastic Modelling and Applied Probability 36 Martingale Methods in Financial Modelling Bearbeitet von Marek Musiela, Marek Rutkowski 2nd ed. 2005. Corr. 3rd printing 2008. Buch. xvi, 638 S. Hardcover

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

Term Structure Models Workshop at AFIR-ERM Colloquium, Panama, 2017

Term Structure Models Workshop at AFIR-ERM Colloquium, Panama, 2017 Term Structure Models Workshop at AFIR-ERM Colloquium, Panama, 2017 Michael Sherris CEPAR and School of Risk and Actuarial Studies UNSW Business School UNSW Sydney m.sherris@unsw.edu.au UNSW August 2017

More information

Frank J. Fabozzi, CFA

Frank J. Fabozzi, CFA SEVENTH EDITION Frank J. Fabozzi, CFA Professor in the Practice of Finance Yale School of Management Boston San Francisco New York London Toronto Sydney Tokyo Singapore Madrid Mexico City Munich Paris

More information

MFIN 7003 Module 2. Mathematical Techniques in Finance. Sessions B&C: Oct 12, 2015 Nov 28, 2015

MFIN 7003 Module 2. Mathematical Techniques in Finance. Sessions B&C: Oct 12, 2015 Nov 28, 2015 MFIN 7003 Module 2 Mathematical Techniques in Finance Sessions B&C: Oct 12, 2015 Nov 28, 2015 Instructor: Dr. Rujing Meng Room 922, K. K. Leung Building School of Economics and Finance The University of

More information

Interest-Rate Models. WWW: andrewc/ Prepared for the Encyclopaedia of Actuarial Science

Interest-Rate Models.   WWW:  andrewc/ Prepared for the Encyclopaedia of Actuarial Science Interest-Rate Models Andrew J.G. Cairns Actuarial Mathematics and Statistics School of Mathematical and Computer Sciences Heriot-Watt University Edinburgh, EH14 4AS, United Kingdom E-mail: A.Cairns@ma.hw.ac.uk

More information

The term structure model of corporate bond yields

The term structure model of corporate bond yields The term structure model of corporate bond yields JIE-MIN HUANG 1, SU-SHENG WANG 1, JIE-YONG HUANG 2 1 Shenzhen Graduate School Harbin Institute of Technology Shenzhen University Town in Shenzhen City

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

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