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Optimization-Based Models for Measuring and Hedging Risk in Fixed Income Markets
Linköping University, Department of Management and Engineering, Production Economics. Linköping University, Faculty of Science & Engineering.ORCID iD: 0000-0001-5867-8242
2020 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

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.

Abstract [sv]

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.

Place, publisher, year, edition, pages
Linköping: Linköping University Electronic Press, 2020. , p. 129
Series
Linköping Studies in Science and Technology. Dissertations, ISSN 0345-7524 ; 2039
Keywords [en]
Finance, Fixed income, Interest rate risk, Credit risk, Risk management, Optimization, Mathematics
National Category
Other Mathematics
Identifiers
URN: urn:nbn:se:liu:diva-162576DOI: 10.3384/diss.diva-162576ISBN: 9789179299279 (print)OAI: oai:DiVA.org:liu-162576DiVA, id: diva2:1376145
Public defence
2020-01-10, ACAS, A-building, Campus Valla, Linköping, 10:15 (English)
Opponent
Supervisors
Available from: 2019-12-09 Created: 2019-12-08 Last updated: 2020-01-16Bibliographically approved
List of papers
1. Simulation and evaluation of the distribution of interest rate risk
Open this publication in new window or tab >>Simulation and evaluation of the distribution of interest rate risk
2019 (English)In: Computational Management Science, ISSN 1619-697X, E-ISSN 1619-6988, Vol. 16, no 1-2, p. 297-327Article in journal (Refereed) Published
Abstract [en]

We study methods to simulate term structures in order to measure interest rate risk more accurately. We use principal component analysis of term structure innovations to identify risk factors and we model their univariate distribution using GARCH-models with Student’s t-distributions in order to handle heteroscedasticity and fat tails. We find that the Student’s t-copula is most suitable to model co-dependence of these univariate risk factors. We aim to develop a model that provides low ex-ante risk measures, while having accurate representations of the ex-post realized risk. By utilizing a more accurate term structure estimation method, our proposed model is less sensitive to measurement noise compared to traditional models. We perform an out-of-sample test for the U.S. market between 2002 and 2017 by valuing a portfolio consisting of interest rate derivatives. We find that ex-ante Value at Risk measurements can be substantially reduced for all confidence levels above 95%, compared to the traditional models. We find that that the realized portfolio tail losses accurately conform to the ex-ante measurement for daily returns, while traditional methods overestimate, or in some cases even underestimate the risk ex-post. Due to noise inherent in the term structure measurements, we find that all models overestimate the risk for 10-day and quarterly returns, but that our proposed model provides the by far lowest Value at Risk measures.

Place, publisher, year, edition, pages
New York: Springer Publishing Company, 2019
Keywords
Interest rate risk, Principal component analysis, Term structure, Value at Risk
National Category
Probability Theory and Statistics
Identifiers
urn:nbn:se:liu:diva-151604 (URN)10.1007/s10287-018-0319-8 (DOI)000458627300013 ()2-s2.0-85048050404 (Scopus ID)
Available from: 2019-03-12 Created: 2019-03-12 Last updated: 2019-12-08Bibliographically approved
2. A generic framework for monetary performance attribution
Open this publication in new window or tab >>A generic framework for monetary performance attribution
2019 (English)In: Journal of Banking & Finance, ISSN 0378-4266, E-ISSN 1872-6372, Vol. 105, p. 121-133Article in journal (Refereed) Published
Abstract [en]

We propose a generic framework for performance attribution in monetary terms. Through a second-order Taylor approximation, the changes in portfolio value are attributed to a set of systematic risk factors. By considering two error terms arising from the Taylor approximation, combined with an exact definition of the carry term, we derive a residual-free performance attribution framework, where we exert control over the size of the error terms. The framework incorporates foreign exchange rates and transaction costs, which is illustrated by simulating a European investor acting on the U.S. fixed income market. For the out-of-sample period, we show that we can attribute almost all portfolio value differences and variance using six risk factors obtained from principal component analysis. The results show that our method, in combination with high-quality estimates of risk factors, outperforms other fixed-income attribution models from the literature. (C) 2019 Elsevier B.V. All rights reserved.

Place, publisher, year, edition, pages
ELSEVIER SCIENCE BV, 2019
Keywords
Performance attribution; Performance analysis; Fixed income
National Category
Economics
Identifiers
urn:nbn:se:liu:diva-158925 (URN)10.1016/j.jbankfin.2019.05.021 (DOI)000472698500009 ()
Available from: 2019-07-20 Created: 2019-07-20 Last updated: 2020-01-15

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