...INTEREST RATE RISK MANAGEMENT: DEVELOPMENTS IN INTEREST RATE TERM STRUCTURE MODELING FOR RISK MANAGEMENT AND VALUATION OF INTEREST-RATE-DEPENDENT CASH FLOWS Andrew Ang* and Michael Sherris† ABSTRACT This paper surveys the main concepts and techniques of recent developments in the modeling of the term structure of interest rates that are used in the risk management and valuation of interest-rate-dependent cash flows. These developments extend the concepts of immunization and matching to a stochastic interest rate environment. Such cash flows include the cash flows on assets such as bonds and mortgage-backed securities as well as those for annuity products, life insurance products with interest-rate-sensitive withdrawals, accrued liabilities for definedbenefit pension funds, and property and casualty liability cash flows. 1. INTRODUCTION The aim of this paper is to discuss recent developments in interest rate term structure modeling and the application of these models to the interest rate risk management and valuation of cash flows that are dependent on future interest rates. Traditional approaches to risk management and valuation are based on the concepts of immunization and matching of cash flows. These ideas were pioneered in the actuarial profession by the British actuary Frank Redington (1952). Interest rates have long been recognized as important to the risk management of insurance liabilities. Recent developments have incorporated a stochastic approach to modeling interest...
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...heteroscedasticity and autocorrelation. Content: 1. Simple Regression Analysis 2. Multiple Regression Analysis 3. Dummy Variables 4. Heteroscedasticity 5. Autocorrelation Main Textbook: Dougherty, C. (2011). Introduction to Econometrics, 4th edition, Oxford. 2. Module Name: Computational Finance Code: P12614 Credits: 10 Semester: Spring 2011/12 Programme classes: 12 1-2 hour lectures/workshops Aims: The module aims to describe and analyse the general finance topics and introduces students to implement basic computational approaches to financial problems using Microsoft Excel. It stresses the fundamentals of finance; provides students with a knowledge and understanding on the key finance subjects such as money market, return metric, portfolio modelling, asset pricing, etc.; and equips students with the essential techniques applied in financial calculations. Contents: 1. Lecture Topic 1: Money Market Instrument : Introduction to the course; Interest rate types;...
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...Returning to the earlier example, there are 3 key points: Why should theoretical price be the market price? This is an important question. If not then there is risk-free money to be made. If C < 50p buy it and hedge to make pro…t. If C > 50p sell it and hedge, make a guaranteed pro…t. Supply and demand should make this price converge to 50p. How do I know to sell 1/2 the stock for hedging (and not another value)? means the amount of stock sold for hedging purposes. The right choice for hedging means that the value of the portfolio does not depend on the direction of the stock. Earlier we had 1 101 = 99 1 0 = = 101 99 1 2 Note it is purely a coincident in this example that delta has the same value as the option. Note = V+ S+ V S = Range of option payo¤s Range of stock prices This model is discrete time, discrete stock. When we go to continuous time continuous stock delta will become @V : @S How does this change if interest rates are non-zero? Everything is as before but we now have a discount factor. Consider the earlier example but with r = 10% over one day, i.e. 1 1 = 1 + rt 1 + 0:1=252 0:9996 Now discount tomorrow’ value to get to todays s V 0:5 100 = 0:5 99 V = 0:51963 0:9996 So the portfolio value today must be the Present Value of the portfolio value tomorrow. Consider a portfolio asset price Si : ; long an option and short assets. Vi denotes the option value corresponding to S+ V+ S0 ...
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...I I ! An Introduction to Derivatives and Risk Management Don M. Chance Louisiana State University Robert Brooks University of Alabama THOMSON oj{ Au s r r ett e . a r e au . C .. nada . ~~".-."~'-~--"'---'"""" MeYlco' 5ing;1lpore· Spain' u nu e d K,.. gdom· umt e c ~t4t~es , c.~ ! , . THOMSON SOUTH-VVESTERN __~ Chapter 1 Preface XlII Iuuoduction PART I Options 21 Chapter 2 Chapter 3 Chapter -! Chapter 5 Chapter 6 Chapter 7 Structure of Options Markets 22 Principles of Option Pricing 54 Option Pricing Models: The Binomial Model 92 Option Pricing Models: The Black-Scholes-Merton Model Basic Option Strategies 181 Advanced Option Strategies 218 An Introduction to Derivatives and Risk Management, Seventh Edition Don M. Chance and Robert Brooks Printer: Transcontinental Louiseville. QC VP/Editorial Director: Jack W. Calhoun Manager of Technology, Editorial: Vicky True VP/Editor-in-Chief: Alex von Rosenberg Senior Technology Project Editor: Matt McKinney Executive Editor: Mike Reynolds Senior Marketing Communications Manager: Jim Overly Internal Designer: Lou Ann Thesing Senior Print Buyer: Sandee Milewski Cover Designer: Paul Neff Design Production House: ICC Macmillan Inc. Cover Images: © Getty Images, Inc, Senior Developmental Editor: Trish Taylor Marketing Manager: Jason Krall Art Director: Bethany Casey PART II The Thomson Corporation...
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...the transaction, with particular regard to: • Price • delivery date • type of asset to be delivered • quantity of asset to be delivered • minimum quality of asset to be delivered o this factor is important for commodity futures Note that, the ‘price’ of the future is the specified amount that is paid by the buyer to the seller on the delivery date. No money passes from the buyer to the seller at outset. Types of futures contracts Futures contracts were originally based on commodities (e.g. sugar, wheat, gold), and have been traded since the 18th Century. However, financial futures have been traded on the Chicago Board of Trade (CBOT) since 1972 and London International Financial Futures and Options Exchange (LIFFE) since 1982. In practice, futures contracts are settled ‘for cash’, rather than by the delivery of the underlying asset. The cash settlement is the difference between the price of the underlying asset at the delivery date and the price agreed at the outset of the contract. The seller of a futures contract is said to ‘short’ of the future, and the buyer is said to be ‘long’. The role of the clearing house When a price is agreed between the buyer and seller of a futures contract, the details are registered with the futures exchange clearing house. The clearing house then acts...
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...Chapter 10 Arbitrage Pricing Theory and Multifactor Models of Risk and Return Multiple Choice Questions 1. ___________ a relationship between expected return and risk. A. APT stipulates B. CAPM stipulates C. Both CAPM and APT stipulate D. Neither CAPM nor APT stipulate E. No pricing model has found Both models attempt to explain asset pricing based on risk/return relationships. Difficulty: Easy 2. ___________ a relationship between expected return and risk. A. APT stipulates B. CAPM stipulates C. CCAPM stipulates D. APT, CAPM, and CCAPM stipulate E. No pricing model has found APT, CAPM, and CCAPM models attempt to explain asset pricing based on risk/return relationships. Difficulty: Easy 3. In a multi-factor APT model, the coefficients on the macro factors are often called ______. A. systemic risk B. factor sensitivities C. idiosyncratic risk D. factor betas E. B and D The coefficients are called factor betas, factor sensitivities, or factor loadings. Difficulty: Easy 6. Which pricing model provides no guidance concerning the determination of the risk premium on factor portfolios? A. The CAPM B. The multifactor APT C. Both the CAPM and the multifactor APT D. Neither the CAPM nor the multifactor APT E. None of the above is a true statement. The multifactor APT provides no guidance as to the determination of the risk premium on the various factors. The CAPM assumes that the excess market return over the risk-free...
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...Theory Covariance: how close two variables move Together The reward-to-volatility = sharpe ratio Serial correlation of daily returns is close to zero => very hard to predict from their past Value-at-Risk (VaR): a measure of downside risk ->Measures the potential loss over a specified horizon such that there is a (low) probability α that the actual loss will be larger No clear guidelines as to the choice of sample length m: small m means that the VaR will be more influenced by recent events; large m is needed for precise estimates - No way to extrapolate the 1-day VaR to a longer n-day horizon (except if nonoverlapping n-period returns are considered to re-calculate the n-day VaR) A risk-averse investor: - Accepts risk-free or speculative prospects with positive risk-premiums - Rejects portfolios that are fair games (or worse) The higher the indifference curve, the higher the utility levelT he steeper the indifference curve, the higher the risk aversion -> higher compensation required for the same level of risk Two major sources of uncertainty for the risky assets in a portfolio: 1. Market risk -? Systematic, non-diversifiable 2. Firm-specific risk -> Non-systematic, diversifiable The minimum-variance frontier, which gives the lowest variance that can be attained for any target level of expected portfolio return The separation property The portfolio choice problem may be separated into two independent tasks -Determination of the optimal...
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...theoretical estimate of the price of European-style options. The formula led to a boom in options trading and legitimised scientifically the activities of the Chicago Board Options Exchange and other options markets around the world.[2] lt is widely used, although often with adjustments and corrections, by options market participants.[3]:751 Many empirical tests have shown that the Black–Scholes price is "fairly close" to the observed prices, although there are well-known discrepancies such as the "option smile".[3]:770–771 The Black–Scholes was first published by Fischer Black and Myron Scholes in their 1973 paper, "The Pricing of Options and Corporate Liabilities", published in the Journal of Political Economy. They derived a stochastic partial differential equation, now called the Black–Scholes equation, which estimates the price of the option over time. The key idea behind the model is to hedge the option by buying and selling the underlying asset in just the right way, and consequently "eliminate risk". This hedge is called delta hedging and is the basis of more complicated hedging strategies such as those engaged in by investment banks and hedge funds. The hedge implies that there is a unique price for the option and this is given by the Black–Scholes formula. Robert C. Merton was the first to publish a paper expanding the mathematical understanding of the options pricing model, and coined the term Black–Scholes options pricing model. Merton and Scholes received the 1997 Nobel...
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...2003 3:04 PM Economy and Society Volume 32 Number 3 August 2003: 349–380 Long-Term Capital Management and the sociology of arbitrage Donald MacKenzie Abstract Arbitrage is a key process in the practice of financial markets and in their theoretical depiction: it allows markets to be posited as efficient without all investors being assumed to be rational. This article explores the sociology of arbitrage by means of an examination of the arbitrageurs, Long-Term Capital Management (LTCM). LTCM’s 1998 crisis is analysed using both qualitative, interview-based data and quantitative examination of price movements. It is suggested that the roots of the crisis lay in an unstable pattern of imitation that had developed in the markets within which LTCM operated. As the resulting ‘superportfolio’ began to unravel, arbitrageurs other than LTCM fled the market, even as arbitrage opportunities became more attractive, causing huge price movements against LTCM. Three features of the sociology of arbitrage are discussed: its conduct by people often personally known to each other; the possibility and consequences of imitation; and the limits on the capacity of arbitrage to close price discrepancies. It is suggested that by 1998 imitative arbitrage formed a ‘global microstructure’ in the sense of Knorr Cetina and Bruegger. Keywords: arbitrage; economic sociology; imitation; Long-Term Capital Management (LTCM); globalization; risk. Introduction Of all the contested boundaries...
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...The Chinese University of Hong Kong CUHK Business School FINA3020 International Finance First Term 2015 – 2016 A. Staff Information Instructor: Office: Phone: Email: Office Hours: Dr. Anson C. K. AU YEUNG Room 1245, Department of Finance, CYT 3943 3780 ansonauyeung@baf.cuhk.edu.hk By Appointment TA: Office: Phone: Email: Office Hours: Miss. Karen LEE Room 1155, Department of Finance, CYT 3943 7840 karenlee@baf.cuhk.edu.hk By Appointment B. Class Schedule Session FINA3020A FINA3020B Day Thursday Monday Time 14:30 – 17:15 14:30 – 17:15 Venue CKB UG04 WMY 406 C. Course Overview Businesses are operating in an increasingly competitive environment. Managing businesses either directly or indirectly exposed to international competition requires an understanding of currency markets, foreign exchange derivatives, exchange risk, exposure and risk management. This course assumes the viewpoint of the financial manager of a multinational corporation (MNC) with investment or financial operations in more than one country. Managers encounter new opportunities as they extend their operations into international markets, as well as new costs and risks. The challenge facing the multinational financial manager is to successfully develop and execute business and financial strategies in more than one national business environment. The aim of this course is to provide you a framework for analyzing financial decisions relating to risk management...
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...Business, Stanford, California, USA INTRODUCTION* Following tradition, I deal here with the Capital Asset Pricing Model, a subject with which I have been associated for over 25 years, and which the Royal Swedish Academy of Sciences has cited in honoring me with the award of the Prize in Economic Sciences in Memory of Alfred Nobel. I first present the Capital Asset Pricing Model (hence, CAPM), incorpo1 rating not only my own contributions but also the outstanding work of Lintner (1965, 1969) and the contributions of Mossin (1966) and others. My goal is to do so succinctly yet in a manner designed to emphasize the economic content of the theory. Following this, I modify the model to reflect an extreme case of an institutional arrangement that can preclude investors from choosing fully optimal portfolios. In particular, I assume that investors are unable to take negative positions in assets. For this version of the model I draw heavily from papers by Glenn (1976), Levy (1978), Merton (1987) and Markowitz (1987, 1990). Finally, I discuss the stock index futures contract - a major financial innovation of worldwide importance that postdates the development of the CAPM. Such contracts can increase the efficiency of capital markets in many ways. In particular, they can bring actual markets closer to the idealized world assumed by the Capital Asset Pricing Model. THE CAPITAL ASSET PRICING MODEL The initial version of the CAPM, developed over 25 years ago, was extremely parsimonious. It dealt...
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...overvalued and undervalued equity securities while neutralizing the portfolio’s exposure to market risk by combining long and short positions. Portfolios are typically structured to be market, industry, sector, and dollar neutral, with a portfolio beta around zero. This is accomplished by holding long and short equity positions with roughly equal exposure to the related market or sector factors. Because many investors face constraints relative to shorting stocks, situations of overvaluation may be slower to correct than those of undervaluation. Because this style seeks an absolute return, the benchmark is typically the risk-free rate. (For more, see: Getting Positive Results With Market-Neutral Funds.) * Convertible arbitrage: These strategies attempt to exploit mis-pricings in corporate convertible securities, such as convertible bonds, warrants, and convertible preferred stock. Managers in this category buy or sell these securities and then hedge part or all of the associated risks. The simplest example is buying convertible bonds and hedging the equity component of the bonds’ risk by shorting the...
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...and/or Finance. This course is aimed at students wishing to acquire a sound understanding of the main opportunities in international investments. For example, the relevance of hedging in the management of currency risk will be studied in light of theoretical results and empirical evidence. We will also briefly cover foreign direct investment (FDI), since in general, the revenue generated from FDI by U.S. firms is about three times as large as the revenue generated from the exporting of U.S. goods by U.S. firms. Due to the ever increasing importance of international corporate governance, there is a corresponding need to decipher and use information in financial reports. At least one class meeting and one case study will touch on some key issues in international financial reporting and analysis, such as financial disclosure/transparency, incentives for off-balance sheet liabilities, hedge accounting, lease accounting, footnote disclosures, and intercorporate equity investments, and international financial reporting differences. We will also use many real-life examples from market practices to emphasize the engineering dimensions of financial contract design (financial engineering), that market practitioners professionalize by blending theory with practice. Real financial contract examples will be discussed along with the relevant sections of the Levich text during the...
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...may take place without the written permission of Cambridge University Press. First published in print format 2002 eBook (EBL) ISBN-13 978-0-511-33725-3 ISBN-10 0-511-33725-6 eBook (EBL) ISBN-13 ISBN-10 paperback 978-0-521-89077-9 paperback 0-521-89077-2 Cambridge University Press has no responsibility for the persistence or accuracy of urls for external or third-party internet websites referred to in this publication, and does not guarantee that any content on such websites is, or will remain, accurate or appropriate. Contents Preface 1 Single period models Summary 1.1 Some definitions from finance 1.2 Pricing a forward 1.3 The one-step binary model 1.4 A ternary model 1.5 A characterisation of no arbitrage 1.6 The risk-neutral probability measure Exercises Binomial trees and discrete parameter martingales Summary 2.1 The multiperiod binary model 2.2 American options 2.3 Discrete parameter martingales and Markov processes 2.4 Some important martingale theorems 2.5 The Binomial Representation Theorem 2.6 Overture to continuous models Exercises Brownian motion Summary 3.1 Definition of the process 3.2 L´ vy’s construction of Brownian motion e 3.3 The reflection principle and scaling 3.4...
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...theory: identical assets have identical prices. In our 1998–2000 sample, holders of a share of company A are expected to receive x shares of company B, but the price of A is less than x times the price of B. A prominent example involves 3Com and Palm. Arbitrage does not eliminate this blatant mispricing due to short-sale constraints, so that B is overpriced but expensive or impossible to sell short. Evidence from options prices shows that shorting costs are extremely high, eliminating exploitable arbitrage opportunities. I. Introduction There are two important implications of the efficient market hypothesis. The first is that it is not easy to earn excess returns. The second is that prices are “correct” in the sense that prices reflect fundamental value. This latter implication is, in many ways, more important than the first. Do asset markets offer rational signals to the economy about where to We thank John Cochrane, Douglas Diamond, Merle Erickson, Lou Harrison, J. B. Heaton, Ravi Jagannathan, Arvind Krishnamurthy, Mark Mitchell, Todd Pulvino, Tuomo Vuolteenaho, an anonymous referee, and seminar participants at the American Finance Association, Harvard Business School, the National Bureau of Economic Research Asset Pricing meeting, and the University of Chicago finance lunch for helpful comments. We thank Joe Cornell and Mark Minichiello of Spin-off Advisors for data and helpful discussions. We thank Frank Fang Yu for excellent research assistance. Lamont gratefully acknowledges...
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