YIELD CURVE ARBITRAGE IN EUR SWAP RATES A Hybrid Neural Network Approach Master’s Thesis Lauri Stark Aalto University School of Business Finance Spring 2020 Aalto University, P.O. BOX 11000, 00076 AALTO www.aalto.fi Abstract of master’s thesis Author Lauri Stark Title of thesis Yield Curve Arbitrage in EUR Swap Rates: A Hybrid Neural Network Approach Degree Master of Science Degree programme Finance Thesis advisor(s) Matti Suominen Year of approval 2020 Number of pages 61 Language English Abstract In this thesis, I analyze the out-of-sample trading performance of a yield curve arbitrage strategy on EUR swap rates. For the implementation of the strategy, I introduce a novel hybrid neural network approach which uses the factors of an affine term structure model as inputs. I compare the results to the performance of a benchmark strategy that is based on the traditional two-factor Vasicek term structure model. The results imply that with reasonable transaction costs, the neural network model produces significant multifactor alpha, positively skewed returns with high kurtosis and a higher Sharpe ratio and higher absolute cumulative performance compared to the Vasicek model. However, the neural network strategy also has exposure to systematic risk factors and tail risk. Keywords yield curve, machine learning, neural network, interest rate, arbitrage Aalto-yliopisto, PL 11000, 00076 AALTO www.aalto.fi Maisterintutkinnon tutkielman tiivistelmä Tekijä Lauri Stark Työn nimi Hybridineuroverkon käyttö korkokäyrän arbitraasistrategiassa euroalueen vaihtoko- roilla Tutkinto Kauppatieteiden maisteri Koulutusohjelma Rahoitus Työn ohjaaja(t) Matti Suominen Hyväksymisvuosi 2020 Sivumäärä 61 Kieli Englanti Tiivistelmä Tässä tutkielmassa analysoin euroalueen vaihtokoroilla toteutettavaa, korkokäyräarbitraasiin poh- jautuvaa sijoitustrategiaa jossa mallintaminen toteutetaan hybridineuroverkolla. Vertaan saamiani tuloksia perinteiseen kahden faktorin Vasicekin malliin pohjautuvaan strategiaan. Saamani tulokset osoittavat, että kohtuullisilla kaupankäyntikustannuksilla neuroverkkomalli tuottaa tilastollisesti merkittävää ylituottoa sekä korkeamman Sharpe-luvun ja kokonaistuoton verrattuna perinteiseen Vasicekin malliin. Neuroverkkomalliin pohjautuva strategia sisältää kuitenkin useaan systemaatti- seen tuottofaktoriin liittyvää riskiä, sekä lisäksi häntäriskiä. Avainsanat korkokäyrä, koneoppiminen, neuroverkko, sijoittaminen, arbitraasi Yield Curve Arbitrage in EUR Swap Rates: AHybridNeuralNetworkApproach Lauri Stark Master’s Thesis Department of Finance Aalto University School of Business Thesis advisor: Professor Matti Suominen April 27, 2020 Abstract In this thesis, I analyze the out-of-sample trading performance of a yield curve arbitrage strategy on EUR swap rates. For the implementation of the strategy, I introduce a novel hybrid neural network approach which uses the factors of an affine term structure model as inputs. I compare the results to the performance of a benchmark strategy that is based on the traditional two-factor Vasicek term structure model. The results imply that with reasonable transaction costs, the neural network model produces significant multifactor alpha, positively skewed returns with high kurtosis and a higher Sharpe ratio and higher absolute cumulative performance compared to the Vasicek model. However, the neural network strategy also has exposure to systematic risk factors and tail risk. Contents 1 Introduction 1 1.1 Background and Motivation ........................... 1 1.2 Hypotheses .................................... 3 2 Related Literature 5 2.1 Risk and Return in Arbitrage Strategies .................... 5 2.1.1 Limits to Arbitrage ............................ 7 2.2 Applications of Term Structure Models ..................... 8 2.3 Machine Learning Models in Asset Pricing ................... 10 2.3.1 Machine Learning in Options Pricing .................. 10 2.3.2 Machine Learning and Interest Rates .................. 11 2.3.3 Other Machine Learning Applications in Asset Pricing ........ 11 3 Overview of Term-Structure Models 13 3.1 Terminology in Term-Structure Models ..................... 13 3.2 One-factor term-structure models ........................ 14 3.2.1 Vasicek (1977) ............................... 14 3.2.2 Dothan (1978) ............................... 15 3.2.3 Cox-Ingersoll-Ross (1985) ........................ 16 3.2.4 Hull-White (1990) ............................ 16 3.2.5 Hull-White extension of the CIR model ................. 18 3.2.6 Black-Karasinski (1991) ......................... 18 3.2.7 CIR with general deterministic shift extension ............. 19 3.3 Two-Factor Short-Rate Models ......................... 20 3.3.1 The Two-Factor Vasicek Model ..................... 20 3.3.2 The Two-Factor Cox-Ingersoll-Ross Model ............... 21 4Data 23 2 5 Methodology 26 5.1 Fitting the Vasicek factors ............................ 26 5.2 Swap Mechanics and Valuation Methodology .................. 28 5.2.1 OIS Discounting ............................. 29 5.3 Modelling Methodology .............................. 30 5.4 Trading Methodology ............................... 30 5.4.1 Hedging methodology ........................... 31 6 Results and Findings 33 6.1 Out-of-sample performance ............................ 33 6.2 Multifactor regressions .............................. 38 6.2.1 Asset-based style factor regressions ................... 42 6.3 Quantile Regressions ............................... 44 7 Conclusions 50 References 52 List of Figures 1 EUR swap rates .................................. 25 2 Neural network mispricings ............................ 34 3Vasicekmodelmispricings............................ 35 4CumulativeperformancesfortheneuralnetworkmodelandtheVasicekmodel36 5 Neural network multifactor quantile regressions ................ 45 6Vasicekmodelmultifactorquantileregressions................. 46 List of Tables 1 Descriptive statistics for the EUR swap rates .................. 24 2 Out-of-sample trading performance ....................... 33 3 3Multifactorregressionresults........................... 40 4 Fung-Hsieh asset-based style factor regression results ............. 43 5Multifactorquantileregressionresultsofdailyexcessreturns,leftandright tails ........................................ 47 4 1 Introduction 1.1 Background and Motivation Historically, fixed income arbitrage strategies such as yield curve arbitrage, swap spread arbitrage and volatility arbitrage have been associated as typical hedge fund strategies. The purpose of such arbitrage strategies is to recognize underpriced or overpriced fixed income instruments and trade the mispricings in a market-neutral way. In this paper, I analyze a yield curve arbitrage strategy on EUR swap curve. The idea is to use a neural network model that identifies the rich or cheap points on the swap curve and provides hedge measures for the mispriced points on the curve in order to make the total position market neutral. Especially, the inputs to the neural network model are the calibrated factor values of the two-factor Vasicek model. Using these factors as inputs for the neural network enables the calculation of the hedging measures so that the strategy is market neutral to the Vasicek risk factors. To my current knowledge, this kind of hybrid model which combines a term structure model with a machine learning framework has not been developed previously. According to Duarte et al. (2006), fixed income arbitrage strategies have become very popular among the hedge fund industry after the beginning of the 21st century. This is despite the fact that the very same strategies also played a major role in the hedge fund crisis of 1998, during which the notorious collapse of the large hedge fund Long Term Capital took place. The aforementioned facts characterize fixed income arbitrage rather well: most of the time, these strategies may earn small positive returns but then as rare tail events occur, these returns are easily wiped out and the strategies su↵er heavy losses. However, based on the results of Duarte et al. (2006), yield curve arbitrage has historically produced positively skewed returns with significant alpha. Despite the attractive nature of its returns, yield curve arbitrage has been explicitly studied by only a few previous papers, namely by Duarte et al. (2006)andKarsimus (2015). Generally, a yield curve arbitrage strategy is a market-neutral strategy that seeks to profit by exploiting pricing inefficiencies between related fixed-income securities while neutralizing exposure to interest rate risk. In the previous studies of yield curve arbitrage, the modelling frameworks of the interest rate dynamics have been based on classical short-rate models. 1 Duarte et al. (2006)usedthetwo-factorversionoftheVasicek (1977)term-structuremodel and Karsimus (2015)usedthetwo-factorversionofCox et al. (1985)andtheLongsta↵and Schwartz (1992) two-factor model. As with any model, also these models have limitations regarding the model assumptions, the dynamics of the model-implied interest rates and calibration of the model parameters. This is why a machine learning framework for modelling the interest rate is presented in this paper. Machine learning models have their limitations for example regarding to overfitting, but the assumptions behind the models are less stringent and the models learn the interest rate dynamics from the data. For a reader who is not acquainted with machine learning models, Goodfellow et al. (2016)provideacomprehensive, self-contained guide