DOCSLIB.ORG

THESIS “An Integrated Optimization Model for Immunizing and Matching

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
THESIS “An Integrated Optimization Model for Immunizing and Matching UNIVERSITY OF THE AEGEAN DEPARTMENT OF FINANCIAL & MANAGEMENT ENGINEERING THESIS “An integrated optimization model for immunizing and matching pension funds bond portfolios” GEORGIOS BOUZIANIS Supervisor: Dr. P. Xidonas Athens, June 2016 UNIVERSITY OF THE AEGEAN DEPARTMENT OF FINANCIAL & MANAGEMENT ENGINEERING THESIS “An integrated optimization model for immunizing and matching pension funds bond portfolios” GEORGIOS BOUZIANIS Supervisor: Dr. Panos Xidonas Approved by the 3-member committee in June 2016. .................................... ................................. .............................. Dr. Panos Xidonas Dr. Vasilis Koutras Dr. Evangelos Vassiliou Adjunct Lecturer Lecturer Adjunct Lecturer Athens, June 2016 GEORGIOS BOUZIANIS Copyright© Georgios Bouzianis, 2016 All rights reserved. Copying, storage and distribution of this paper for commercial purposes is forbidden. Reproduction, storage and distribution of this paper for research purposes, is allowed as long as the source is mentioned. The views and conclusions drawn in this document express only authors’ opinions and do not represent official views of the Department of Financial & Management Engineering. ABSTRACT The primary purpose of this thesis is to develop two innovative bond portfolio optimization models, based on the portfolio dedication and immunization strategies. The first mathematical program minimizes the initial capital required for the creation of a bond portfolio, and is best suited to a defined liability-driven investment strategy. The second mathematical program operates under the uncertainty of term structure alterations, approached with Hull-White recombining trinomial lattice. In both cases, the exposure of transaction costs as well as the diversification and investment policy constraints regarding the portfolio structure, are strongly taken into account. In this sense, two mixed-integer linear programs are formulated. The validity of the proposed approach for the first model is verified through duration and convexity empirical testing. For the second model, it is verified through scenario evaluation in a well- diversified investment universe of bonds, including: US corporate bonds, European corporate bonds and sovereign bonds. Keywords: Bond portfolio optimization; Stochastic dynamic integrative asset and liability management strategy; Matching, immunization mathematical programming PROLOGUE I would like to express my profound gratitude to my supervisor, Dr. Panos Xidonas, for the assignment of this particular thesis and huge inspiration he provided me with. His excellent guidance, teaching ability and overall assistance were critical success factors for the completion of this work. I would also like to thank Professor Dimosthenis Drivaliaris, since he was the one who gave robust and mature shape in the mathematical skills and thinking potential of mine. His contribution to my progress was very important. My interaction with these two men changed the way I approach both science and life. I would also like to express my sincere thanks to the members of my thesis committee, Dr. Vasilis Koutras and Dr. Evangelos Vassiliou, for their useful comments and their overall contribution. Moreover, I would also like to thank all the people who contributed in their own unique way in supporting me during the time of my thesis elaboration. Finally, I dedicate this endeavor to my father Stavros, whose presence and input have been invaluable. Georgios Bouzianis Athens, 2016 TABLE OF CONTENTS CHAPTER 1 - INTRODUCTION ............................................................. 11 1.1 The problem ......................................................................................... 11 1.2 The Subject and the Aim of the Thesis .......................................... 19 1.3 The Contribution of the Thesis ........................................................ 20 1.4 The Structure of the Thesis .............................................................. 21 CHAPTER 2 - PROPOSED METHODOLOGY FOR SMALL AND PARALLEL SHIFTS IN THE TERM STRUCTURE ............................ 24 2.1 Objective function .............................................................................. 25 2.2 Cashflow matching constraint ........................................................ 26 2.3 Immunization constraints ................................................................ 27 2.4 Investment policy adjustment ......................................................... 32 CHAPTER 3 - STOCHASTIC SHORT RATE MODELS ...................... 36 3.1 Vasicek Model ...................................................................................... 37 3.2 Hull-White Model ................................................................................ 39 3.3 Dothan Model ...................................................................................... 43 3.4 Black-Derman-Toy Model ................................................................. 44 3.5 Cox Ingersoll Ross Model .................................................................. 46 CHAPTER 4 - PROPOSED METHODOLOGY WITH EMBEDDED HULL - WHITE STOCHASTIC SHORT RATE MODEL ..................... 50 4.1 Hull-White scenario structures ....................................................... 51 4.2 General Methodological approach.................................................. 55 CHAPTER 5 - EMPIRICAL TESTING ................................................... 59 5.1 Data and field of application............................................................ 59 5.2 Results and discussion for the proposed methodology for small and parallel shifts in the term structure ............................................. 60 5.3 Results and discussion for the proposed methodology with embedded Hull-White stochastic short rate model ........................... 65 CHAPTER 6 - CONCLUSIONS - PERSPECTIVES ............................. 72 6.1 Conclusions .......................................................................................... 72 6.2 Perspectives ......................................................................................... 73 APPENDIXES A Programming code for the proposed methodology for small and parallel shifts in the term structure ..................................................... 76 B Programming code for the proposed methodology with embedded Hull-White stochastic short rate model ........................... 82 REFERENCES .......................................................................................... 91 LIST OF FIGURES CHAPTER 1 Figure 1.1.1 Depiction of a normal yield curve. ................................. 15 Figure 1.1.2 Depiction of a flat yield curve. ........................................ 15 Figure 1.1.3 Depiction of an inverted yield curve. ............................ 16 Figure 1.1.4 The u.s. bond market size is (in billions) according to the securities industry and financial markets association (SIFMA) as of Q4 2013 ............................................................................................... 17 Figure 1.1.5 Outstanding u.s. bond market debt (in billions) from 1980 to 2014, according to sifma. ........................................................... 17 Figure 1.1.6 Components of an alm system and basic procedure…………………………………………………………………………19 CHAPTER 2 Figure 2.2.1 A liability (lt) and the total inflows from mismatched portfolios (A and B), and from a perfectly matched portfolio (C)..27 Figure 2.3.1 The price-yield curve with approximations of duration and convexity. .......................................................................... 32 CHAPTER 4 Figure 4.1.1 Recombining trinomial Hull-White lattice, with five trading dates. ............................................................................................. 51 Figure 4.1.2 A scenario structure derived from the trinomial lattice in figure 4.1.1. ................................................................................ 53 Figure 4.1.3 A scenario structure with common states up to t=3, derived from the trinomial lattice in figure 4.1.1. ............................. 54 CHAPTER 5 Figure 5.2.1 Investment to the i-th bond of the portfolio and expected earnings. .................................................................................... 64 Figure 5.2.2 Bond portfolio incomes, necessary overflows and liabilities. .................................................................................................... 64 Figure 5.3.1 Shifts in the term structure in the form of trinomial lattice, with Hull-White model. .............................................................. 69 LIST OF TABLES Table 5.2.1 Individual characteristics of the 70 bonds in the optimized portfolio ................................................................................... 61 Table 5.2.2 Monetary synthesis of the portfolio and evaluation of the earnings (in USD) from every incorporated bond...................... 61 Table 5.2.3 Required overflows and overall inflows at any period t and corresponding liabilities (in USD). ............................................... 62 Table 5.3.1 Individual characteristics of the 170 bonds in the optimized portfolio. .................................................................................. 66 Table 5.3.2 Monetary synthesis of the portfolio and evaluation of the earnings (in USD) from every incorporated bond...................... 66 Table 5.3.3 Required overflows and overall inflows at any period t and state stv(t), and corresponding liabilities
Load more

Recommended publications
  • Immunization of Fixed-Income Portfolios Using an Exponential Parametric Model*
    Immunization of Fixed-Income Portfolios Using an Exponential Parametric Model* Bruno Lund** Caio Almeida*** Abstract Litterman and Scheinkman (1991) showed that even a duration immunized fixed-income portfolio (neutral) can bear great losses and, therefore, propose hedging the portfolio using a principal component's analysis. The problem is that this approach is only pos- sible when the interest rates are observable. Therefore, when the interest rates are not observable, as is the case of most international and domestic debt markets in many emerging market economies, it is not possible to apply this method directly. The present study proposes an alternative approach: hedging based on factors of a parametric term structure model. The immunization done using this approach is not only simple and efficient but also equivalent to the immunization procedure proposed by Litterman and Scheinkman when the rates are observable. Examples of the method for hedging and leveraging operations in the Brazilian inflation-indexed public debt securities market are presented. This study also describes how to construct and to price portfolios that repli- cate the model risk factors, which makes possible to extract some information on the expectations of agents in regards to future behavior of the interest rate curve. Keywords: Fixed Income, Term Structure, Asset Pricing, Inflation Expectation, Immu- nization, Hedge, Emerging Markets, Debt, Derivatives. JEL Codes: E43, G12, G13. *Submitted in ??. Revised in ??. **Securities, Commodities and Futures Exchange { BM&FBovespa, Brazil. E-mail: [email protected] ***Funda¸c~aoGetulio Vargas, EPGE/FGV, Brazil. Caio Almeida thanks CNPq for the research productivity grant. E-mail: [email protected] Brazilian Review of Econometrics v.
    [Show full text]
  • Immunization Strategies for Funding Multiple Inflation-Linked Retirement
    risks Article Immunization Strategies for Funding Multiple Inflation-Linked Retirement Income Benefits Cláudia Simões 1,2,*, Luís Oliveira 3 and Jorge M. Bravo 4,5 1 Risk Management Department, Banco de Portugal, 1100-150 Lisboa, Portugal 2 Alumni, Lisbon University Institute (ISCTE-IUL), 1649-026 Lisboa, Portugal 3 Department of Finance, Lisbon University Institute (ISCTE-IUL) and Business Research Unit (BRU-IUL), 1649-026 Lisboa, Portugal; [email protected] 4 NOVA IMS—Information Management School, New University of Lisbon, 1070-312 Lisboa, Portugal; [email protected] 5 Department of Economics, Université Paris-Dauphine PSL, 75775 Paris, France * Correspondence: [email protected] Abstract: Protecting against unexpected yield curve, inflation, and longevity shifts are some of the most critical issues institutional and private investors must solve when managing post-retirement income benefits. This paper empirically investigates the performance of alternative immunization strategies for funding targeted multiple liabilities that are fixed in timing but random in size (inflation- linked), i.e., that change stochastically according to consumer price or wage level indexes. The immunization procedure is based on a targeted minimax strategy considering the M-Absolute as the interest rate risk measure. We investigate to what extent the inflation-hedging properties of ILBs in asset liability management strategies targeted to immunize multiple liabilities of random size are superior to that of nominal bonds. We use two alternative datasets comprising daily closing prices for U.S. Treasuries and U.S. inflation-linked bonds from 2000 to 2018. The immunization Citation: Simões, Cláudia, Luís performance is tested over 3-year and 5-year investment horizons, uses real and not simulated bond Oliveira, and Jorge M.
    [Show full text]
  • 33:390:490 COURSE TITLE: Fixed Income
    Department of Finance and Economics COURSE NUMBER: 33:390:490 COURSE TITLE: Fixed Income COURSE DESCRIPTION The course is intended to give students an in-depth treatment of fixed income analytics. A solid understanding of the bond pricing and yield curve material from the Investments course is necessary. There are three sections to the semester. A.) The first part of the course will cover bond valuation and various measures of bond risk. We will study: bootstrapping and the creation of a theoretical spot curve; valuing bonds with embedded options; many kinds of duration; and convexity. B.) The second part of the course will cover the securitization process. We will study the general securitization process and the specific attributes of various mortgage-backed securities. We will use Monte Carlo simulations to value asset-backed securities. C.) The third part of the course will deal with measures of portfolio risk and how factors such as spread risk and convexity affect the value of a bond portfolio when interest rates change. We will also look at return and risk attribution for the individual bonds in a portfolio that I will supply. COURSE MATERIALS Required Texts. 1.) Fixed Income Analysis, 2nd edition, by Frank Fabozzi, John Wiley Publisher, 2007. 2.) Fixed Income Analysis Workbook, 2nd edition, by Frank Fabozzi, John Wiley Publisher, 2007. (Recommended). The text is comprehensive and challenging. The text has an accompanying workbook, which is superb. There are as many concept questions as there are quantitative questions, and both types help students learn the material. The workbook provides thorough solutions to all questions Learning Objectives.
    [Show full text]
  • Immunization and Hedging of Fixed-Income Securities in Comparison
    Dipartimento di Impresa e Management Cattedra di Matematica Finanziaria IMMUNIZATION AND HEDGING OF FIXED-INCOME SECURITIES IN COMPARISON RELATORE Prof. Gennaro Olivieri CANDIDATO Gianmarco Vitiello Matr. 187381 ANNO ACCADEMICO 2016/2017 TABLE OF CONTENTS Introduction I. Chapter 1: Basic concepts 1. Interest Rate 2. Bond 3. Duration II. Chapter 2: Immunization 1. Investment Accumulation and Duration 2. Classic Immunization Theory 3. Master Immunization III. Chapter 3: Hedging fixed income securities 1. Introduction to Hedging 2. Interest Rate Futures 3. Hedging with Duration and Convexity Conclusion References 2 INTRODUCTION At the basis of this thesis there is the analysis of two important strategies implemented by portfolio managers in order to cover the risk of the interest risk, that is the immunization theory and the hedging of fixed-income securities. In particular the two arguments are presented from a theoretical point of view by treating important theorem of the immunization and the basis of the use of the derivatives such as the interest rate future. The motivations that allow to be interested in this subjects have two different aspects. First, I like to solve problem and face complexities: during my three-years undergraduate program I satisfy this aptitude in quantitative exams such as financial mathematics and markets and derivatives. Second, in a more and more globalized and at the same time more fragile and breakable economy, I have been interested in how to face the uncertainty technically. The objective of the thesis is the introduction of two different strategies in facing the uncertainty in the fixed income market and, finally, a comparison between them in order to show the strength points and weaknesses.
    [Show full text]
  • Immunization
    Debt Instruments and Markets Professor Carpenter Immunization Reading Tuckman, chapter 7. Immunization 1 Debt Instruments and Markets Professor Carpenter Immunizing / Hedging Interest Rate Risk Suppose you have liabilities or obligations consisting of a stream of fixed cash flows you must pay in the future. Bond defeasance Pension liabilities? Insurance liabilities? How can you structure an asset portfolio to fund these liabilities? Dedication The only completely riskless approach is to construct an asset portfolio with cash flows that exactly match the liability cash flows. This funding method is called dedication. This approach may be infeasible or excessively costly. In some situations, risk managers may want more flexibility. Immunization 2 Debt Instruments and Markets Professor Carpenter Immunization Consider a more flexible but more risky approach, called matching. The liabilities have a certain market value. That market value changes as time passes and as interest rates change. Construct an asset portfolio with the same market value and the same interest rate sensitivity as the liabilities so that the asset value tracks the liability value over time. Immunization If the assets and liabilities have - the same market value and - interest rate sensitivity, the net position is said to be hedged or immunized against interest rate risk. The approach can be extended to settings with debt instruments that do not have fixed cash flows. Immunization 3 Debt Instruments and Markets Professor Carpenter Duration Matching The most common form of immunization: matches the duration and market value of the assets and liabilities This hedges the net position against small parallel shifts in the yield curve. Recall: Change in value ~-dollar duration x change in rates ¾Matching the dollar duration of assets and liabilities means matching their changes in value if all rates change by the same amount.
    [Show full text]
  • Immunization and Hedging of Longevity Risk
    Immunization and Hedging of Longevity Risk Prepared by Changyu Liu and Michael Sherris Presented to the Actuaries Institute ASTIN, AFIR/ERM and IACA Colloquia 23-27 August 2015 Sydney This paper has been prepared for the Actuaries Institute 2015 ASTIN, AFIR/ERM and IACA Colloquia. The Institute’s Council wishes it to be understood that opinions put forward herein are not necessarily those of the Institute and the Council is not responsible for those opinions. CEPAR and School of Risk and Actuarial Studies UNSW Business School, UNSW Australia 2052 The Institute will ensure that all reproductions of the paper acknowledge the author(s) and include the above copyright statement. Institute of Actuaries of Australia ABN 69 000 423 656 Level 2, 50 Carrington Street, Sydney NSW Australia 2000 t +61 (0) 2 9233 3466 f +61 (0) 2 9233 3446 e [email protected] w www.actuaries.asn.au Immunization and Hedging of Longevity Risk Changyu Liu, Michael Sherris CEPAR and School of Risk and Actuarial Studies UNSW Business School, University of New South Wales, Sydney, Australia, 2052 April 20, 2015 Abstract Pension funds and life insurers offering annuities hold long term liabilities linked to longevity. Risk management of life annuity portfolios aims to immunize or hedge both interest rate and mortality risks. Standard fixed interest duration-convexity hedging must be adapted to allow for both interest rate and longevity risk. We develop an immunization approach along with a delta-gamma based approach al- lowing for both risks incorporating models for mortality and interest rate risk. The immunization and hedge effectiveness of fixed-income coupon bonds, annuity bonds, as well as longevity bonds, is compared and assessed using simulations of portfolio surplus outcomes for an annuity portfolio.
    [Show full text]
  • MATH 4512 — Fundamentals of Mathematical Finance Topic One
    MATH 4512 | Fundamentals of Mathematical Finance Topic One | Bond portfolio management and immunization 1.1 Duration measures and convexity 1.2 Horizon rate of return: return from the bond investment over a time horizon 1.3 Immunization of bond investment 1.4 Optimal management and dynamic programming 1 1.1 Duration measures and convexity Fixed coupon bond Let i be the interest rate applicable to the cash flows arising from a fixed coupon bond, giving constant coupon c paid at times 1; 2;:::;T and par amount BT paid at maturity T . The fair bond value B is the sum of the coupons and par in present value, where c c B B = + ··· + + T T T 12 + i (1 +3i) (1 + i) " # 1 − 1 6 1 (1+ )T 7 B c 1 B = c 4 i 5 + T = 1 − + T : 1 + i − 1 (1 + i)T i (1 + i)T (1 + i)T 1 1+i 2 Annuity factor and present value factor The discrete coupons paid at times 1; 2;:::;T is called an annuity stream over the time period [0;T ]. We define the annuity factor (i; T ) to be " # 1 1 annuity factor (i; T ) = 1 − : i (1 + i)T The present value factor over [0;T ] at interest rate i is defined by 1 PV factor (i; T ) = : (1 + i)T 1 • When T ! 1, the annuity factor becomes . For example, when i i = 5%, one needs to put $20 upfront in order to generate a perpetual stream of annuity of $1 paid annually. • For an annuity of finite time horizon T , it can be visualized as the difference of two perpetual annuities starting on today and time T .
    [Show full text]
  • Olin Business School (08/31/21)
    Bulletin 2021-22 Olin Business School (08/31/21) B50 ACCT 3610 Intermediate Financial Accounting Theory I Olin Business School The first of a two-course sequence in corporate financial reporting. Examines the environment of financial accounting, the standards-setting process and the conceptual framework Phone: 314-935-6315 that underlies financial accounting in the United States. Topics: Email: [email protected] review accounting basics, events and transactions that impact financial statements, comprehension of corporate financial Website: http://olin.wustl.edu reports, and examination of political and economic factors influencing accounting policy. Prerequisite: ACCT 2610. Courses Credit 3 units. Courses include the following: B50 ACCT 3620 Intermediate Financial Accounting II • B50 ACCT (Accounting) (p. 1) Continuation of ACCT 3610. Focus on the accounting • B52, B62 FIN (Finance) (p. 3) and reporting of various stakeholders' claims against the corporate entity. Claims of shareholders, long-term creditors, • B99 INTL (International Business) (p. 5) employees and governmental bodies are examined. An in-depth • B53 MGT (Management) (p. 6) understanding of applicable generally accepted accounting principles is developed by examining the strengths and • B54 MEC (Managerial Economics) (p. 12) weaknesses of these principles and alternative accounting • B55 MKT (Marketing) (p. 14) practices. Prerequisite: ACCT 3610. Credit 3 units. • B58 OSCM (Operations and Supply Chain Management) (p. 16) B50 ACCT 363 Cost Analysis and Control • B56, B66 OB (Organizational Behavior) (p. 16) This course will focus on the impact of changes in markets, • B59 DAT (Data Analytics) (p. 18) in operations, and in information technology that affect the design of management accounting systems. Emphasis is on the strategic role of cost information in planning and controlling Accounting operations.
    [Show full text]
  • 11 Generalization of Redington's Theory of Immunization
    11 Generalization of Redington's Theory of Immunization Elias 5. W. Shiu ABSTRACT In the classical model of immunization, there is no distinction between short term and long term interest rates, i.e., all yield curves are assumed to be flat. This is a violation of the no-arbitrage principle. Moreover, the interest rate shocks are assumed to be small. In this paper we generalize the theory to the case where the interest rate is a function of time and the shock is of arbitrary magnitude. 1. INTRODUCTION Consider a block of insurance business and its associated assets. For t ~ 0, let At denote the asset cash flow expected at time t , i.e. the investment income and capital maturities expected at that time. Let Lt denote the liability cash flow expected at time t , i.e. the policy claims plus policy surrenders plus expenses minus premium income expected at that time. Define the net cash flow at time t, t ~ 0, as Nt=At-Lt · The theory of immunization is concerned with two kinds of risk that may occur due to interest rate fluctuations: (I) positive net cash flows may have to be reinvested at lower interest rates, (2) negative net cash flows may involve the liquidations of assets at depreciated values because of then higher interest rates. -69- 2. REDINGTON'S THEORY OF IMM~IZATION Let 5(&) denote the surplus of the blodc of business evaluated at a given force of interest &. Thus 5(&) is the present value of the net cash flows, 5(&) = 2: Nt e-&t t~O If the force of interest changes from & to & + f, the surplus value changes from 5(&) to 5(& + f).
    [Show full text]
  • Modern Portfolio Theory 1
    Page 1 of 129 MODERN PORTFOLIO THEORY 1. Modern Portfolio Theory § Background o The Primary principle upon which Modern Portfolio Theory is based (MPT) is the RANDOM WALK HYPOTHESIS which sates that the movement of asset prices follows an Unpredictable path: the path as a TREND that is based on the long-run nominal growth of corporate earnings per share, but fluctuations around the trend are random. There are 3 Forms of the Hypothesis: § Weak Form: Security Prices reflect ALL information about price & trading behavior in the market. Thus, analyzing the security’s or market’s data contains NO information that enables predictions on future price to be made. Thus, CHARTING & TECHNICAL ANALYSIS do NOT Work § Semi-strong Form: The Markets react quickly to new public information, whether it relates to trading activity (weak form) or fundamental earnings. Studying historical information, thus, is not too relevant and won’t enable superior results.. § Strong Form: All relevant information knowable about a company is already imbedded in the price of a security Only new information produces systematic (non-random) price changes. Since new information enters the marketplace randomly, asset price movements are random. § Efficient Pricing Structure o The EFFICIENT MARKET THEORY states that asset prices are set in the market by the MARGINAL Buyer & Seller. These buyers & sellers are motivated by various factors; both rational & irrational. The market is not efficient in the sense that it prices securities correctly, but it is efficient in the sense that the market is a reasonable speculation. Efficiency means there is even odds on winning or losing.
    [Show full text]
  • A Numerical Examination of Asset-Liability Management Strategies
    A Numerical Examination of Asset-Liability Management Strategies Meije Smink’ University of Groningen, POBox 800, 9700 AV Groningen, The Netherlands Telephone: 31-50-63.45.39 Fax: 31-50-63.72.07 Summary This article presents a detailed analysis of Asset-Liability Management Strategies. In the paper these strategies are classified according to three categories. These are: [l] static techniques, e.g. gap-analysis, static duration analysis; [2] dynamic value driven strategies, e.g. immunization, key-rate immunization, model-dependent immunization, contingent immunization, portfolio insurance, pay-off distribution optimization; and [3] return driven strategies, e.g. spread management, rate of return optimization. Each strategy is analyzed using of multi-period framework based on the Vasicek interest-rate model. This model is represented through a trinomial interest rate-tree. The analysis thus obtains a high degree of comparability with regard to the risks and possible rewards associated to each strategy. The article’s final section discusses the potential for application of each strategy, as part of the financial institution’s ALM policy. The author gratefully acknowledges helpfull comments from T.K. Dijkstra and R.A.H. van der Meer. 969 Examen numkrique des strategies de gestion actif-passif Meije Smink ’ Universite de Groningue, Pays-Bas Telephone : 31-50-63.45.39 TClCcopie : 3 I-50-63.72.07 . R&sum6 Le present article propose une analyse detaillee des strategies de gestion actif-passif. Ces strategies sont classees en trois categories : [l] Les techniques statiques, a savoir analyse des &arts, analyse de duration statique ; [2] Les strategies dynamiques axles sur la valeur, a savoir immunisation, immunisation aux taux cl&, immunisation dependante de modeles, immunisation contingente, assurance de portefeuille, optimisation de la repartition des pay-offs; et [3] Les strategies ax&es sur le rendement, a savoir gestion des spreads et optimisation des taux de rendement.
    [Show full text]
  • We Know That the Immunized Portfolio Doesn't Exist in Most Cases
    Alina Kondratiuk-Janyska1, Marek Kaluszka2 BOND PORTFOLIO IMMUNIZATION IN ARBITRAGE FREE MODELS Acta Universitatis Lodziensis. Folia Oeconomica, Łódź University Press, Accepted 2005 Abstract The aim of this paper is to examine arbitrage free models and investigate which of them imply well known and widely applied classical duration strategy. Problem of a noncallable and default-free bond portfolio immunization is studied in a 3-period model of time with a fixed investment strategy either under known optimization criterions such as maxmin, Bayesian, Gamma-maxmin, Markowitz-type and others. In some models there are anomalies since, it is proved that, any strategy is optimal. A notable fact is that the Markowitz approach is free from such anomalies and, moreover, in some cases occurs to be a duration strategy. Keywords: Bond portfolio; Immunization; Duration; Maxmin Procedure; Bayesian Method; Markowitz Criterion; Gamma-maxmin Approach JEL Classification: G11, G19 1. Introduction 1 Assistant in the Center of Mathematics and Physics, Technical University of Lodz ; Institute of Mathematics, Technical University of Lodz. E-mail address:[email protected] 2 Assistant Professor in the Institute of Mathematics, Technical University of Lodz 1 Early work on immunization was based upon the Macaulay definition of duration (1938) and it was shown by Samuelson (1945) and Redington (1952) that if the Macaulay duration of assets and liabilities are equal, the portfolio is protected against a local parallel change in the yield curve. Fisher and Weil (1971) formalized the traditional theory of immunization defining the conditions under which the value of an investment in a bond portfolio is hedged against any parallel shifts in the forward rates.
    [Show full text]