This study applies the Vasicek stochastic interest rate model in order to determine optimal capital structures for listed firms. A Swedish interest rate data set is used to estimate Vasicek model parameter that are reliable and independent of initial start values. These interest rate parameters are then used in a capital structure model which is evaluated through a sensitivity analysis and a firm-specific analysis which is applied to listed Swedish firms. The tax benefits of debt must be balanced against transaction costs and bankruptcy costs when determining optimal leverage ratio and optimal debt maturity. The results imply that firms should primarily focus on the long-term mean parameter of the interest rate process, the volatility of its firm value, the transaction cost of issuing debt and the effective corporate tax rate when choosing a capital structure. The capital structure model is well-founded in previous research and yields results which align with empirical data quite well. The conclusions of this study has implications for corporate finance, as the Vasicek model provides a better understanding of the stochastic nature of interest rates and its influence in determining optimal capital structures. / Denna studie tillämpar Vasiceks stokastiska räntemodell för att bestämma optimala kapitalstrukturer för noterade företag. Vasicekmodellen anpassas till ett Svensk dataset över räntor för att estimera parametrar. Dessa parametrar används sedan i en kapitalstruktursmodell för att analysera modellens känslighet för variationer i parametrar samt för att härleda optimala kapitalstrukturer för en rad Svenska noterade bolag. Skattefördelarna av skuld måste balanseras mot transaktionskostnader av skuldemissioner och konkurskostnader vid bestämning av optimal skuldsättningsgrad och optimal skuldlöptid. Resultaten antyder att företag bör primärt fokusera på det långsiktiga medelvärdet av den stokastiska ränteprocessen, volatiliteten av bolagsvärdet, transaktionskostnaden av skuldemissioner och effektiva bolagsskatten när de väljer en kapitalstruktur. Denna studie har implikationer för finansieringsteori då Vasiceks modell närmare modellerar räntors stokastiska dynamiker och dess påverkan på bestämning av bolags kapitalstrukturer.

In this dissertation, we consider the Hull-White term structure problem with the boundary value condition given as the payoff of a European bond option. We restrict ourselves to the case where the parameters of the Hull-White model are strictly positive constants and from the risk neutral valuation formula, we first derive simple closed–form expression for pricing European bond option in the Hull-White extended Vasicek model framework. As the European option can be exercised only on the maturity date, we then examine the case of early exercise opportunity commonly called American option. With the analytic representation of American bond option being very hard to handle, we are forced to resort to numerical experiments. To do it excellently, we transform the Hull-White term structure equation into the diffusion equation and we first solve it through implicit, explicit and Crank-Nicolson (CN) difference methods. As these standard finite difference methods (FDMs) require truncation of the domain from infinite to finite one, which may deteriorate the computational efficiency for American bond option, we try to build a CN method over an unbounded domain. We introduce an exact artificial boundary condition in the pricing boundary value problem to reduce the original to an initial boundary problem. Then, the CN method is used to solve the reduced problem. We compare our performance with standard FDMs and the results through illustration show that our method is more efficient and accurate than standard FDMs when we price American bond option. / Mathematical Sciences / (M.Sc. (Mathematics))

In this dissertation, we consider the Hull-White term structure problem with the boundary value condition given as the payoff of a European bond option. We restrict ourselves to the case where the parameters of the Hull-White model are strictly positive constants and from the risk neutral valuation formula, we first derive simple closed–form expression for pricing European bond option in the Hull-White extended Vasicek model framework. As the European option can be exercised only on the maturity date, we then examine the case of early exercise opportunity commonly called American option. With the analytic representation of American bond option being very hard to handle, we are forced to resort to numerical experiments. To do it excellently, we transform the Hull-White term structure equation into the diffusion equation and we first solve it through implicit, explicit and Crank-Nicolson (CN) difference methods. As these standard finite difference methods (FDMs) require truncation of the domain from infinite to finite one, which may deteriorate the computational efficiency for American bond option, we try to build a CN method over an unbounded domain. We introduce an exact artificial boundary condition in the pricing boundary value problem to reduce the original to an initial boundary problem. Then, the CN method is used to solve the reduced problem. We compare our performance with standard FDMs and the results through illustration show that our method is more efficient and accurate than standard FDMs when we price American bond option. / Mathematical Sciences / (M.Sc. (Mathematics))

This thesis focuses on modelling non-maturing deposits (NMD) and has been written in collaboration with Svenska Handelsbanken. The methodology includes regression analysis and time series analysis, with the Repo rate serving as an exogenous variable in both models. A Vasicek model is employed to generate future Repo rates, which are then used as inputs for forecasting the NMD volume. These simulated rates are then compared to forecasted Repo rates with discrete changes from an external source. The results are utilised to analyze how net interest income can vary in the case of constant volume and in the case of interest rate-dependent volume. Effective liquidity management is crucial for banks, and NMDs are an important source of funding. By using regression analysis and time series analysis, combined with the Repo rate as the exogenous variable, this thesis provides insights into the behaviour of NMD volumes, and how it is affected by the Repo rate. The models also enable the forecasting of future trends based on future Repo rates. Additionally, by using different data sets as input for future Repo rates, the behaviour of the model can be evaluated based on how well it coincides with reality. The results obtained from this analysis can also be used to compare the value and interest rate sensitivity of NMD products. In conclusion, this thesis provides an approach to modelling the NMD volumes using exogenous factors and demonstrates how this can affect the net interest income from deposit volumes. / Denna avhandling fokuserar på modellering av icke tidsbunden inlåning (non-maturing deposits, NMD) och har skrivits i samarbete med Svenska Handelsbanken. Metoden omfattar regressionsanalys och tidsserieanalys, där reporäntan fungerar som en exogen variabel i båda modellerna. En Vasicek-modell används för att generera framtida reporäntor, som sedan används som indata för att prognostisera NMD-volymen. Dessa simulerade räntor jämförs sedan med prognostiserade reporäntor med diskreta förändringar från en extern källa. Resultaten används sedan för att analysera hur räntenettot kan variera mellan fallet med konstant volym och fallet med ränteberoende volym. En effektiv likviditetshantering är avgörande för banker, och NMD:er är en viktig finansieringskälla. Genom att använda regressionsanalys och tidsserieanalys, i kombination med reporäntan som exogen variabel , ger denna avhandling värdefulla insikter i NMD-volymernas beteende och hur de påverkas av reporäntan. Modellerna gör det också möjligt att prognostisera framtida trender utifrån framtida reporäntor. Genom att använda olika datamängder som indata för de framtida reporäntorna kan modellens beteende dessutom värderas utifrån hur väl det sammanfaller med verkligheten. Resultaten från denna analys kan också användas för att jämföra NMD-produkternas värde- och räntekänslighet. Sammanfattningsvis ger denna avhandling ett tillvägagångssätt för att modellera NMD-volymerna med hjälp av exogena faktorer och visar på hur det kan påverka inlåningens räntenetto.