Modeling of Non-Maturing Deposits
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DEGREE PROJECT IN MATHEMATICS, SECOND CYCLE, 30 CREDITS STOCKHOLM, SWEDEN 2019 Modeling of non-maturing deposits NIKITA DOMIN FREDRIK STAVRÉN KTH ROYAL INSTITUTE OF TECHNOLOGY SCHOOL OF ENGINEERING SCIENCES Modeling of non-maturing Deposits NIKITA DOMIN FREDRIK STAVRÉN Degree Projects in Financial Mathematics (30 ECTS credits) Master's Programme in Applied and Computational Mathematics (120 credits) KTH Royal Institute of Technology year 2019 Supervisor at SEB: Jakob Nuldén Supervisor at KTH: Anja Janssen Examiner at KTH: Anja Janssen TRITA-SCI-GRU 2019:066 MAT-E 2019:23 Royal Institute of Technology School of Engineering Sciences KTH SCI SE-100 44 Stockholm, Sweden URL: www.kth.se/sci Abstract The interest in modeling non-maturing deposits has skyrocketed ever since the financial crisis 2008. Not only from a regulatory and legislative perspective, but also from an investment and funding perspective. Modeling of non-maturing deposits is a very broad subject. In this thesis some of the topics within the subject are investigated, where the greatest focus in on the modeling of the deposit volumes. The main objective is to provide the bank with an analysis of the majority of the topics that needs to be cov- ered when modeling non-maturing deposits. This includes short-rate model- ing using Vasicek’s model, deposit rate modeling using a regression approach and a method proposed by Jarrow and Van Deventer, volume modeling using SARIMA, SARIMAX and a general additive model, a static replicating port- folio based on Maes and Timmerman’s to model the behaviour of the deposit accounts and finally a liquidity risk model that was suggested by Kalkbrener and Willing. All of these models have been applied on three different account types: private transaction accounts, savings accounts and corporate savings accounts. The results are that, due to the current market, the static replicating portfolio does not achieve the desired results. Furthermore, the best volume model for the data provided is a SARIMA model, meaning the effect of the exogenous variables are seemingly already embedded in the lagged volume. Finally, the liquidity risk results are plausible and thus deemed satisfactory. Sammanfattning Intresset för att modellera inlåningsvolymer utan en kontrakterad förfallodag har ökat markant sedan finanskrisen 2008. Inte bara sett utifrån ett perspek- tiv att uppfylla krav som ställs av tillsynsmyndigheter, men också sett utifrån bankens investerings-och finansieringsperspektiv. Målet med det här arbetet är att förse banken med en analys av majoriteten av de olika områdena som man behöver ta hänsyn till när man ska model- lera inlåningar utan förfallodatum, men med ett fokus på volymmodellering. I den här rapporten modelleras räntor (kortränta och kontoränta), kontovoly- merna, kontobeteendet samt likviditetsrisken. Detta görs med hjälp av Vasicek för korträntan, en regressionsmetod samt en metod som föreslagits av Jarrow och Van Deventer för kontoräntan, SARIMA, SARIMAX och en generell ad- ditiv regressionsmetod för volymerna, en statisk replikeringsportfölj baserad på Maes och Timmermans modell för att imitera kontona och slutligen så mo- delleras likviditetsrisken med ett ramverk som föreslagits av Kalkbrener och Willing. Alla dessa nämnda modeller appliceras, där det är möjligt, på de tre olika kontotyperna: privatkonton, sparkonton samt företagssparkonto. Resultatet är att räntemodelleringen samt replikeringsportföljen inte ger ade- kvata resultat på grund av den rådande marknaden. Vidare så ger en SARIMA- modell den bästa prediktionen, vilket gör att slutsatsen är att andra exogena variabler redan är inneslutna i den fördröjda volymvariabeln. Avslutningsvis så ger likviditetsmodellen tillfredsställande resultat och antas vara rimlig. Acknowledgements We would like to give a special thanks to our supervisor at KTH, Anja Janssen, for always being available and helpful throughout the project. Furthermore, we would also like to give our sincerest thanks to SEB for giving us this oppor- tunity and our supervisor at SEB, Jakob Nuldén, for his support and encour- agement. Additionally, we would also like to thank all of the people at SEB who took their time to answer our questions and teach us new things. Finally, a big thank you to our friends and families who have pushed and supported us, without whom this would not have been possible. Contents 1 Introduction 1 1.1 Background . .1 1.2 Regulations and guidelines . .2 1.3 Aim and delimitations . .3 1.4 Structure of the report . .5 2 Previous works 6 3 Theoretical background 9 3.1 Market interest rates . .9 3.1.1 Zero rates . .9 3.1.2 Modeling of the short rate . 10 3.1.3 Calibration of Vasicek’s model . 11 3.2 Deposit interest rates . 12 3.2.1 Jarrow and Van Deventer . 12 3.2.2 Regression model . 12 3.3 Time series models . 13 3.3.1 ARIMA models . 13 3.3.2 Augmented Dickey-Fuller test . 16 3.4 Regression models . 16 3.4.1 Random Forest Regression . 16 3.4.2 Multiple linear regression and OLS . 18 3.4.3 Modified generalized additive model . 19 3.5 Risk management . 22 3.5.1 Static replicating portfolio: Maes and Timmerman . 22 3.5.2 Liquidity risk . 23 4 Data 24 4.1 Description of the data . 24 4.1.1 Volume data . 24 vi 4.1.2 Market rate data . 25 4.1.3 Deposit rate data . 26 4.1.4 Additional data . 27 4.2 Analysis of the data . 27 4.2.1 Trends and seasonality in the volumes . 27 4.2.2 Market and deposit rates . 28 4.3 Extracurricular volume data . 29 5 Methodology 31 5.1 Volume models . 32 5.1.1 ARIMA models . 32 5.1.2 Modified generalized additive model . 33 5.2 Risk management . 34 6 Results 37 6.1 Short rate . 37 6.2 Deposit rate . 39 6.3 Volume modeling . 41 6.3.1 Econometric analysis . 41 6.3.2 Forecasting of exogenous variables . 43 6.3.3 ARIMA . 45 6.3.4 Modified generalized additive model . 53 6.4 Risk management . 60 6.4.1 Static replicating portfolio . 60 6.4.2 Liquidity risk . 64 7 Discussion 67 7.1 Evolvement and future work . 70 8 Conclusions 72 Bibliography 73 List of Figures 1.1 The different topics that need to be modeled . .4 3.1 An illustration of a random forest with decision tree one, two and n shown. Each circle represents a node where a split is done. 18 4.1 Volumes of different deposit types . 24 4.2 Seasonal plots of scaled volumes for different deposit types . 25 4.3 Swedish market rates . 26 4.4 Deposit rates . 26 4.5 Deposit rates vs market rate . 29 4.6 Daily aggregated data for the private transaction accounts . 30 6.1 Simulations of the market rate using the Vasicek short rate model for the complete data-set . 38 6.2 Simulations of the market rate using the Vasicek short rate model for a shorter time period . 38 6.3 Deposit rate of savings accounts (left) and corporate savings accounts (right) . 40 6.4 JvD: Deposit rate for savings accounts (left) and corporate sav- ings accounts (right) . 41 6.5 Average salaries for private sector (left) and unemployment (right) . 43 6.6 Fitted private salaries (left) and predicted private salaries (right) 44 6.7 Fitted unemployment rate (left) and predicted unemployment rate (right) . 44 6.8 ACF plot of residuals: residuals for private salaries (left) and unemployment rate (right) . 45 6.9 Decomposition of original time series . 46 6.10 ACF and PACF of the original time series . 46 6.11 Plot of differenced time series . 47 viii 6.12 ACF and PACF plot of differenced time series . 47 6.13 Importance of different lagged volumes for the private trans- action accounts . 48 6.14 a) and b) is the fit and prediction respectively of the SARIMA models for the private accounts. c) and d) is the fit and pre- diction respectively of the SARIMAX models for the private accounts . 49 6.15 Diagnostic plots of residuals . 49 6.16 a) and b) is the fit and prediction respectively of the SARIMA models for the savings accounts. c) and d) is the fit and pre- diction respectively of the SARIMAX models for the savings accounts . 50 6.17 a) and b) is the fit and prediction respectively of the SARIMA models for the corporate savings accounts. c) and d) is the fit and prediction respectively of the SARIMAX models for the corporate savings accounts . 51 6.18 ACF plots of the residuals for the SARIMA models . 52 6.19 ACF plots of the residuals for the SARIMAX models . 53 6.20 Fit and prediction of the private transaction accounts . 54 6.21 Fit and prediction of the savings accounts . 54 6.22 Fit and prediction of the corporate savings accounts . 55 6.23 Fit and prediction of the first vanilla model . 56 6.24 Decomposition of the first vanilla model . 57 6.25 Diagnostic plot, MAPE . 58 6.26 Diagnostic plot, RMSE . 58 6.27 Fit and prediction of the second model (improved model) with dummy variables and seasonal adjustment . 59 6.28 Diagnostic plots of residuals, MAPE . 59 6.29 Diagnostic plots of residuals, RMSE . 59 6.30 Efficient frontier of 50 000 randomly generated weight sets . 60 6.31 Return of different portfolios . 62 6.32 Duration of different portfolios . 63 6.33 Liquidity risk quantiles . 65 6.34 Liquidity risk quantiles . 66 List of Tables 1.1 Caps on core % for investment and maturity for each deposit type by BCBS . .3 4.1 Correlations between different market rates . 28 5.1 Models for each deposit type . 32 6.1 Parameters of calibrated Vasicek’s model . 37 6.2 Values of parameters for the regression model .