Introduction to Credit Risk
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BASIC BOND ANALYSIS Joanna Place
Handbooks in Central Banking No. 20 BASIC BOND ANALYSIS Joanna Place Series editor: Juliette Healey Issued by the Centre for Central Banking Studies, Bank of England, London EC2R 8AH Telephone 020 7601 3892, Fax 020 7601 5650 December 2000 © Bank of England 2000 ISBN 1 85730 197 8 1 BASIC BOND ANALYSIS Joanna Place Contents Page Abstract ...................................................................................................................3 1 Introduction ......................................................................................................5 2 Pricing a bond ...................................................................................................5 2.1 Single cash flow .....................................................................................5 2.2 Discount Rate .........................................................................................6 2.3 Multiple cash flow..................................................................................7 2.4 Dirty Prices and Clean Prices.................................................................8 2.5 Relationship between Price and Yield .......................................................10 3 Yields and Yield Curves .................................................................................11 3.1 Money market yields ..........................................................................11 3.2 Uses of yield measures and yield curve theories ...............................12 3.3 Flat yield..............................................................................................12 -
Bootstrapping the Interest-Rate Term Structure
Bootstrapping the interest-rate term structure Marco Marchioro www.marchioro.org October 20th, 2012 Advanced Derivatives, Interest Rate Models 2010-2012 c Marco Marchioro Bootstrapping the interest-rate term structure 1 Summary (1/2) • Market quotes of deposit rates, IR futures, and swaps • Need for a consistent interest-rate curve • Instantaneous forward rate • Parametric form of discount curves • Choice of curve nodes Advanced Derivatives, Interest Rate Models 2010-2012 c Marco Marchioro Bootstrapping the interest-rate term structure 2 Summary (2/2) • Bootstrapping quoted deposit rates • Bootstrapping using quoted interest-rate futures • Bootstrapping using quoted swap rates • QuantLib, bootstrapping, and rate helpers • Derivatives on foreign-exchange rates • Sensitivities of interest-rate portfolios (DV01) • Hedging portfolio with interest-rate risk Advanced Derivatives, Interest Rate Models 2010-2012 c Marco Marchioro Bootstrapping the interest-rate term structure 3 Major liquid quoted interest-rate derivatives For any given major currency (EUR, USD, GBP, JPY, ...) • Deposit rates • Interest-rate futures (FRA not reliable!) • Interest-rate swaps Advanced Derivatives, Interest Rate Models 2010-2012 c Marco Marchioro Bootstrapping the interest-rate term structure 4 Quotes from Financial Times Advanced Derivatives, Interest Rate Models 2010-2012 c Marco Marchioro Bootstrapping the interest-rate term structure 5 Consistent interest-rate curve We need a consistent interest-rate curve in order to • Understand the current market conditions -
Fixed Income 2
2 | Fixed Income Fixed 2 CFA Society Italy CFA Society Italy è l’associazione Italiana dei professionisti che lavorano nell’industria Fixed finanziaria italiana. CFA Society Italy nata nel 1999 come organizzazione no profit, è affiliata a CFA Institute, l’associazione globale di professionisti degli investimenti che definisce gli Income standard di eccellenza per il settore. CFA Society Italy ha attualmente oltre 400 soci attivi, nel mondo i professionisti certificati CFA® sono oltre 150.000. Assegnato per la prima volta nel 1963, CFA® è la designazione di eccellenza professionale per la comunità finanziaria internazionale. Il programma CFA® offre una sfida educativa davvero globale in cui è possibile creare una conoscenza fondamentale dei principi di investimento, rilevante per ogni mercato mondiale. I soci che hanno acquisito la certificazione CFA® incarnano le quattro virtù che sono le caratteristiche distintive di CFA Institute: Etica, Tenacia, Rigore e Analisi. CFA Society Italia offre una gamma di opportunità educative e facilita lo scambio aperto di informazioni e opinioni tra professionisti degli investimenti, grazie ad una serie continua di eventi per i propri membri. I nostri soci hanno la possibilità di entrare in contatto con la comunità finanziaria italiana aumentando il proprio network lavorativo. I membri di CFA Society Italy hanno inoltre la posibilità di partecipare attivamente ad iniziative dell’associazione, che Guida a cura di Con la collaborazione di consentono di fare leva sulle proprie esperienze lavorative. L’iscrizione e il completamento degli esami del programma CFA®, anche se fortemente raccomandati, non sono un requisito per l’adesione e incoraggiamo attivamente i professionisti italiani del settore finanziario a unirsi alla nostra associazione. -
Asset Allocation, Time Diversification and Portfolio Optimization for Retirement
Technology and Investment, 2011, 2, 92-104 doi:10.4236/ti.2011.22010 Published Online May 2011 (http://www.SciRP.org/journal/ti) Asset Allocation, Time Diversification and Portfolio Optimization for Retirement Kamphol Panyagometh NIDA Business School, Bangkok, Thailand E-mail: [email protected], [email protected] Received February 17, 2011; revised April 6, 2011; accepted April 10, 2011 Abstract Using the data of stock, commodity and bond indexes from 2002 to November 2010, this research was car- ried out by employing Bootstrapping Simulation technique to find an optimal portfolio (portfolio optimiza- tion) for retirement, and the effect of diversification based on increased length of investment period (time diversification) with respect to the lengths of retirement investment period and the amounts required for spending after retirement in various occasions. The study analyzed for an optimal allocation of common stock, commodity and government bond to achieve the target rate of return for retirement by minimizing the portfolio risk as measured from the standard deviation. Apart from the standard deviation of the rate of return of the investment portfolio, this study also viewed the risk based on the Value at Risk concept to study the downside risk of the investment portfolio for retirement. Keywords: Asset Allocation, Time Diversification, Portfolio Optimization, Bootstrapping Simulation 1. Introduction bond in investment portfolio (portfolio optimization) for retirement, and the effect of diversification based on in- Nowadays -
Implied Correlations in CDO Tranches
Implied Correlations in CDO Tranches a, b c,⋆ Nicole Lehnert ∗, Frank Altrock , Svetlozar T. Rachev , Stefan Tr¨uck d, Andr´eWilch b aUniversit¨at Karlsruhe, Germany bCredit Risk Management, WestLB AG, Germany cUniversit¨at Karlsruhe, Germany and University of California, Santa Barbara, USA dQueensland University of Technology, Australia Abstract Market quotes of CDO tranches constitute a market view on correlation at differ- ent points in the portfolio capital structure and thus on the shape of the portfolio loss distribution. We investigate different calibrations of the CreditRisk+ model to examine its ability to reproduce iTraxx tranche quotes. Using initial model calibra- tion, CreditRisk+ clearly underestimates senior tranche losses. While sensitivities to correlation are too low, by increasing PD volatility up to about 3 times of the default probability for each name CreditRisk+ produces tails which are fat enough to meet market tranche losses. Additionally, we find that, similar to the correlation skew in the large pool model, to meet market quotes for each tranche a different PD volatility vector has to be used. ⋆ Rachev gratefully acknowledges research support by grants from Division of Math- ematical, Life and Physical Sciences, College of Letters and Science, University of California, Santa Barbara, the German Research Foundation (DFG) and the Ger- man Academic Exchange Service (DAAD). ∗ Corresponding author. email: nicole.lehnert@d-fine.de 20 December 2005 1 Introduction Credit derivatives started actively trading in the mid 1990s, exhibiting im- pressive growth rates over the last years. Due to new regulatory requirements there is an increasing demand by holders of securitisable assets to sell assets or to transfer risks of their assets. -
Introduction to Repo Markets
Understanding Repo Markets Moorad Choudhry Objectives of the Course g Defining and describing the mechanics of Repo g Understanding market fundamentals and applying knowledge gained to daily work in the repo markets g Introducing trading theory and strategy (c) 2000 The Securities Institute (Services) Ltd 2 Agenda g Introduction and Market Background g Financial Arithmetic g Uses and Economic Functions g Mechanics of Repo g Risks in trading Repo g Legal, Accounting, Tax and Capital g Repo netting g Overseas and Central Bank Repo g Case study - repo trades (c) 2000 The Securities Institute (Services) Ltd 3 Agenda (cont.) g The UK Gilt Repo Market g Trading and Hedging Strategy g Electronic Repo Trading g The Implied Repo Rate and Basis Trading g The Yield Curve TM g Using Bloomberg Screens g Introduction to Equity repo (c) 2000 The Securities Institute (Services) Ltd 4 Introduction (c) 2000 The Securities Institute (Services) Ltd 5 Definition of a Repo g The term “Repo” is from “Sale and Repurchase Agreement” Repo is a money market instrument. There are two usually two parties to a repo transaction. g One party “sells” bonds to the other while simultaneously agreeing to repurchase them or receive them back at a specified future date g One party requires either the cash or the bonds and provides collateral to the other as well as compensation for the temporary use of the desired asset g Although legal title to the collateral is transferred, the seller/lender retains both the economic benefits and the market risk of owning them g If cash -
Bloomberg Integration in Fixed Income
Bloomberg Integration in Fixed Income Bloomberg for Education Seminar July 21, 2017 San Francisco Paul Fjeldsted, CFA Senior Lecturer Jon M. Huntsman School of Business Utah State University Outline Overview • Rationale • Class Overview • Bloomberg Market Concepts • Problem Sets • Bloomberg In-Class Integration • Investing Practicum Integration Rationale Why Bloomberg? Pros Cons • Connection to practice • Cost • Dynamic • Interface • Robust Rationale Configuration • 9 desktop licenses in dedicated lab for students • 3 Bloomberg Anywhere licenses for professors • Bloomberg Anywhere can be launched in any classroom Fixed Income Course Overview FIN 5300 FIXED INCOME • 20-25 students, masters level course • CFA Curriculum integration – Level 1 and Level 2 Fixed Income volumes Fixed Income Course Overview Grading Exams (4 @ 100 each) 400 Problem Sets 50 Investment Activity 30 In-Class Questions 20 Total 500 Bloomberg Market Concepts Bloomberg Market Concepts • Required within first two weeks of semester • Prerequisite to handing in first problem set • Overview – high level • Brings students up to speed on language of finance Bloomberg Problem Sets Bond Valuation Problem Sets – General Approach • Select a bond in Bloomberg • Model its cashflows in excel • Replicate price • Replicate risk measures Bloomberg Problem Sets Example – US Treasury Note Problem Set • In Bloomberg, select US Treasury note or bond with at least 10 years remaining • Pull up the bond in Bloomberg. Assume $1,000,000 face value • Type "YA" for yield analysis. Download this -
Estimation of Zero-Coupon Curves in Datametrics
Estimation of zero-coupon curves in DataMetrics Allan Malz RiskMetrics Group [email protected] DataMetrics is modifying its technique for estimating zero-coupon interbank and gov- ernment benchmark curves. The new algorithm is employed together with additional synchronized input data to deliver better-quality curves. The modified technique assumes the instantaneous forward rate is a constant between the maturity dates of observable interest rates. Together, the flat forward technique and new input data increase pricing and risk measurement accuracy, particularly at the short end. The flat forward technique is shown to be preferable to plausible alternative approaches. DataMetrics is modifying the bootstrapping technique it uses to estimate zero-coupon curves. The modified bootstrapping technique assumes the instantaneous forward interest rate is a constant between observed bond or other security maturities. We therefore refer to it as the “flat forward” technique. DataMetrics applies it to a range of interbank and government benchmark zero-coupon curves in both key currencies and emerging markets. The new algorithm is being employed together with additional input data to deliver better-quality curves. Together, the flat forward technique and new input data provide several advantages: • The underlying data for the interbank and government curves, particularly the government bonds, can be sparse. For example, there are only 6 U.S. Treasury benchmarks, of which 3 are T-bills and 3 are coupon bonds. The flat forward approach avoids potentially adding spurious information to that contained in the modest available underlying data set, while still permitting accurate pricing. • It permits DataMetrics to estimate time series of spot interest rates with any time to maturity ranging from overnight to 30 years, applying any desired compounding interval or day count convention uniformly across the curve. -
Fixed Rate Bond Valuation and Risk
Fixed Rate Bond Valuation and Risk FinPricing Fixed Rate Bond Summary ▪ Fixed Rate Bond Introduction ▪ The Use of Fixed Rate Bond ▪ Valuation: Yield-to-Maturity Approach ▪ Valuation: Credit Spread Approach ▪ Practical Guide ▪ A Real World Example Fixed Rate Bond Fixed Rate Bond Introduction ▪ A bond is a debt instrument in which an investor loans money to the issuer for a defined period of time. ▪ The investor will receive coupons paid by the issuer at a predetermined interest rate at specified dates before bond maturity. ▪ The bond principal will be returned at maturity date. ▪ A fixed rate bond is usually a long term paper. ▪ Bonds are usually issued by companies, municipalities, states/provinces and countries to finance a variety of projects and activities. Fixed Rate Bond The Use of Fixed Rate Bond ▪ Fixed rate bonds generally pay higher coupons than interest rates. ▪ An investor who wants to earn a guaranteed interest rate for a specified term can choose fixed rate bonds. ▪ The benefit of a fixed rate bond is that investors know for certain how much interest rate they will earn and for how long. ▪ Due to the fixed coupon, the market value of a fixed rate bond is susceptible to fluctuation in interest rate and therefore has a significant interest rate risk. ▪ The long maturity schedule and fixed coupon rate offers an investor a solidified return. ▪ The real value of a fixed rate bond is also susceptible to inflation rate given its long term Fixed Rate Bond Valuation: Yield-to-Maturity Approach ▪ There are two types of bond valuation approaches in the market: yield-to-maturity approach and credit spread approach. -
Fabozzi Course.Pdf
Asset Valuation Debt Investments: Analysis and Valuation Joel M. Shulman, Ph.D, CFA Study Session # 15 – Level I CFA CANDIDATE READINGS: Fixed Income Analysis for the Chartered Financial Analyst Program: Level I and II Readings, Frank J. Fabozzi (Frank J. Fabozzi Associates, 2000) “Introduction to the Valuation of Fixed Income Securities,” Ch. 5 “Yield Measures, Spot Rates, and Forward Rates,” Ch. 6 “Introduction to Measurement of Interest Rate Risk,” Ch. 7 © 2002 Shulman Review/The Princeton Review Fixed Income Valuation 2 Learning Outcome Statements Introduction to the Valuation of Fixed Income Securities Chapter 5, Fabozzi The candidate should be able to a) Describe the fundamental principles of bond valuation; b) Explain the three steps in the valuation process; c) Explain what is meant by a bond’s cash flow; d) Discuss the difficulties of estimating the expected cash flows for some types of bonds and identify the bonds for which estimating the expected cash flows is difficult; e) Compute the value of a bond, given the expected cash flows and the appropriate discount rates; f) Explain how the value of a bond changes if the discount rate increases or decreases and compute the change in value that is attributable to the rate change; g) Explain how the price of a bond changes as the bond approaches its maturity date and compute the change in value that is attributable to the passage of time; h) Compute the value of a zero-coupon bond; i) Compute the dirty price of a bond, accrued interest, and clean price of a bond that is between coupon -
Credit Derivatives – Pricing and Bootstrapping
Credit Derivatives – Pricing and Bootstrapping Author: Mi Sun University College London MSc Financial Computing Project 2009-2010 Project Supervisor: Christopher Clack Submission Date: 15 September 2010 Disclaimer: This report is submitted as part requirement for the MSc Degree in Financial Computing at University College London. It is substantially the result of my own work except where explicitly indicated in the text. The report may be freely copied and distributed provided the source is explicitly acknowledged. MSc Financial Computing Project 2009-2010 by Mi Sun Abstract This project explores different pricing models for credit derivatives and implements the bootstrapping method for the survival curve and base correlation. The credit derivatives discussed in this report include credit default swap (CDS) and collateralized debt obligation (CDO). The main aim of the project is to make sure that there is no arbitrage opportunity between quoted (CDS and index CDO tranches) instruments and unquoted (bespoke CDO tranches) instruments. In doing so, the objectives include obtaining the CDS survival curve from market spreads. Then together with the standardized index CDO tranche spreads, the CDS survival curve is an input parameter for obtaining the base correlation. Finally using the base correlation, the bespoke (i.e. customized) CDO tranche can be priced consistently. There are seven chapters. The first one introduces the background and underlying logic of the whole project. The second chapter starts to introduce the pricing of credit default swaps (CDSs), and discusses the bootstrapping and interpolation of the CDS survival curve. The third chapter moves on to introduce the pricing of collateralized debt obligations (CDOs), and investigates two models for building the CDO tranche survival curve. -
Bootstrapping the Illiquidity by Ametrano and Bianchetti
BOOTSTRAPPING THE ILLIQUIDITY MULTIPLE YIELD CURVES CONSTRUCTION FOR MARKET COHERENT FORWARD RATES ESTIMATION FERDINANDO M. AMETRANO AND MARCO BIANCHETTI Abstract. The large basis spreads observed on the interest rate mar- ket since the liquidity crisis of summer 2007 imply that di®erent yield curves are required for market coherent estimation of forward rates with di®erent tenors (e.g. Euribor 3 months, Euribor 6 months, etc.). In this paper we review the methodology for bootstrapping multi- ple interest rate yield curves, each homogeneous in the underlying rate tenor, from non-homogeneous plain vanilla instruments quoted on the market, such as Deposits, Forward Rate Agreements, Futures, Swaps, and Basis Swaps. The approach includes turn of year e®ects and is ro- bust to deliver smooth yield curves and to ensure non-negative rates also in highly stressed market situations, characterized by crazy roller coaster shapes of the market quotations. The concrete EUR market case is analyzed in detail, using the open source QuantLib implementation of the proposed algorithms. 1. Introduction Pricing complex interest rate derivatives requires modeling the future dy- namics of the yield curve term structure. Most of the literature assumes the existence of the current yield curve as given, and its construction is often neglected, or even obscured, as it is considered more an art than a sci- ence. Actually any yield curve term structure modeling approach will fail to produce good/reasonable prices if the current term structure is not correct. Financial institutions, software houses and practitioners have developed their own proprietary methodologies in order to extract the yield curve term structure from quoted prices of a ¯nite number of liquid market instruments.