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When You Hedge Discretely
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Book Synopsis Frequently Asked Questions in Quantitative Finance by : Paul Wilmott
Download or read book Frequently Asked Questions in Quantitative Finance written by Paul Wilmott and published by John Wiley & Sons. This book was released on 2010-07-29 with total page 631 pages. Available in PDF, EPUB and Kindle. Book excerpt: Getting agreement between finance theory and finance practice is important like never before. In the last decade the derivatives business has grown to a staggering size, such that the outstanding notional of all contracts is now many multiples of the underlying world economy. No longer are derivatives for helping people control and manage their financial risks from other business and industries, no, it seems that the people are toiling away in the fields to keep the derivatives market afloat! (Apologies for the mixed metaphor!) If you work in derivatives, risk, development, trading, etc. you'd better know what you are doing, there's now a big responsibility on your shoulders. In this second edition of Frequently Asked Questions in Quantitative Finance I continue in my mission to pull quant finance up from the dumbed-down depths, and to drag it back down to earth from the super-sophisticated stratosphere. Readers of my work and blogs will know that I think both extremes are dangerous. Quant finance should inhabit the middle ground, the mathematics sweet spot, where the models are robust and understandable, and easy to mend. ...And that's what this book is about. This book contains important FAQs and answers that cover both theory and practice. There are sections on how to derive Black-Scholes (a dozen different ways!), the popular models, equations, formulae and probability distributions, critical essays, brainteasers, and the commonest quant mistakes. The quant mistakes section alone is worth trillions of dollars! I hope you enjoy this book, and that it shows you how interesting this important subject can be. And I hope you'll join me and others in this industry on the discussion forum on wilmott.com. See you there!” FAQQF2...including key models, important formulae, popular contracts, essays and opinions, a history of quantitative finance, sundry lists, the commonest mistakes in quant finance, brainteasers, plenty of straight-talking, the Modellers' Manifesto and lots more.
Book Synopsis The Volatility Smile by : Emanuel Derman
Download or read book The Volatility Smile written by Emanuel Derman and published by John Wiley & Sons. This book was released on 2016-08-15 with total page 532 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Volatility Smile The Black-Scholes-Merton option model was the greatest innovation of 20th century finance, and remains the most widely applied theory in all of finance. Despite this success, the model is fundamentally at odds with the observed behavior of option markets: a graph of implied volatilities against strike will typically display a curve or skew, which practitioners refer to as the smile, and which the model cannot explain. Option valuation is not a solved problem, and the past forty years have witnessed an abundance of new models that try to reconcile theory with markets. The Volatility Smile presents a unified treatment of the Black-Scholes-Merton model and the more advanced models that have replaced it. It is also a book about the principles of financial valuation and how to apply them. Celebrated author and quant Emanuel Derman and Michael B. Miller explain not just the mathematics but the ideas behind the models. By examining the foundations, the implementation, and the pros and cons of various models, and by carefully exploring their derivations and their assumptions, readers will learn not only how to handle the volatility smile but how to evaluate and build their own financial models. Topics covered include: The principles of valuation Static and dynamic replication The Black-Scholes-Merton model Hedging strategies Transaction costs The behavior of the volatility smile Implied distributions Local volatility models Stochastic volatility models Jump-diffusion models The first half of the book, Chapters 1 through 13, can serve as a standalone textbook for a course on option valuation and the Black-Scholes-Merton model, presenting the principles of financial modeling, several derivations of the model, and a detailed discussion of how it is used in practice. The second half focuses on the behavior of the volatility smile, and, in conjunction with the first half, can be used for as the basis for a more advanced course.
Book Synopsis Dynamic Hedging by : Nassim Nicholas Taleb
Download or read book Dynamic Hedging written by Nassim Nicholas Taleb and published by John Wiley & Sons. This book was released on 1997-01-14 with total page 536 pages. Available in PDF, EPUB and Kindle. Book excerpt: Destined to become a market classic, Dynamic Hedging is the only practical reference in exotic options hedgingand arbitrage for professional traders and money managers Watch the professionals. From central banks to brokerages to multinationals, institutional investors are flocking to a new generation of exotic and complex options contracts and derivatives. But the promise of ever larger profits also creates the potential for catastrophic trading losses. Now more than ever, the key to trading derivatives lies in implementing preventive risk management techniques that plan for and avoid these appalling downturns. Unlike other books that offer risk management for corporate treasurers, Dynamic Hedging targets the real-world needs of professional traders and money managers. Written by a leading options trader and derivatives risk advisor to global banks and exchanges, this book provides a practical, real-world methodology for monitoring and managing all the risks associated with portfolio management. Nassim Nicholas Taleb is the founder of Empirica Capital LLC, a hedge fund operator, and a fellow at the Courant Institute of Mathematical Sciences of New York University. He has held a variety of senior derivative trading positions in New York and London and worked as an independent floor trader in Chicago. Dr. Taleb was inducted in February 2001 in the Derivatives Strategy Hall of Fame. He received an MBA from the Wharton School and a Ph.D. from University Paris-Dauphine.
Download or read book Derivatives written by Espen Gaarder Haug and published by John Wiley & Sons. This book was released on 2013-10-18 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt: Derivatives Models on Models takes a theoretical and practical look at some of the latest and most important ideas behind derivatives pricing models. In each chapter the author highlights the latest thinking and trends in the area. A wide range of topics are covered, including valuation methods on stocks paying discrete dividend, Asian options, American barrier options, Complex barrier options, reset options, and electricity derivatives. The book also discusses the latest ideas surrounding finance like the robustness of dynamic delta hedging, option hedging, negative probabilities and space-time finance. The accompanying CD-ROM with additional Excel sheets includes the mathematical models covered in the book. The book also includes interviews with some of the world’s top names in the industry, and an insight into the history behind some of the greatest discoveries in quantitative finance. Interviewees include: Clive Granger, Nobel Prize winner in Economics 2003, on Cointegration Nassim Taleb on Black Swans Stephen Ross on Arbitrage Pricing Theory Emanuel Derman the Wall Street Quant Edward Thorp on Gambling and Trading Peter Carr the Wall Street Wizard of Option Symmetry and Volatility Aaron Brown on Gambling, Poker and Trading David Bates on Crash and Jumps Andrei Khrennikov on Negative Probabilities Elie Ayache on Option Trading and Modeling Peter Jaeckel on Monte Carlo Simulation Alan Lewis on Stochastic Volatility and Jumps Paul Wilmott on Paul Wilmott Knut Aase on Catastrophes and Financial Economics Eduardo Schwartz the Yoga Master of Quantitative Finance Bruno Dupire on Local and Stochastic Volatility Models
Book Synopsis Risk Management: The State of the Art by : Stephen Figlewski
Download or read book Risk Management: The State of the Art written by Stephen Figlewski and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: Very often, we associate the dawn of modern financial theory with Harry Markowitz who in the 1950s introduced the formal mathematics of probability theory to the problem of managing risk in an asset portfolio. The 1970s saw the advent of formal models for pricing options and other derivative contracts, whose primary purpose was also financial risk management and hedging. But events in the 1990s made it clear that effective risk management is a critical element for success, and indeed, for long term survival, not only for financial institutions, but also for industrial firms, and even for nonprofit organizations and governmental bodies. These recent events vividly show that the world is filled with all manner of risks, and so risk management must extend far beyond the use of standard derivative instruments in routine hedging applications. The articles in this volume cover two broad themes. One theme emphasizes methods for identifying, modeling, and hedging specific types of financial and business risks. Articles in this category consider the technology of risk measurement, such as Value at Risk and extreme value theory; new classes of risk, such as liquidity risk; new financial instruments and markets for risk management, such as derivative contracts based on weather and on catastrophic insurance risks; and finally, credit risk, which has become one of the most important areas of practical interest for risk management. The second theme stresses risk management from the perspective of the firm and the financial system as a whole. Articles in this category analyze risk management in the international arena, including payment and settlement risks and sovereign risk pricing, risk management from the regulator's viewpoint, and risk management for financial institutions. The articles in this volume examine the "State of the Art" in risk management from the standpoint of academic researchers, market analysts and practitioners, and government observers.
Book Synopsis Paul Wilmott Introduces Quantitative Finance by : Paul Wilmott
Download or read book Paul Wilmott Introduces Quantitative Finance written by Paul Wilmott and published by John Wiley & Sons. This book was released on 2013-10-18 with total page 743 pages. Available in PDF, EPUB and Kindle. Book excerpt: Paul Wilmott Introduces Quantitative Finance, Second Edition is an accessible introduction to the classical side of quantitative finance specifically for university students. Adapted from the comprehensive, even epic, works Derivatives and Paul Wilmott on Quantitative Finance, Second Edition, it includes carefully selected chapters to give the student a thorough understanding of futures, options and numerical methods. Software is included to help visualize the most important ideas and to show how techniques are implemented in practice. There are comprehensive end-of-chapter exercises to test students on their understanding.
Book Synopsis Probability Theory and Applications by : Elton P. Hsu
Download or read book Probability Theory and Applications written by Elton P. Hsu and published by American Mathematical Soc.. This book was released on 1999 with total page 386 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume, with contributions by leading experts in the field, is a collection of lecture notes of the six minicourses given at the IAS/Park City Summer Mathematics Institute. It introduces advanced graduates and researchers in probability theory to several of the currently active research areas in the field. Each course is self-contained with references and contains basic materials and recent results. Topics include interacting particle systems, percolation theory, analysis on path and loop spaces, and mathematical finance. The volume gives a balanced overview of the current status of probability theory. An extensive bibliography for further study and research is included. This unique collection presents several important areas of current research and a valuable survey reflecting the diversity of the field.
Book Synopsis Sustainable Life Insurance by : Aymeric Kalife
Download or read book Sustainable Life Insurance written by Aymeric Kalife and published by CRC Press. This book was released on 2023-08-18 with total page 766 pages. Available in PDF, EPUB and Kindle. Book excerpt: Sustainable Life Insurance: Managing Risk Appetite for Insurance Savings and Retirement Products gives an overview of all relevant aspects of traditional and non-traditional savings and retirement products from both insurers’ and policyholders’ respective risk appetites. Examples of such products include general accounts, whole life, annuities (variable, fixed and fixed indexed, structured), index-linked products, CPPI-based products, etc. The book contains technical details associated with both practice and theory, specifically related to modelling, product design, investments and risk management challenges and solutions, tailored to both insurers’ and policyholders’ perspectives. Features The book offers not only theoretical background but also concrete, cutting-edge "quick wins" across strategic and operational business axes. It will be an asset for professionals in the insurance industry, and a great teaching/learning resource for courses in risk management, insurance modelling, and more. The book highlights the operational challenges encountered across modelling, product designs and hedging.
Book Synopsis A Course in Derivative Securities by : Kerry Back
Download or read book A Course in Derivative Securities written by Kerry Back and published by Springer Science & Business Media. This book was released on 2005-10-11 with total page 358 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Deals with pricing and hedging financial derivatives.... Computational methods are introduced and the text contains the Excel VBA routines corresponding to the formulas and procedures described in the book. This is valuable since computer simulation can help readers understand the theory....The book...succeeds in presenting intuitively advanced derivative modelling... it provides a useful bridge between introductory books and the more advanced literature." --MATHEMATICAL REVIEWS
Download or read book Risk written by and published by . This book was released on 2007 with total page 632 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Lady of Saron written by Jayne Kinch and published by Jayne Kinch. This book was released on 2021-12-01 with total page 616 pages. Available in PDF, EPUB and Kindle. Book excerpt: A new tale in The Land of the Blood of Allaron Legend series, set over four hundred years before events in The Daughter of Teragon. A time when vampires are nothing more than a myth and the Blood of Allaron Legend is yet to come into being. When Princess Felicity Saron helps Prince Viktor Allaron and his brothers obtain the power contained within a magical dagger said to belong to the long-dead Mages of Thiar, little does she know it will release an ancient evil that will see two of the brothers following a dark path which will eventually lead to the murder of their brother and Prime, and will turn Viktor's love for Felicity into an obsession, with devastating consequences. But while it may be too late for Viktor and his brothers, Felicity still has the chance to save the Allaron blood line. Each book in The Land of the Blood of Allaron Legend series is stand-alone, but for the greatest enjoyment, the following reading order is recommended: The Daughter of Teragon The Fair Isle Princess The Guardsman's Lover The Duchess of Farrow The Warrior Queen The Lady of Saron Note to readers: please be aware that this book contains depictions of domestic violence and sexual violence that some readers may find distressing. Contains content of a sexual nature. Mature readers only.
Book Synopsis Pricing, Hedging, and Trading Exotic Options by : Israel Nelken
Download or read book Pricing, Hedging, and Trading Exotic Options written by Israel Nelken and published by Irwin Professional Publishing. This book was released on 2000 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt: "In describing the major types of exotic options Pricing, Hedging, and Trading Exotic Options also reveals their key applications.
Book Synopsis Alternative Investments And Strategies by : Rudiger Kiesel
Download or read book Alternative Investments And Strategies written by Rudiger Kiesel and published by World Scientific. This book was released on 2010-06-18 with total page 414 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book combines academic research and practical expertise on alternative assets and trading strategies in a unique way. The asset classes that are discussed include: credit risk, cross-asset derivatives, energy, private equity, freight agreements, alternative real assets (ARA), and socially responsible investments (SRI). The coverage on trading and investment strategies are directed at portfolio insurance, especially constant proportion portfolio insurance (CPPI) and constant proportion debt obligation (CPDO) strategies, robust portfolio optimization, and hedging strategies for exotic options.
Download or read book Options written by Simon Vine and published by John Wiley & Sons. This book was released on 2011-08-24 with total page 271 pages. Available in PDF, EPUB and Kindle. Book excerpt: The key concepts and essential strategies behind the successful use of options Written by Simon Vine, a seasoned trader who has over ten years of experience on Wall Street under his belt, Options is the definitive book on options for traders, investors, and risk professionals. Options provides a step-by-step approach to trading, hedging, and investing using options, and shares the key concepts essential to successful options use. Options also explores how to use a wide variety of options strategies and shows readers how to select the strategy that best fits their own psychological risk profile. Filled with real-world examples and proven strategies, this invaluable resource will be of interest to all professionals-and newcomers-who'd like to exploit options for strategic advantage, risk management, or profit. Simon Vine (Moscow, Russia) is deputy head of the investment banking division at Alfa Bank, the largest private financial institution in Russia. He holds an MBA from Columbia Business School and a BA from the Institute for Finance and Economics in Moscow.
Download or read book Options written by Michael C. Thomsett and published by Walter de Gruyter GmbH & Co KG. This book was released on 2018-07-23 with total page 447 pages. Available in PDF, EPUB and Kindle. Book excerpt: With over 300,000 copies sold, the new edition of this comprehensive mentoring guide clearly presents all of the essential information needed to learn to trade options. Whereas most options books focus on profit and loss opportunities, this book addresses the issues of hedging market risks in an equity portfolio head on. The author presents the compelling argument that options should not be thought of as risky stand-alone trading vehicles, but offer greater value as a coordinated strategic methodology for managing equity portfolio risks as presented in numerous examples in this book. Divided into four parts, Options reflects a guiding standard of the past nine editions and includes: Crystal clear explanations of the attributes and strategies of calls and puts. A chapter on the short life of an option. This, missing in almost every options book, is a key to understanding options trading. Examples in Part 1 showing different trading strategies on both sides of the trade. The second part of the book is about closing positions; taking profit, exercising, expirations or rolling forward your position, risk analysis, profit calculations, and the impact of volatility. The third part simplifies the complex issues of advanced strategies including the various spreads, combining spreads to successfully hedge other positions and how certain strategies work. Each spread is covered in at least one detailed example. The final part is on evaluating risk. The unquestioned benefits of hedging risk and strategies that are virtually guaranteed to succeed that are generally the domain of the investment giants along with many examples are discussed. The book’s broad coverage makes it an incredibly valuable desk reference to any trader in options. You won’t get explanations like these on the internet. Michael C. Thomsett is a market expert, author, speaker, and coach. His many books include Stock Market Math, Candlestick Charting, The Mathematics of Options, and A Technical Approach to Trend Analysis. Click here to see an interview with the author. https://youtu.be/8bgrgLB3Mx4
Book Synopsis Tombstone, 1881 (The Symbiont Time Travel Adventures Series, Book 2) by : T.L.B. Wood
Download or read book Tombstone, 1881 (The Symbiont Time Travel Adventures Series, Book 2) written by T.L.B. Wood and published by ePublishing Works!. This book was released on 2016-02-11 with total page 233 pages. Available in PDF, EPUB and Kindle. Book excerpt: "When the stagecoach journey from Tucson began, I felt dusty and my back ached from sitting on the bench seat so long in very uncomfortable clothing....Makes me want to go back." - Nadine, verified reviewer What kind of vacation starts with a gunfight between Cowboys and the Earp brothers at the OK Corral? Time traveling historians, Petra and Kipp, plan a relaxing vacation to 1881 Tombstone, Arizona. To the casual observer, Petra appears to be an attractive young woman, while Kipp plays her canine companion. But fun turns to danger when Doc Holliday assumes the role of Petra's protector. Now the symbiotic duo risk becoming entangled in the power struggle between warring factions and breaking the Symbiont Code: never interfere with history's natural progression. THE SYMBIONT TIME TRAVEL ADVENTURES, i>The Symbiont Tombstone, 1881 Whitechapel, 1888 The Great Locomotive Chase, 1862 Titanic, 1912 A Conspiracy to Murder, 1865 Robin Hood, 1192
Book Synopsis Optimization-Based Models for Measuring and Hedging Risk in Fixed Income Markets by : Johan Hagenbjörk
Download or read book Optimization-Based Models for Measuring and Hedging Risk in Fixed Income Markets written by Johan Hagenbjörk and published by Linköping University Electronic Press. This book was released on 2019-12-09 with total page 156 pages. Available in PDF, EPUB and Kindle. Book excerpt: The global fixed income market is an enormous financial market whose value by far exceeds that of the public stock markets. The interbank market consists of interest rate derivatives, whose primary purpose is to manage interest rate risk. The credit market primarily consists of the bond market, which links investors to companies, institutions, and governments with borrowing needs. This dissertation takes an optimization perspective upon modeling both these areas of the fixed-income market. Legislators on the national markets require financial actors to value their financial assets in accordance with market prices. Thus, prices of many assets, which are not publicly traded, must be determined mathematically. The financial quantities needed for pricing are not directly observable but must be measured through solving inverse optimization problems. These measurements are based on the available market prices, which are observed with various degrees of measurement noise. For the interbank market, the relevant financial quantities consist of term structures of interest rates, which are curves displaying the market rates for different maturities. For the bond market, credit risk is an additional factor that can be modeled through default intensity curves and term structures of recovery rates in case of default. By formulating suitable optimization models, the different underlying financial quantities can be measured in accordance with observable market prices, while conditions for economic realism are imposed. Measuring and managing risk is closely connected to the measurement of the underlying financial quantities. Through a data-driven method, we can show that six systematic risk factors can be used to explain almost all variance in the interest rate curves. By modeling the dynamics of these six risk factors, possible outcomes can be simulated in the form of term structure scenarios. For short-term simulation horizons, this results in a representation of the portfolio value distribution that is consistent with the realized outcomes from historically observed term structures. This enables more accurate measurements of interest rate risk, where our proposed method exhibits both lower risk and lower pricing errors compared to traditional models. We propose a method for decomposing changes in portfolio values for an arbitrary portfolio into the risk factors that affect the value of each instrument. By demonstrating the method for the six systematic risk factors identified for the interbank market, we show that almost all changes in portfolio value and portfolio variance can be attributed to these risk factors. Additional risk factors and approximation errors are gathered into two terms, which can be studied to ensure the quality of the performance attribution, and possibly improve it. To eliminate undesired risk within trading books, banks use hedging. Traditional methods do not take transaction costs into account. We, therefore, propose a method for managing the risks in the interbank market through a stochastic optimization model that considers transaction costs. This method is based on a scenario approximation of the optimization problem where the six systematic risk factors are simulated, and the portfolio variance is weighted against the transaction costs. This results in a method that is preferred over the traditional methods for all risk-averse investors. For the credit market, we use data from the bond market in combination with the interbank market to make accurate measurements of the financial quantities. We address the notoriously difficult problem of separating default risk from recovery risk. In addition to the previous identified six systematic risk factors for risk-free interests, we identify four risk factors that explain almost all variance in default intensities, while a single risk factor seems sufficient to model the recovery risk. Overall, this is a higher number of risk factors than is usually found in the literature. Through a simple model, we can measure the variance in bond prices in terms of these systematic risk factors, and through performance attribution, we relate these values to the empirically realized variances from the quoted bond prices. De globala ränte- och kreditmarknaderna är enorma finansiella marknader vars sammanlagda värden vida överstiger de publika aktiemarknadernas. Räntemarknaden består av räntederivat vars främsta användningsområde är hantering av ränterisker. Kreditmarknaden utgörs i första hand av obligationsmarknaden som syftar till att förmedla pengar från investerare till företag, institutioner och stater med upplåningsbehov. Denna avhandling fokuserar på att utifrån ett optimeringsperspektiv modellera både ränte- och obligationsmarknaden. Lagstiftarna på de nationella marknaderna kräver att de finansiella aktörerna värderar sina finansiella tillgångar i enlighet med marknadspriser. Därmed måste priserna på många instrument, som inte handlas publikt, beräknas matematiskt. De finansiella storheter som krävs för denna prissättning är inte direkt observerbara, utan måste mätas genom att lösa inversa optimeringsproblem. Dessa mätningar görs utifrån tillgängliga marknadspriser, som observeras med varierande grad av mätbrus. För räntemarknaden utgörs de relevanta finansiella storheterna av räntekurvor som åskådliggör marknadsräntorna för olika löptider. För obligationsmarknaden utgör kreditrisken en ytterligare faktor som modelleras via fallissemangsintensitetskurvor och kurvor kopplade till förväntat återvunnet kapital vid eventuellt fallissemang. Genom att formulera lämpliga optimeringsmodeller kan de olika underliggande finansiella storheterna mätas i enlighet med observerbara marknadspriser samtidigt som ekonomisk realism eftersträvas. Mätning och hantering av risker är nära kopplat till mätningen av de underliggande finansiella storheterna. Genom en datadriven metod kan vi visa att sex systematiska riskfaktorer kan användas för att förklara nästan all varians i räntekurvorna. Genom att modellera dynamiken i dessa sex riskfaktorer kan tänkbara utfall för räntekurvor simuleras. För kortsiktiga simuleringshorisonter resulterar detta i en representation av fördelningen av portföljvärden som väl överensstämmer med de realiserade utfallen från historiskt observerade räntekurvor. Detta möjliggör noggrannare mätningar av ränterisk där vår föreslagna metod uppvisar såväl lägre risk som mindre prissättningsfel jämfört med traditionella modeller. Vi föreslår en metod för att dekomponera portföljutvecklingen för en godtycklig portfölj till de riskfaktorer som påverkar värdet för respektive instrument. Genom att demonstrera metoden för de sex systematiska riskfaktorerna som identifierats för räntemarknaden visar vi att nästan all portföljutveckling och portföljvarians kan härledas till dessa riskfaktorer. Övriga riskfaktorer och approximationsfel samlas i två termer, vilka kan användas för att säkerställa och eventuellt förbättra kvaliteten i prestationshärledningen. För att eliminera oönskad risk i sina tradingböcker använder banker sig av hedging. Traditionella metoder tar ingen hänsyn till transaktionskostnader. Vi föreslår därför en metod för att hantera riskerna på räntemarknaden genom en stokastisk optimeringsmodell som också tar hänsyn till transaktionskostnader. Denna metod bygger på en scenarioapproximation av optimeringsproblemet där de sex systematiska riskfaktorerna simuleras och portföljvariansen vägs mot transaktionskostnaderna. Detta resulterar i en metod som, för alla riskaverta investerare, är att föredra framför de traditionella metoderna. På kreditmarknaden använder vi data från obligationsmarknaden i kombination räntemarknaden för att göra noggranna mätningar av de finansiella storheterna. Vi angriper det erkänt svåra problemet att separera fallissemangsrisk från återvinningsrisk. Förutom de tidigare sex systematiska riskfaktorerna för riskfri ränta, identifierar vi fyra riskfaktorer som förklarar nästan all varians i fallissemangsintensiteter, medan en enda riskfaktor tycks räcka för att modellera återvinningsrisken. Sammanlagt är detta ett större antal riskfaktorer än vad som brukar användas i litteraturen. Via en enkel modell kan vi mäta variansen i obligationspriser i termer av dessa systematiska riskfaktorer och genom prestationshärledningen relatera dessa värden till de empiriskt realiserade varianserna från kvoterade obligationspriser.
