Policyholder Exercise Behavior for Variable Annuities including Guaranteed Minimum Withdrawal Benefits 1

Size: px
Start display at page:

Download "Policyholder Exercise Behavior for Variable Annuities including Guaranteed Minimum Withdrawal Benefits 1"

Transcription

1 Policyholder Exercise Behavior for Variable Annuiies including Guaraneed Minimum Wihdrawal Benefis 1 2 Deparmen of Risk Managemen and Insurance, Georgia Sae Universiy 35 Broad Sree, 11h Floor; Alana, GA 30303; USA horsen@gsu.edu June We graefully acknowledge sponsorship by he Sociey of Acuaries. 2 Join work wih Dr. Daniel Bauer, Georgia Sae Universiy

2 Page 2 / 23 Overview 1 Inroducion 2 A Lifeime Uiliy Model for Variable Annuiies 3 Resuls 4 Conclusions and Fuure Research

3 Page 3 / 23 Inroducion 1 Inroducion Moivaion Risk-Neural Valuaion Approach 2 A Lifeime Uiliy Model for Variable Annuiies 3 Resuls 4 Conclusions and Fuure Research

4 Page 4 / 23 Inroducion Moivaion Variable Annuiies: Popular long-erm invesmen vehicles Tax-deferred growh Invesmen evolves according o underlying (risky) porfolio Uncerain payou Guaraneed Minimum (Deah / Income / Accumulaion / Wihdrawal) Benefis Insurers offer guaraneed paymens Policyholders can purchase securiy Similar o (combinaion of) financial opions

5 Page 5 / 23 Inroducion Moivaion Wihdrawal uncerainy Could miigae or inensify insurer s exposure o invesmen and/or moraliy risks Ineracions non-rivial Affecs pricing and risk managemen Insurers in rouble Disinermediaion in 1970s Equiable Life closed o new business in 2000 The Harford acceped $3.4B in TARP money in June 2009 afer losing $2.75B in 2008, hur by invesmen losses and he cos of VA guaranees

6 Page 6 / 23 Inroducion Risk-Neural Valuaion Approach Used in acuarial lieraure o price variey of opions: Milevsky and Posner (2001): GMDB Ulm (2006): Real opion o ransfer Zaglauer and Bauer (2008): Paricipaing life insurance conracs To analyze wihdrawal behavior for GMWBs: Milevsky and Salisbury (2006) Bauer, Kling and Russ (2008) Opimal sopping problem, akin o pricing American pu opion Exercise / Wihdraw if exercise value exceeds coninuaion value Wors-case scenario, calculae correc upper bound VA marke incomplee: canno sell or repurchase policy a is risk-neural value Wihdrawing means giving up possible guaranees and ax benefis

7 Page 7 / 23 A Lifeime Uiliy Model for Variable Annuiies 1 Inroducion 2 A Lifeime Uiliy Model for Variable Annuiies The Model Bellman Equaion Implemenaion in a Black-Scholes Framework Parameer Assumpions 3 Resuls 4 Conclusions and Fuure Research

8 Page 8 / 23 A Lifeime Uiliy Model for Variable Annuiies The Model Consider wihdrawal decisions in life-cycle model wih ouside invesmen PH maximizes expeced lifeime uiliy Consumpion and bequess Iniial wealh W 0 Annual (deerminisic) income I Invess P 0 in VA wih finie mauriy T, remainder in ouside accoun Includes GMWB, possibly oher guaranees Reurn-of-invesmen guaranees Oher ypes possible, a cos of larger sae space All guaranee accouns idenical o benefis base, G Annual guaranee fee φ as percenage of concurren accoun value

9 Page 9 / 23 A Lifeime Uiliy Model for Variable Annuiies The Model VAs grow ax-deferred Wihdrawals axed on las-in firs-ou basis Early wihdrawal ax (10%) if PH wihdraws prior o age 59.5 Resric all acions o policy anniversary daes Four sae variables VA accoun X Ouside accoun A Benefis base G Tax base H Three choice variables Wihdrawal amoun w Consumpion C Risk allocaion in ouside accoun ν

10 Page 10 / 23 A Lifeime Uiliy Model for Variable Annuiies Bellman Equaion V (y ) = max C,w,ν u C (C )+e β E [q x+ u B (b +1 S +1 ) + p x+ V +1 (y +1 S +1 )], (1) y (A, X, G, H ), ( ) + X + = X w, A + = A + I + w C fee I fee G axes, fee I = s max { w min(g W, G W ) }, fee G = s g (w fee I ) I {x+<59.5}, axes = τ min{w fee I fee G, (X H ) + }, ( G w ) + : w g ( { } ) W G +1 = min G w, G X + + X : w > g W ( ( ) ) + + H +1 = H w X H, [ ( ) ] + A +1 = A + ν S+1 κ ν S S+1 1, S [ ] X +1 = X + e φ ν X S+1, S b +1 = A +1 + max{x +1, GD +1 }, ν 0, i ν (i) = 1,,

11 Page 11 / 23 A Lifeime Uiliy Model for Variable Annuiies Implemenaion in a Black-Scholes Framework Solve by recursive dynamic programming: (I) Creae appropriae sae space grid (II) For = T : for all grid poins (A, X, G, H), compue V T (A, X, G, H). (III) For = T 1, T 2,..., 1: Given V +1, calculae V (A, X, G, H) recursively for each (A, X, G, H) on he grid using an approximaion of he inegral in (1) Discreize reurn space and evaluae via Green s funcion Gauss-Hermie quadraure (IV) For = 0: For he given saring values A 0 = W 0 P 0, X 0 = P 0, G 0 = G 1 = P 0 and H 0 = H 1 = P 0, compue V 0 (W 0 P 0, P 0, P 0, P 0 ) recursively from Equaion (1)

12 Page 12 / 23 A Lifeime Uiliy Model for Variable Annuiies Parameer Assumpions Policyholder is 55 years old, T = 15 years o mauriy P 0 = 100K ; W 0 = 2 P 0 = 200K ; I = 40K CRRA(γ = 3) uiliies; B = 1; β = r τ = 30%, κ = 15% Guaranee fee φ = 50 bps Surrender fee s = 5%, { g W 0 : 5 = 20, 000 : > 5 r = 4%, µ = 8%, σ = 15% Meron raio: µ r = σ2 γ ν X = 100% equiy exposure in VA

13 Page 13 / 23 Resuls 1 Inroducion 2 A Lifeime Uiliy Model for Variable Annuiies 3 Resuls Wihdrawal Behavior Pricing and Sensiiviies 4 Conclusions and Fuure Research

14 Page 14 / 23 Resuls Wihdrawal Behavior Lile wihdrawal aciviy (approx. 12K per PH on average) No wihdrawals during accumulaion period No premaure wihdrawals in 67% of cases PH empies guaranee accoun in 6% of cases < 1% chance of excessive wihdrawal during conrac phase Two main reasons o wihdraw premaurely: VA accoun below ax base (approx. 7K on average) Nuanced paerns Ineracion of in-he-moneyness of guaranee, ax consideraions and excess wihdrawal charge VA accoun much greaer han ouside accoun (approx. 5K on average) To reduce overall risk exposure (Meron raio)

15 Page 15 / 23 Resuls Wihdrawal Behavior Fig. 1: =14, A 15 x 104 = 180K, Gṫ = 100K, H = 100K. w 14 max(guaranee,x ) w X x 10 4

16 Page 16 / 23 Resuls Wihdrawal Behavior Fig. 3: =10, A 15 x 104 = 180K, Gṫ = 100K, H = 100K. w 14 max(guaranee,x ) w X x 10 4

17 Page 17 / 23 Resuls Wihdrawal Behavior Fig. 7: =10, A 8 x 104 = 20K, Gṫ = 100K, H = 100K. w C A + I = 60K w,c X x 10 5

18 Page 18 / 23 Resuls Pricing and Sensiiviies Guaranee fee of φ = 50 bps sufficien o cover expeced coss In-he-moneyness appears o be OK proxy for pricing Differen source o wihdrawals Eliminaing excess wihdrawal fee increases ne profis (win-win) Base Case w/d if X G s = 0% E Q [Fees] 6, 252 5, 925 5, 907 E Q [Excess-Fee] E Q [Guaranee] 4, 558 4, 761 2, 136 %(Guaranee > 0) 24.34% 33.97% 31.94% E[agg. w/d] 12, , , 374 E[agg. w/d & 6] 0 0 4, 374 E[agg. w/d & X H ] 6, , 119 6, 047 E[agg. w/d & X > H ] 5, , 816

19 Page 19 / 23 Resuls Pricing and Sensiiviies Wihdrawal paerns highly sensiive o volailiy Considering axes imporan BC: σ = 15% σ = 20% σ = 25% No Taxes E Q [Fees] 6, 252 6, 047 5, 152 4, 734 E Q [Excess-Fee] , E Q [Guaranee] 4, 558 8, , 533 4, 746 %(Guaranee > 0) 24.34% 36.48% 45.57% 28.16% E[agg. w/d] 12, , , , 791 E[agg. w/d & 6] , E[agg. w/d & X H ] 6, , , , 500 E[agg. w/d & X > H ] 5, , , , 033

20 Page 20 / 23 Conclusions and Fuure Research 1 Inroducion 2 A Lifeime Uiliy Model for Variable Annuiies 3 Resuls 4 Conclusions and Fuure Research

21 Page 21 / 23 Conclusions and Fuure Research Develop lifeime-uiliy model o analyze wihdrawal behavior for VA wih guaranees Numerically solve policyholder s decision making problem in Black-Scholes framework Reurn-of-invesmen GMWB Infrequen wihdrawals PH wihdraws when VA accoun is below ax base Ineracion of in-he-moneyness of guaranee, ax consideraions and excess w/d fee PH wihdraws when VA accoun is large To lower overall risk exposure

22 Page 22 / 23 Conclusions and Fuure Research Exend policyholder environmen Unemploymen Risk Subjecive moraliies Wihdrawal paerns highly sensiive w.r.. volailiy σ Sochasic volailiy framework Alernaives o EUT Epsein-Zin preferences Correlaion Aversion

23 Page 23 / 23 THANK YOU!

A pricing model for the Guaranteed Lifelong Withdrawal Benefit Option

A pricing model for the Guaranteed Lifelong Withdrawal Benefit Option A pricing model for he Guaraneed Lifelong Wihdrawal Benefi Opion Gabriella Piscopo Universià degli sudi di Napoli Federico II Diparimeno di Maemaica e Saisica Index Main References Survey of he Variable

More information

Pricing Guaranteed Annuity Option with Surrender Rates Consideration

Pricing Guaranteed Annuity Option with Surrender Rates Consideration Pricing Guaraneed Annuiy Opion wih Surrender Raes Consideraion Shing-Her Juang Deparmen of Financial Engineering & Acuarial Mahemaics, Soochow Universiy, Taiwan Shu-Chuan Chen Acuarial Deparmen, Bank Taiwan

More information

Analyzing Surplus Appropriation Schemes in Participating Life Insurance from the Insurer s and the Policyholder s Perspective

Analyzing Surplus Appropriation Schemes in Participating Life Insurance from the Insurer s and the Policyholder s Perspective Analyzing Surplus Appropriaion Schemes in Paricipaing Life Insurance from he Insurer s and he Policyholder s Perspecive AFIR Colloquium Madrid, Spain June 22, 2 Alexander Bohner and Nadine Gazer Universiy

More information

Fee Structure and Surrender Incentives in Variable Annuities

Fee Structure and Surrender Incentives in Variable Annuities Fee Srucure and Surrender Incenives in Variable Annuiies by Anne MacKay A hesis presened o he Universiy of Waerloo in fulfillmen of he hesis requiremen for he degree of Docor of Philosophy in Acuarial

More information

You should turn in (at least) FOUR bluebooks, one (or more, if needed) bluebook(s) for each question.

You should turn in (at least) FOUR bluebooks, one (or more, if needed) bluebook(s) for each question. UCLA Deparmen of Economics Spring 05 PhD. Qualifying Exam in Macroeconomic Theory Insrucions: This exam consiss of hree pars, and each par is worh 0 poins. Pars and have one quesion each, and Par 3 has

More information

The Impact of Stochastic Volatility on Pricing, Hedging, and Hedge Efficiency of Variable Annuity Guarantees

The Impact of Stochastic Volatility on Pricing, Hedging, and Hedge Efficiency of Variable Annuity Guarantees The Impac of Sochasic Volailiy on Pricing, Hedging, and Hedge Efficiency of Variable Annuiy Guaranees Alexander Kling *, Frederik Ruez and Jochen Ruß This Version: Augus 14, 2009 Absrac We analyze differen

More information

Li Gan Guan Gong Michael Hurd. April, 2006

Li Gan Guan Gong Michael Hurd. April, 2006 Ne Inergeneraional Transfers from an Increase in Social Securiy Benefis Li Gan Guan Gong Michael Hurd April, 2006 ABSTRACT When he age of deah is uncerain, individuals will leave bequess even if hey have

More information

FAIR VALUATION OF INSURANCE LIABILITIES. Pierre DEVOLDER Université Catholique de Louvain 03/ 09/2004

FAIR VALUATION OF INSURANCE LIABILITIES. Pierre DEVOLDER Université Catholique de Louvain 03/ 09/2004 FAIR VALUATION OF INSURANCE LIABILITIES Pierre DEVOLDER Universié Caholique de Louvain 03/ 09/004 Fair value of insurance liabiliies. INTRODUCTION TO FAIR VALUE. RISK NEUTRAL PRICING AND DEFLATORS 3. EXAMPLES

More information

Option Valuation of Oil & Gas E&P Projects by Futures Term Structure Approach. Hidetaka (Hugh) Nakaoka

Option Valuation of Oil & Gas E&P Projects by Futures Term Structure Approach. Hidetaka (Hugh) Nakaoka Opion Valuaion of Oil & Gas E&P Projecs by Fuures Term Srucure Approach March 9, 2007 Hideaka (Hugh) Nakaoka Former CIO & CCO of Iochu Oil Exploraion Co., Ld. Universiy of Tsukuba 1 Overview 1. Inroducion

More information

Constructing Out-of-the-Money Longevity Hedges Using Parametric Mortality Indexes. Johnny Li

Constructing Out-of-the-Money Longevity Hedges Using Parametric Mortality Indexes. Johnny Li 1 / 43 Consrucing Ou-of-he-Money Longeviy Hedges Using Parameric Moraliy Indexes Johnny Li Join-work wih Jackie Li, Udiha Balasooriya, and Kenneh Zhou Deparmen of Economics, The Universiy of Melbourne

More information

FINAL EXAM EC26102: MONEY, BANKING AND FINANCIAL MARKETS MAY 11, 2004

FINAL EXAM EC26102: MONEY, BANKING AND FINANCIAL MARKETS MAY 11, 2004 FINAL EXAM EC26102: MONEY, BANKING AND FINANCIAL MARKETS MAY 11, 2004 This exam has 50 quesions on 14 pages. Before you begin, please check o make sure ha your copy has all 50 quesions and all 14 pages.

More information

UCLA Department of Economics Fall PhD. Qualifying Exam in Macroeconomic Theory

UCLA Department of Economics Fall PhD. Qualifying Exam in Macroeconomic Theory UCLA Deparmen of Economics Fall 2016 PhD. Qualifying Exam in Macroeconomic Theory Insrucions: This exam consiss of hree pars, and you are o complee each par. Answer each par in a separae bluebook. All

More information

The macroeconomic effects of fiscal policy in Greece

The macroeconomic effects of fiscal policy in Greece The macroeconomic effecs of fiscal policy in Greece Dimiris Papageorgiou Economic Research Deparmen, Bank of Greece Naional and Kapodisrian Universiy of Ahens May 22, 23 Email: dpapag@aueb.gr, and DPapageorgiou@bankofgreece.gr.

More information

NBER WORKING PAPER SERIES THE EFFECT OF UNCERTAIN LABOR INCOME AND SOCIAL SECURITY ON LIFE-CYCLE PORTFOLIOS

NBER WORKING PAPER SERIES THE EFFECT OF UNCERTAIN LABOR INCOME AND SOCIAL SECURITY ON LIFE-CYCLE PORTFOLIOS NBER WORKING PAPER SERIES THE EFFECT OF UNCERTAIN LABOR INCOME AND SOCIAL SECURITY ON LIFE-CYCLE PORTFOLIOS Raimond Maurer Olivia S. Michell Ralph Rogalla Working Paper 15682 hp://www.nber.org/papers/w15682

More information

Fundamental Basic. Fundamentals. Fundamental PV Principle. Time Value of Money. Fundamental. Chapter 2. How to Calculate Present Values

Fundamental Basic. Fundamentals. Fundamental PV Principle. Time Value of Money. Fundamental. Chapter 2. How to Calculate Present Values McGraw-Hill/Irwin Chaper 2 How o Calculae Presen Values Principles of Corporae Finance Tenh Ediion Slides by Mahew Will And Bo Sjö 22 Copyrigh 2 by he McGraw-Hill Companies, Inc. All righs reserved. Fundamenal

More information

Actuarial Research Paper No. 186

Actuarial Research Paper No. 186 Faculy of Acuarial Science and Insurance Acuarial Research Paper No. 86 Opimal Funding and Invesmen Sraegies in Defined Conribuion Pension Plans under Epsein-Zin Uiliy David Blake Douglas Wrigh Yumeng

More information

Risk Management of Variable Annuities

Risk Management of Variable Annuities Fakulä für Mahemaik und Wirschafswissenschafen Insiu für Versicherungswissenschafen Risk Managemen of Variable Annuiies Disseraion zur Erlangung des akademischen Grades eines Dokors der Wirschafswissenschafen

More information

INSTITUTE OF ACTUARIES OF INDIA

INSTITUTE OF ACTUARIES OF INDIA INSIUE OF ACUARIES OF INDIA EAMINAIONS 23 rd May 2011 Subjec S6 Finance and Invesmen B ime allowed: hree hours (9.45* 13.00 Hrs) oal Marks: 100 INSRUCIONS O HE CANDIDAES 1. Please read he insrucions on

More information

On the Interaction between Transfer Restrictions and Crediting Strategies in Guaranteed Funds

On the Interaction between Transfer Restrictions and Crediting Strategies in Guaranteed Funds Georgia Sae Universiy ScholarWorks @ Georgia Sae Universiy Risk Managemen and Insurance Faculy Publicaions Deparmen of Risk Managemen and Insurance 2015 On he Ineracion beween Transfer Resricions and Crediing

More information

1. Interest Rate Gap. Duration

1. Interest Rate Gap. Duration . Ineres Rae Gap. Duraion Mauriy Gap Problem. Mauriy Gap A bank invess $00 million in 3-year, 0% fixed rae bonds (assume hese are all asses) In he same ime, i issuses $90 million in -year, 0% percen fixed

More information

MORNING SESSION. Date: Wednesday, October 30, 2013 Time: 8:30 a.m. 11:45 a.m. INSTRUCTIONS TO CANDIDATES

MORNING SESSION. Date: Wednesday, October 30, 2013 Time: 8:30 a.m. 11:45 a.m. INSTRUCTIONS TO CANDIDATES SOCIETY OF ACTUARIES Quaniaive Finance and Invesmens Core Exam QFI CORE MORNING SESSION Dae: Wednesday, Ocober 30, 013 Time: 8:30 a.m. 11:45 a.m. INSTRUCTIONS TO CANDIDATES General Insrucions 1. This examinaion

More information

Risk Management of a DB Underpin Pension Plan

Risk Management of a DB Underpin Pension Plan Risk Managemen of a DB Underpin Pension Plan Kai Chen upervisor: Mary Hardy Acknowledge he UW Insiue for Quaniaive Finance and Insurance CKER ARC Travel Gran for heir uppor Ouline Inroducion and Background

More information

(1 + Nominal Yield) = (1 + Real Yield) (1 + Expected Inflation Rate) (1 + Inflation Risk Premium)

(1 + Nominal Yield) = (1 + Real Yield) (1 + Expected Inflation Rate) (1 + Inflation Risk Premium) 5. Inflaion-linked bonds Inflaion is an economic erm ha describes he general rise in prices of goods and services. As prices rise, a uni of money can buy less goods and services. Hence, inflaion is an

More information

Optimizing the Retirement Portfolio: Asset Allocation, Annuitization, and Risk Aversion

Optimizing the Retirement Portfolio: Asset Allocation, Annuitization, and Risk Aversion Opimizing he Reiremen Porfolio: Asse Allocaion, Annuiizaion, and Risk Aversion WOLFRAM J. HORNEFF, RAIMOND MAURER, OLIVIA S. MITCHELL, AND IVICA DUS PRC WP 2006-10 Pension Research Council Working Paper

More information

The Interaction of Guarantees, Surplus Distribution, and Asset Allocation in With Profit Life Insurance Policies

The Interaction of Guarantees, Surplus Distribution, and Asset Allocation in With Profit Life Insurance Policies The Ineracion of Guaranees, Surplus Disribuion, and Asse Allocaion in Wih Profi Life Insurance Policies Alexander Kling Universiy of Ulm, Germany phone: +49 731 5031183, fax: +49 731 5031239 alkli@mahemaik.uni-ulm.de

More information

An Incentive-Based, Multi-Period Decision Model for Hierarchical Systems

An Incentive-Based, Multi-Period Decision Model for Hierarchical Systems Wernz C. and Deshmukh A. An Incenive-Based Muli-Period Decision Model for Hierarchical Sysems Proceedings of he 3 rd Inernaional Conference on Global Inerdependence and Decision Sciences (ICGIDS) pp. 84-88

More information

The Mathematics Of Stock Option Valuation - Part Four Deriving The Black-Scholes Model Via Partial Differential Equations

The Mathematics Of Stock Option Valuation - Part Four Deriving The Black-Scholes Model Via Partial Differential Equations The Mahemaics Of Sock Opion Valuaion - Par Four Deriving The Black-Scholes Model Via Parial Differenial Equaions Gary Schurman, MBE, CFA Ocober 1 In Par One we explained why valuing a call opion as a sand-alone

More information

Optimal Early Exercise of Vulnerable American Options

Optimal Early Exercise of Vulnerable American Options Opimal Early Exercise of Vulnerable American Opions March 15, 2008 This paper is preliminary and incomplee. Opimal Early Exercise of Vulnerable American Opions Absrac We analyze he effec of credi risk

More information

Government Expenditure Composition and Growth in Chile

Government Expenditure Composition and Growth in Chile Governmen Expendiure Composiion and Growh in Chile January 2007 Carlos J. García Cenral Bank of Chile Saniago Herrera World Bank Jorge E. Resrepo Cenral Bank of Chile Organizaion of he presenaion:. Inroducion

More information

May 2007 Exam MFE Solutions 1. Answer = (B)

May 2007 Exam MFE Solutions 1. Answer = (B) May 007 Exam MFE Soluions. Answer = (B) Le D = he quarerly dividend. Using formula (9.), pu-call pariy adjused for deerminisic dividends, we have 0.0 0.05 0.03 4.50 =.45 + 5.00 D e D e 50 e = 54.45 D (

More information

Parameter Uncertainty: The Missing Piece of the Liquidity Premium Puzzle?

Parameter Uncertainty: The Missing Piece of the Liquidity Premium Puzzle? Parameer Uncerainy: The Missing Piece of he Liquidiy Premium Puzzle? Ferenc Horvah Tilburg Universiy November 14, 2016 Absrac I analyze a dynamic invesmen problem wih sochasic ransacion cos and parameer

More information

INSTITUTE OF ACTUARIES OF INDIA

INSTITUTE OF ACTUARIES OF INDIA INSTITUTE OF ACTUARIES OF INDIA EXAMINATIONS 05 h November 007 Subjec CT8 Financial Economics Time allowed: Three Hours (14.30 17.30 Hrs) Toal Marks: 100 INSTRUCTIONS TO THE CANDIDATES 1) Do no wrie your

More information

IJRSS Volume 2, Issue 2 ISSN:

IJRSS Volume 2, Issue 2 ISSN: A LOGITIC BROWNIAN MOTION WITH A PRICE OF DIVIDEND YIELDING AET D. B. ODUOR ilas N. Onyango _ Absrac: In his paper, we have used he idea of Onyango (2003) he used o develop a logisic equaion used in naural

More information

Betting on Death and Capital Markets in Retirement: A Shortfall Risk Analysis of Life Annuities versus Phased Withdrawal Plans

Betting on Death and Capital Markets in Retirement: A Shortfall Risk Analysis of Life Annuities versus Phased Withdrawal Plans Being on Deah and Capial Markes in Reiremen: A Shorfall Risk Analysis of Life Annuiies versus Phased Wihdrawal Plans Ivica Dus, Raimond Maurer, and Olivia S. Michell PRC WP 2004-1 Pension Research Council

More information

Efficient Annuitization: Optimal Strategies for Hedging Mortality Risk

Efficient Annuitization: Optimal Strategies for Hedging Mortality Risk Efficien Annuiizaion: Opimal Sraegies for Hedging Moraliy Risk Jason S. Sco, John G. Wason, and Wei-Yin Hu* PRC WP2007-09 Pension Research Council Working Paper Pension Research Council The Wharon School,

More information

EFFICIENT POST-RETIREMENT ASSET ALLOCATION

EFFICIENT POST-RETIREMENT ASSET ALLOCATION EFFICIENT POST-RETIREMENT ASSET ALLOCATION Barry Freedman* ABSTRACT To examine pos-reiremen asse allocaion, an exension o he classic Markowiz risk-reurn framework is suggesed. Assuming ha reirees make

More information

Pricing Vulnerable American Options. April 16, Peter Klein. and. Jun (James) Yang. Simon Fraser University. Burnaby, B.C. V5A 1S6.

Pricing Vulnerable American Options. April 16, Peter Klein. and. Jun (James) Yang. Simon Fraser University. Burnaby, B.C. V5A 1S6. Pricing ulnerable American Opions April 16, 2007 Peer Klein and Jun (James) Yang imon Fraser Universiy Burnaby, B.C. 5A 16 pklein@sfu.ca (604) 268-7922 Pricing ulnerable American Opions Absrac We exend

More information

No. 2004/01. Betting on Death and Capital Markets in Retirement: A Shortfall Risk Analysis of Life Annuities versus Phased Withdrawal Plans

No. 2004/01. Betting on Death and Capital Markets in Retirement: A Shortfall Risk Analysis of Life Annuities versus Phased Withdrawal Plans No. 2004/01 Being on Deah and Capial Markes in Reiremen: A Shorfall Risk Analysis of Life Annuiies versus Phased Wihdrawal Plans Ivica Dus, Raimond Maurer, Olivia S. Michell Cener for Financial Sudies

More information

Chapter Outline CHAPTER

Chapter Outline CHAPTER 8-0 8-1 Chaper Ouline CHAPTER 8 Sraegy and Analysis in Using Ne Presen Value 8.1 Decision Trees 8.2 Sensiiviy Analysis, Scenario Analysis, and Break-Even Analysis 8.3 Mone Carlo Simulaion 8. Opions 8.5

More information

On the Edge of Completeness

On the Edge of Completeness On he Edge of Compleeness May 2000 Jean-Paul LAURENT Professor, ISFA Acuarial School, Universiy of Lyon, Scienific Advisor, BNP Paribas Correspondence lauren.jeanpaul@online.fr On he Edge of Compleeness:

More information

Volatility and Hedging Errors

Volatility and Hedging Errors Volailiy and Hedging Errors Jim Gaheral Sepember, 5 1999 Background Derivaive porfolio bookrunners ofen complain ha hedging a marke-implied volailiies is sub-opimal relaive o hedging a heir bes guess of

More information

Acceleration Techniques for Life Cash Flow Projection Based on Many Interest Rates Scenarios Cash Flow Proxy Functions

Acceleration Techniques for Life Cash Flow Projection Based on Many Interest Rates Scenarios Cash Flow Proxy Functions Acceleraion Techniques for Life Cash Flow Projecion Based on Many Ineres Raes Scenarios Cash Flow Proxy Funcions Auhor: Marin Janeček, Tools4F, s.r.o. and Economic Universiy in Prague, 207 Acknowledgmen:

More information

Supplement to Models for Quantifying Risk, 5 th Edition Cunningham, Herzog, and London

Supplement to Models for Quantifying Risk, 5 th Edition Cunningham, Herzog, and London Supplemen o Models for Quanifying Risk, 5 h Ediion Cunningham, Herzog, and London We have received inpu ha our ex is no always clear abou he disincion beween a full gross premium and an expense augmened

More information

Econ 546 Lecture 4. The Basic New Keynesian Model Michael Devereux January 2011

Econ 546 Lecture 4. The Basic New Keynesian Model Michael Devereux January 2011 Econ 546 Lecure 4 The Basic New Keynesian Model Michael Devereux January 20 Road map for his lecure We are evenually going o ge 3 equaions, fully describing he NK model The firs wo are jus he same as before:

More information

HEDGING SYSTEMATIC MORTALITY RISK WITH MORTALITY DERIVATIVES

HEDGING SYSTEMATIC MORTALITY RISK WITH MORTALITY DERIVATIVES HEDGING SYSTEMATIC MORTALITY RISK WITH MORTALITY DERIVATIVES Workshop on moraliy and longeviy, Hannover, April 20, 2012 Thomas Møller, Chief Analys, Acuarial Innovaion OUTLINE Inroducion Moraliy risk managemen

More information

Valuing Real Options on Oil & Gas Exploration & Production Projects

Valuing Real Options on Oil & Gas Exploration & Production Projects Valuing Real Opions on Oil & Gas Exploraion & Producion Projecs March 2, 2006 Hideaka (Hugh) Nakaoka Former CIO & CCO of Iochu Oil Exploraion Co., Ld. Universiy of Tsukuba 1 Overview 1. Inroducion 2. Wha

More information

Models of Default Risk

Models of Default Risk Models of Defaul Risk Models of Defaul Risk 1/29 Inroducion We consider wo general approaches o modelling defaul risk, a risk characerizing almos all xed-income securiies. The srucural approach was developed

More information

A BLACK-SCHOLES APPROACH FOR THE PRICING OF ELECTRIC POWER OPTIONS IN TURKISH POWER MARKET

A BLACK-SCHOLES APPROACH FOR THE PRICING OF ELECTRIC POWER OPTIONS IN TURKISH POWER MARKET A BLACK-SCHOLES APPROACH FOR THE PRICING OF ELECTRIC POWER OPTIONS IN TURKISH POWER MARKET AHMET YUCEKAYA Deparmen of Indusrial Engineering, Kadir Has Universiy, Faih, Isanbul, Turkey E-mail: ahmey@khas.edu.r

More information

Macroeconomics II THE AD-AS MODEL. A Road Map

Macroeconomics II THE AD-AS MODEL. A Road Map Macroeconomics II Class 4 THE AD-AS MODEL Class 8 A Road Map THE AD-AS MODEL: MICROFOUNDATIONS 1. Aggregae Supply 1.1 The Long-Run AS Curve 1.2 rice and Wage Sickiness 2.1 Aggregae Demand 2.2 Equilibrium

More information

Appendix B: DETAILS ABOUT THE SIMULATION MODEL. contained in lookup tables that are all calculated on an auxiliary spreadsheet.

Appendix B: DETAILS ABOUT THE SIMULATION MODEL. contained in lookup tables that are all calculated on an auxiliary spreadsheet. Appendix B: DETAILS ABOUT THE SIMULATION MODEL The simulaion model is carried ou on one spreadshee and has five modules, four of which are conained in lookup ables ha are all calculaed on an auxiliary

More information

SIMPLE DSGE MODELS OF MONEY DEMAND: PART I OCTOBER 14, 2014

SIMPLE DSGE MODELS OF MONEY DEMAND: PART I OCTOBER 14, 2014 SIMPLE DSGE MODELS OF MONEY DEMAND: PART I OCTOBER 4, 204 Inroducion BASIC ISSUES Money/moneary policy issues an enduring fascinaion in macroeconomics How can/should cenral bank conrol he economy? Should

More information

APRA Research Methodology for Analysis of Superannuation Funds

APRA Research Methodology for Analysis of Superannuation Funds Curren Research Quesions APRA Research Mehodology for Analysis of Superannuaion Funds Wha are he deerminans of he cross-secional variaion in superannuaion reurns? Asse allocaion, manager skill, expenses/axes

More information

Optimal Tax-Timing and Asset Allocation when Tax Rebates on Capital Losses are Limited

Optimal Tax-Timing and Asset Allocation when Tax Rebates on Capital Losses are Limited Opimal Tax-Timing and Asse Allocaion when Tax Rebaes on Capial Losses are Limied Marcel Marekwica This version: January 15, 2007 Absrac Since Consaninides (1983) i is well known ha in a marke where capial

More information

Incorporating Risk Preferences into Real Options Models. Murat Isik

Incorporating Risk Preferences into Real Options Models. Murat Isik Incorporaing Risk Preferences ino Real Opions Models Mura Isik Assisan Professor Agriculural Economics and Rural Sociology Universiy of Idaho 8B Ag Science Building Moscow, ID 83844 Phone: 08-885-714 E-mail:

More information

Inventory Investment. Investment Decision and Expected Profit. Lecture 5

Inventory Investment. Investment Decision and Expected Profit. Lecture 5 Invenory Invesmen. Invesmen Decision and Expeced Profi Lecure 5 Invenory Accumulaion 1. Invenory socks 1) Changes in invenory holdings represen an imporan and highly volaile ype of invesmen spending. 2)

More information

CEBR/CESIFO CONFERENCE ON PENSION REFORM

CEBR/CESIFO CONFERENCE ON PENSION REFORM CEBR/CESIFO CONFERENCE ON PENSION REFORM Copenhagen, 11 12 June 2005 Being on Deah and Capial Markes in Reiremen: A Shorfall Risk Analysis of Life Annuiies versus Phased Wihdrawal Plans Ivica Dus, Raimond

More information

Revisiting the Risk-Neutral Approach to Optimal Policyholder Behavior: A Study of Withdrawal Guarantees in Variable Annuities 1

Revisiting the Risk-Neutral Approach to Optimal Policyholder Behavior: A Study of Withdrawal Guarantees in Variable Annuities 1 Revisiting the Risk-Neutral Approach to Optimal Policyholder Behavior: A Study of Withdrawal Guarantees in Variable Annuities 1 Daniel Bauer Department of Risk Management and Insurance Georgia State University

More information

BUDGET ECONOMIC AND FISCAL POSITION REPORT

BUDGET ECONOMIC AND FISCAL POSITION REPORT BUDGET ECONOMIC AND FISCAL POSITION REPORT - 2004 Issued by he Hon. Miniser of Finance in Terms of Secion 7 of he Fiscal Managemen (Responsibiliy) Ac No. 3 of 1. Inroducion Secion 7 of he Fiscal Managemen

More information

THIS study focuses on the valuation problem of an

THIS study focuses on the valuation problem of an IAENG Inernaional Journal of Applied Mahemaics, 46:4, IJAM_46_4_ The Valuaion of an Equiy-inked ife Insurance Using he Theory of Indifference ricing Jungmin Choi Absrac This sudy addresses he valuaion

More information

Corporate Finance. Capital budgeting. Standalone risk of capital project

Corporate Finance. Capital budgeting. Standalone risk of capital project Corporae Finance Capial budgeing Iniial oulay = FCInv + NWCInv Sal afer ax operaing cashflow = 0 + T ( Sal0 B0 ) ( R C)( 1 ax) + ax Ter min al year non opereaing cashflow = Sal T Dep + NWCInv ax ( Sal

More information

Chapter 8 Consumption and Portfolio Choice under Uncertainty

Chapter 8 Consumption and Portfolio Choice under Uncertainty George Alogoskoufis, Dynamic Macroeconomic Theory, 2015 Chaper 8 Consumpion and Porfolio Choice under Uncerainy In his chaper we examine dynamic models of consumer choice under uncerainy. We coninue, as

More information

1. To express the production function in terms of output per worker and capital per worker, divide by N: K f N

1. To express the production function in terms of output per worker and capital per worker, divide by N: K f N THE LOG RU Exercise 8 The Solow Model Suppose an economy is characerized by he aggregae producion funcion / /, where is aggregae oupu, is capial and is employmen. Suppose furher ha aggregae saving is proporional

More information

Aid, Policies, and Growth

Aid, Policies, and Growth Aid, Policies, and Growh By Craig Burnside and David Dollar APPENDIX ON THE NEOCLASSICAL MODEL Here we use a simple neoclassical growh model o moivae he form of our empirical growh equaion. Our inenion

More information

Jarrow-Lando-Turnbull model

Jarrow-Lando-Turnbull model Jarrow-Lando-urnbull model Characerisics Credi raing dynamics is represened by a Markov chain. Defaul is modelled as he firs ime a coninuous ime Markov chain wih K saes hiing he absorbing sae K defaul

More information

Surrender Risk in the Context of the Quantitative Assessment of Participating Life Insurance Contracts under Solvency II

Surrender Risk in the Context of the Quantitative Assessment of Participating Life Insurance Contracts under Solvency II risks Aricle Surrender Risk in he Conex of he Quaniaive Assessmen of Paricipaing Life Insurance Conracs under Solvency II Tobias Burkhar ifa (Insiue for Finance and Acuarial Sciences), Lise-Meiner-Srasse

More information

EVA NOPAT Capital charges ( = WACC * Invested Capital) = EVA [1 P] each

EVA NOPAT Capital charges ( = WACC * Invested Capital) = EVA [1 P] each VBM Soluion skech SS 2012: Noe: This is a soluion skech, no a complee soluion. Disribuion of poins is no binding for he correcor. 1 EVA, free cash flow, and financial raios (45) 1.1 EVA wihou adjusmens

More information

Bringing cost transparency to the life annuity market

Bringing cost transparency to the life annuity market Bringing cos ransparency o he life annuiy marke Caherine Donnelly Monserra Guillén Jens Perch Nielsen January 24, 2014 Absrac The financial indusry has recenly seen a push away from srucured producs and

More information

City, University of London Institutional Repository

City, University of London Institutional Repository Ciy Research Online Ciy, Universiy of London Insiuional Reposiory Ciaion: Zhang, Y. (2009). Opimal Plan Design and Dynamic Asse Allocaion of Defined Conribuion Pension Plans: Lessons from Behavioural Finance

More information

Money/monetary policy issues an enduring fascination in macroeconomics. How can/should central bank control the economy? Should it/can it at all?

Money/monetary policy issues an enduring fascination in macroeconomics. How can/should central bank control the economy? Should it/can it at all? SIMPLE DSGE MODELS OF MONEY PART I SEPTEMBER 22, 211 Inroducion BASIC ISSUES Money/moneary policy issues an enduring fascinaion in macroeconomics How can/should cenral bank conrol he economy? Should i/can

More information

Labor Cost and Sugarcane Mechanization in Florida: NPV and Real Options Approach

Labor Cost and Sugarcane Mechanization in Florida: NPV and Real Options Approach Labor Cos and Sugarcane Mechanizaion in Florida: NPV and Real Opions Approach Nobuyuki Iwai Rober D. Emerson Inernaional Agriculural Trade and Policy Cener Deparmen of Food and Resource Economics Universiy

More information

MATURITY GUARANTEES EMBEDDED IN UNIT-LINKED CONTRACTS VALUATION & RISK MANAGEMENT *

MATURITY GUARANTEES EMBEDDED IN UNIT-LINKED CONTRACTS VALUATION & RISK MANAGEMENT * ABSRAC MAURIY GUARANEES EMBEDDED IN UNI-LINKED CONRACS VALUAION & RISK MANAGEMEN * Floren PERNOUD hierry FAVRE-BONVIN A key feaure of mauriy guaranees aached o uni-linked life insurance conracs is he uncerainy

More information

MAFS Quantitative Modeling of Derivative Securities

MAFS Quantitative Modeling of Derivative Securities MAFS 5030 - Quaniaive Modeling of Derivaive Securiies Soluion o Homework Three 1 a For > s, consider E[W W s F s = E [ W W s + W s W W s Fs We hen have = E [ W W s F s + Ws E [W W s F s = s, E[W F s =

More information

Stochastic Interest Rate Approach of Pricing Participating Life Insurance Policies with Embedded Surrender Option

Stochastic Interest Rate Approach of Pricing Participating Life Insurance Policies with Embedded Surrender Option American Journal of Mahemaical and Compuer Modelling 28; 3(): -2 hp://www.sciencepublishinggroup.com/j/ajmcm doi:.648/j.ajmcm.283.2 Sochasic Ineres Rae Approach of ricing aricipaing Life Insurance olicies

More information

A combined stochastic programming and optimal control approach to personal finance and pensions

A combined stochastic programming and optimal control approach to personal finance and pensions A combined sochasic programming and opimal conrol approach o personal finance and pensions Agnieszka Karolina Konicz agko@du.dk Kourosh Marjani Rasmussen kmra@du.dk David Pisinger dapi@du.dk Mogens Seffensen

More information

Real Options in Dynamic Pricing and Revenue Management

Real Options in Dynamic Pricing and Revenue Management Real Opions in Dynamic ricing and Revenue Managemen Chris Anderson Ivey School of Business, Univ. of Wesern Onario London, Onario, Canada canderson@ivey.ca Real Opions and Dynamic ricing 1 Agenda Financial

More information

Principles of Finance CONTENTS

Principles of Finance CONTENTS Principles of Finance CONENS Value of Bonds and Equiy... 3 Feaures of bonds... 3 Characerisics... 3 Socks and he sock marke... 4 Definiions:... 4 Valuing equiies... 4 Ne reurn... 4 idend discoun model...

More information

Frank de Jong and Yang Zhou Portfolio and Consumption Choice with Habit Formation under Inflation

Frank de Jong and Yang Zhou Portfolio and Consumption Choice with Habit Formation under Inflation Frank de Jong and Yang Zhou Porfolio and Consumpion Choice wih Habi Formaion under Inflaion DP 08/2013-023 Porfolio and Consumpion Choice wih Habi formaion under inflaion Preliminary Version: Commens Welcome

More information

Supplement to Chapter 3

Supplement to Chapter 3 Supplemen o Chaper 3 I. Measuring Real GD and Inflaion If here were only one good in he world, anchovies, hen daa and prices would deermine real oupu and inflaion perfecly: GD Q ; GD Q. + + + Then, he

More information

Market Models. Practitioner Course: Interest Rate Models. John Dodson. March 29, 2009

Market Models. Practitioner Course: Interest Rate Models. John Dodson. March 29, 2009 s Praciioner Course: Ineres Rae Models March 29, 2009 In order o value European-syle opions, we need o evaluae risk-neural expecaions of he form V (, T ) = E [D(, T ) H(T )] where T is he exercise dae,

More information

CENTRO DE ESTUDIOS MONETARIOS Y FINANCIEROS T. J. KEHOE MACROECONOMICS I WINTER 2011 PROBLEM SET #6

CENTRO DE ESTUDIOS MONETARIOS Y FINANCIEROS T. J. KEHOE MACROECONOMICS I WINTER 2011 PROBLEM SET #6 CENTRO DE ESTUDIOS MONETARIOS Y FINANCIEROS T J KEHOE MACROECONOMICS I WINTER PROBLEM SET #6 This quesion requires you o apply he Hodrick-Presco filer o he ime series for macroeconomic variables for he

More information

Capital Flows, Institutions, and Financial Fragility

Capital Flows, Institutions, and Financial Fragility Capial Flows, Insiuions, and Financial Fragiliy By Wipawin Promboon Kenan-Flagler Business School UNC-Chapel Hill February 11, 2009 Model Esimaion Globalizaion Liberalizaion Greaer volume of capial flows:

More information

VERIFICATION OF ECONOMIC EFFICIENCY OF LIGNITE DEPOSIT DEVELOPMENT USING THE SENSITIVITY ANALYSIS

VERIFICATION OF ECONOMIC EFFICIENCY OF LIGNITE DEPOSIT DEVELOPMENT USING THE SENSITIVITY ANALYSIS 1 Beaa TRZASKUŚ-ŻAK 1, Kazimierz CZOPEK 2 MG 3 1 Trzaskuś-Żak Beaa PhD. (corresponding auhor) AGH Universiy of Science and Technology Faculy of Mining and Geoengineering Al. Mickiewicza 30, 30-59 Krakow,

More information

Lifecycle Impacts of the Financial Crisis on. Optimal Consumption-Portfolio Choice, and Labor Supply

Lifecycle Impacts of the Financial Crisis on. Optimal Consumption-Portfolio Choice, and Labor Supply Lifecycle Impacs of he Financial Crisis on Opimal Consumpion-Porfolio Choice, and Labor Supply Jingjing Chai, Raimond Maurer, Olivia S. Michell, and Ralph Rogalla Sepember 2011 PRC WP2011-12 Pension Research

More information

Pricing options on defaultable stocks

Pricing options on defaultable stocks U.U.D.M. Projec Repor 2012:9 Pricing opions on defaulable socks Khayyam Tayibov Examensarbee i maemaik, 30 hp Handledare och examinaor: Johan Tysk Juni 2012 Deparmen of Mahemaics Uppsala Universiy Pricing

More information

Optimal life-contingent insurance under bid-ask spreads

Optimal life-contingent insurance under bid-ask spreads Opimal life-coningen insurance under bid-ask spreads 20 May 207 Geoffrey Kingson Deparmen of Economics, Macquarie Universiy 4 Easern Road, orh Ryde, Sydney, SW 209, usralia E: geoff.kingson@mq.edu.au T:

More information

The Correlation Risk Premium: Term Structure and Hedging

The Correlation Risk Premium: Term Structure and Hedging : erm Srucure and Hedging Gonçalo Faria (1),* and Rober Kosowski (2),* (1) CEF.UP, Universiy of Poro; (2) Imperial College Business School, CEPR, Oxford-Man Insiue of Quaniaive Finance. Nespar Inernaional

More information

Stylized fact: high cyclical correlation of monetary aggregates and output

Stylized fact: high cyclical correlation of monetary aggregates and output SIMPLE DSGE MODELS OF MONEY PART II SEPTEMBER 27, 2011 Inroducion BUSINESS CYCLE IMPLICATIONS OF MONEY Sylized fac: high cyclical correlaion of moneary aggregaes and oupu Convenional Keynesian view: nominal

More information

ANSWER ALL QUESTIONS. CHAPTERS 6-9; (Blanchard)

ANSWER ALL QUESTIONS. CHAPTERS 6-9; (Blanchard) ANSWER ALL QUESTIONS CHAPTERS 6-9; 18-20 (Blanchard) Quesion 1 Discuss in deail he following: a) The sacrifice raio b) Okun s law c) The neuraliy of money d) Bargaining power e) NAIRU f) Wage indexaion

More information

Loss Functions in Option Valuation: A Framework for Model Selection

Loss Functions in Option Valuation: A Framework for Model Selection Loss Funcions in Opion Valuaion: A Framework for Model Selecion Dennis Bams, Thorsen Lehner, Chrisian C.P. Wolff * Limburg Insiue of Financial Economics (LIFE), Maasrich Universiy, P.O. Box 616, 600 MD

More information

Introduction to Black-Scholes Model

Introduction to Black-Scholes Model 4 azuhisa Masuda All righs reserved. Inroducion o Black-choles Model Absrac azuhisa Masuda Deparmen of Economics he Graduae Cener, he Ciy Universiy of New York, 365 Fifh Avenue, New York, NY 6-439 Email:

More information

Spring 2011 Social Sciences 7418 University of Wisconsin-Madison

Spring 2011 Social Sciences 7418 University of Wisconsin-Madison Economics 32, Sec. 1 Menzie D. Chinn Spring 211 Social Sciences 7418 Universiy of Wisconsin-Madison Noes for Econ 32-1 FALL 21 Miderm 1 Exam The Fall 21 Econ 32-1 course used Hall and Papell, Macroeconomics

More information

Dynamic Programming Applications. Capacity Expansion

Dynamic Programming Applications. Capacity Expansion Dynamic Programming Applicaions Capaciy Expansion Objecives To discuss he Capaciy Expansion Problem To explain and develop recursive equaions for boh backward approach and forward approach To demonsrae

More information

Data-Driven Demand Learning and Dynamic Pricing Strategies in Competitive Markets

Data-Driven Demand Learning and Dynamic Pricing Strategies in Competitive Markets Daa-Driven Demand Learning and Dynamic Pricing Sraegies in Compeiive Markes Pricing Sraegies & Dynamic Programming Rainer Schlosser, Marin Boissier, Mahias Uflacker Hasso Planer Insiue (EPIC) April 30,

More information

How Risky is Electricity Generation?

How Risky is Electricity Generation? How Risky is Elecriciy Generaion? Tom Parkinson The NorhBridge Group Inernaional Associaion for Energy Economics New England Chaper 19 January 2005 19 January 2005 The NorhBridge Group Agenda Generaion

More information

STRESS TESTING OF PROBABILITY OF DEFAULT OF INDIVIDUALS

STRESS TESTING OF PROBABILITY OF DEFAULT OF INDIVIDUALS STRESS TESTING OF PROBABILITY OF DEFAULT OF INDIVIDUALS Per Kadeøábek, Aleš Slabý, Josef Vodièka Absrac: This paper inroduces a model for sress esing of probabiliy of defaul of individuals. The model ress

More information

An Analysis of Trend and Sources of Deficit Financing in Nepal

An Analysis of Trend and Sources of Deficit Financing in Nepal Economic Lieraure, Vol. XII (8-16), December 014 An Analysis of Trend and Sources of Defici Financing in Nepal Deo Narayan Suihar ABSTRACT Defici financing has emerged as an imporan ool of financing governmen

More information

(a) Assume that the entrepreneur is willing to undertake the project, and analyze the problem from the point of view of the outside investor.

(a) Assume that the entrepreneur is willing to undertake the project, and analyze the problem from the point of view of the outside investor. Problem Se # Soluions Course 4.454 Macro IV TA: Todd Gormley, gormley@mi.edu Disribued: November 9, 004 Due: Tuesday, November 3, 004 [in class]. Financial Consrains (via Cosly Sae Verificaion) Consider

More information

Money-Back Guarantees in Individual Pension Accounts: Evidence from the German Pension Reform

Money-Back Guarantees in Individual Pension Accounts: Evidence from the German Pension Reform Money-Back Guaranees in Individual Pension Accouns: Evidence from he German Pension Reform Raimond Maurer and Chrisian Schlag PRC WP 22-11 Pension Research Council Working Paper Pension Research Council

More information

An Indian Journal FULL PAPER. Trade Science Inc. The principal accumulation value of simple and compound interest ABSTRACT KEYWORDS

An Indian Journal FULL PAPER. Trade Science Inc. The principal accumulation value of simple and compound interest ABSTRACT KEYWORDS [Type ex] [Type ex] [Type ex] ISSN : 0974-7435 Volume 0 Issue 8 BioTechnology 04 An Indian Journal FULL PAPER BTAIJ, 08), 04 [0056-006] The principal accumulaion value of simple and compound ineres Xudong

More information

Advanced Tools for Risk Management and Asset Pricing

Advanced Tools for Risk Management and Asset Pricing MSc. Finance/CLEFIN 214/215 Ediion Advanced Tools for Risk Managemen and Asse Pricing May 215 Exam for Non-Aending Sudens Soluions Time Allowed: 13 minues Family Name (Surname) Firs Name Suden Number (Mar.)

More information