The aim of the thesis is devoted to creation of working sheets which are designed to teach selected topics of financial mathematics at high school. The thesis will focus on loan products (consumer loans, hire purchase, mortgage) insurance products (life and non-life insurance) and the rights of consumers. The thesis issues on the framework educational programs for high schools.

The decision of the Swiss National Bank from January 2015 to drop the exchange rate profit of the Swiss franc caused a significant shock to the financial market. The Swiss franc boost strongly influenced Poland because many of a mortgage loan was granted precisely in this currency. The goal of the MA thesis is to analyze the impact of the Swiss franc boost on the Polish commercial banks and to describe individual measures taken and solutions found in Poland. The introductory part deals with the beginning of the expansion of foreign currency loans not only in Poland but also in the greater context of Poland´s neighbouring countries. Furthermore, the Recommendation S is described in more detail. The second chapter contains analysis of loans development in Poland. Here, the Bank Millennium is used as an example to demonstrate the loan portfolio composition. The final part of this work talks about the Polish reaction to the change of the Swiss monetary policy and to the specifics of these provisions.

Dissertation submitted in fulfillment of the requirement for the Degree of Master of Technology: Quantity Surveying at Technikon Natal, 2002. / This research investigates the key question of whether banks discriminate against black people in the process of granting mortgage bonds which consequently affects homeownership in South Africa in general, and KwaZulu-Natal in particular / M

Syfte: Syftet med uppsatsen är att undersöka vilka risker de fyra storbankerna tar vid kreditgivningen av bostadslån och hur privatrådgivare hanterar risker och osäkerheter som kan uppstå vid ett bostadslån. Teoretisk referensram: Studiens teoretiska referensram består av teorier och vetenskapliga antaganden, där de flesta behandlar begreppet risk. Det presenteras även vetenskapliga artiklar som tar upp vad tidigare forskning bidragit med i detta område. Metod: Denna studie utgår från ett hermeneutiskt förhållningssätt och präglas av en deduktiv forskningsansats. Undersökningen tillämpar den kvalitativa forskningsmetoden och datainsamlingen sker genom semistrukturerade personliga intervjuer. Studiens urval är privatrådgivare från storbankerna Nordea i Tumba, Swedbank i Tumba, Handelsbanken i S:t Eriksplan och SEB i Sergelstorg. Empiri: I empirin presenteras den insamlade datan från de fyra genomförda personliga intervjuerna. Respondenterna som deltagit i intervjuerna och bidragit med värdefull information är anonyma. / Purpose: The purpose of this paper is to examine what risks the four major banks takes when they give credit of a mortgage loan and how the private adviser manages risks and uncertainties that can arise in a mortgage loan. Theoretical Framework: The theoretical framework consists of theories and scientific assumptions, most of which deal with the concept of risk. It also presents scientific articles dealing with what previous research has contributed in this field. Methodology: This study is based on a hermeneutic approach and is characterized by a deductive research approach. The study applies qualitative research methodology and the data collection is done through semi-structured individual interviews. The study's sample is private advisors from the four major banks that is Nordea in Tumba, Swedbank in Tumba, Handelsbanken in S:t Eriksplan and SEB in Sergelstorg. Result: The empirical analysis presents the data that is collected from the four completed personal interviews. Respondents who participated in the interviews and contributed with valuable information are anonymous. Conclusion: The study shows that the biggest risk that may arise for the bank with a mortgage loan is the customer's repayment capacity if it becomes impaired due to various factors. Private advisors manages risks by creating an understanding of the customer about what a mortgage loan means and provide advice and recommendations to prevent an impaired ability to repay.

This thesis focuses on alternative ways of house financing in the Czech Republic. The attention is basically concentrated on mortgages and loans provided by the building society, including bridging loans and bridging different combinations of mortgage loans. Individual variations of financing options for housing are analyzed and then compared with each other.

Macroeconomic conditions can impact the payment capacity of individual mortgage holders' household loans. If the clients of a bank's retail credit portfolio experience deteriorating paymentcapacity it will reflect on the probability of default of the overall portfolio. With IFRS 9, banks are expected to sophisticate their calculations of expected credit loss, demanding forward-looking estimates of probability of default by incorporation of macroeconomic forecasts. Finding what macroeconomic factors have a statistical significant relationship to the actual default frequency of a portfolio can aid banks in estimating probability of default with reference to current and forecasted macroeconomic conditions. This study aims to explore the relationship between macroeconomic factors and the default frequency in a Swedish retail credit portfolio. The research is based on quantitative data analysis of historical default data, complemented by implications of the macroeconomic condition on the payment capacity of households from a theoretical perspective. Macroeconomic factors studied are the Swedish gross domestic product, house price index, reporate and unemployment rate. The supporting data consists of default data from Nordea's Swedishretail credit portfolio. The time period covers 2008-2015 and provides basis for analysis of a timeperiod with different conditions in the macroeconomy, including effects of the 2008 financial crisis. A multiple linear regression model is used as a method to suggest the relationship between themacroeconomic factors and the default frequency. The model coefficients are estimated with calculations of Ordinary Least Squares and the significance supported by statistical test. Results show that gross domestic product and repo rate are statistically significant macroeconomic variables in explaining changes in the default frequency and thus probability of default of a Swedish retail credit portfolio. / Makroekonomiska omständigheter kan påverka hushållens betalningsförmåga och i sin tur återbetalningsförmågan hos bolånetagare. Om flertalet låntagare inom en banks retailportfölj upplever en försämrad betalningsförmåga kommer det att avspeglas på sannolikheten för fallissemang (probability of default) i den totala portföljen. Med IFRS 9 förväntas banker förfina sina beräkningar av förväntade kreditförluster, vilket kräver framåtblickande beräkningar av probability of default med makroekonomiska prognoser i åtanke. Genom att identifiera vilka makroekonomiska faktorer som har statistisk signifikans för förändringar i historisk fallissemangsfrekvens i en portfölj förväntas banker kunna integrera dessa i, och därmed förbättra, sina beräkningar av probability of default. Denna studie syftar till att utreda sambandet mellan makroekonomiska faktorer och fallissemangsfrekvensen i en svensk retailportfölj. Den kvantitativa analysen av data över historiska fallissemang och makroekonomiska faktorer kompletteras med teoretiska implikationer av makroekonomiska omständigheter för hushållens betalningsförmåga. De makroekonomiska faktorer som studeras är svensk BNP, Boprisindex, Reporänta och Arbetslöshet. Fallissemangsfrekvensen baseras på data från Nordeas svenska retailportfölj som täcker åren 2008-2015 och därmed inkluderar följdeffekter av finanskrisen 2008. En multipel linjär regressionsmodell används för att förklara relationen mellan de makroekonomiska faktorerna och fallissemangsfrekvensen. Regressionskoefficienterna estimeras med hjälp av minstakvadratmetoden och kompletteras med diagnostiska test. Resultaten visar att BNP och Reporäntan är statistiskt signifikanta makroekonomiska faktorer för påvisandet av förändringar i fallissemangsfrekvensen och följaktligen Probability of Default i en svensk retailkreditportfölj.

Um dos aspectos regulatórios fundamentais para o mercado imobiliário no Brasil são os limites para obtenção de financiamento no Sistema Financeiro de Habitação. Esses limites podem ser definidos de forma a aumentar ou reduzir a oferta de crédito neste mercado, alterando o comportamento dos seus agentes e, com isso, o preço de mercado dos imóveis. Neste trabalho, propomos um modelo de formação de preços no mercado imobiliário brasileiro com base no comportamento dos agentes que o compõem. Os agentes vendedores têm comportamento heterogêneo e são influenciados pela demanda histórica, enquanto que os agentes compradores têm o seu comportamento determinado pela disponibilidade de crédito. Esta disponibilidade de crédito, por sua vez, é definida pelos limites para concessão de financiamento no Sistema Financeiro de Habitação. Verificamos que o processo markoviano que descreve preço de mercado converge para um sistema dinâmico determinístico quando o número de agentes aumenta, e analisamos o comportamento deste sistema dinâmico. Mostramos qual é a família de variáveis aleatórias que representa o comportamento dos agentes vendedores de forma que o sistema apresente um preço de equilíbrio não trivial, condizente com a realidade. Verificamos ainda que o preço de equilíbrio depende não só das regras de concessão de financiamento no Sistema Financeiro de Habitação, como também do preço de reserva dos compradores e da memória e da sensibilidade dos vendedores a alterações na demanda. A memória e a sensibilidade dos vendedores podem levar a oscilações de preços acima ou abaixo do preço de equilíbrio (típicas de processos de formação de bolhas); ou até mesmo a uma bifurcação de Neimark-Sacker, quando o sistema apresenta dinâmica oscilatória estável. / One of the fundamental regulatory aspects for the housing market in Brazil are the limits for obtaining a residential mortgage loan within the Sistema Financeiro de Habitação. These limits can be defined so as to increase or reduce credit supply in this market, changing its agents behavior and, therefore, the housing market price. In this work we propose a pricing model for the brazilian housing market based on the behavior of its agents. Sellers have heterogeneous behavior and are influenced by the historical demand, while buyers behavior is determined by credit availability. The availability of credit is, in its turn, defined by the regulatory limits for obtaining a residential mortgage loan. We have verified that the Markov process which describes the market price converges to a deterministic dynamical system as the number of agents increase, and we have analyzed the behavior of this emerging system. We show which family of random variables may represent the behavior of sellers so that the system has a nontrivial equilibrium price, consistent with reality. We have also verified that the equilibrium price depends not only on the regulatory limits for obtaing a loan, but also on buyers reserve price and on sellers memory and sensitivity to changes in the demand. Sellers memory and sensitivity to changes in the demand can result in price oscillations above or below the equilibrium level, which is typical in bubble formation processes; or even in a Neimark-Sacker bifurcation, when the price has a stable oscillatory dynamics.

Um dos aspectos regulatórios fundamentais para o mercado imobiliário no Brasil são os limites para obtenção de financiamento no Sistema Financeiro de Habitação. Esses limites podem ser definidos de forma a aumentar ou reduzir a oferta de crédito neste mercado, alterando o comportamento dos seus agentes e, com isso, o preço de mercado dos imóveis. Neste trabalho, propomos um modelo de formação de preços no mercado imobiliário brasileiro com base no comportamento dos agentes que o compõem. Os agentes vendedores têm comportamento heterogêneo e são influenciados pela demanda histórica, enquanto que os agentes compradores têm o seu comportamento determinado pela disponibilidade de crédito. Esta disponibilidade de crédito, por sua vez, é definida pelos limites para concessão de financiamento no Sistema Financeiro de Habitação. Verificamos que o processo markoviano que descreve preço de mercado converge para um sistema dinâmico determinístico quando o número de agentes aumenta, e analisamos o comportamento deste sistema dinâmico. Mostramos qual é a família de variáveis aleatórias que representa o comportamento dos agentes vendedores de forma que o sistema apresente um preço de equilíbrio não trivial, condizente com a realidade. Verificamos ainda que o preço de equilíbrio depende não só das regras de concessão de financiamento no Sistema Financeiro de Habitação, como também do preço de reserva dos compradores e da memória e da sensibilidade dos vendedores a alterações na demanda. A memória e a sensibilidade dos vendedores podem levar a oscilações de preços acima ou abaixo do preço de equilíbrio (típicas de processos de formação de bolhas); ou até mesmo a uma bifurcação de Neimark-Sacker, quando o sistema apresenta dinâmica oscilatória estável. / One of the fundamental regulatory aspects for the housing market in Brazil are the limits for obtaining a residential mortgage loan within the Sistema Financeiro de Habitação. These limits can be defined so as to increase or reduce credit supply in this market, changing its agents behavior and, therefore, the housing market price. In this work we propose a pricing model for the brazilian housing market based on the behavior of its agents. Sellers have heterogeneous behavior and are influenced by the historical demand, while buyers behavior is determined by credit availability. The availability of credit is, in its turn, defined by the regulatory limits for obtaining a residential mortgage loan. We have verified that the Markov process which describes the market price converges to a deterministic dynamical system as the number of agents increase, and we have analyzed the behavior of this emerging system. We show which family of random variables may represent the behavior of sellers so that the system has a nontrivial equilibrium price, consistent with reality. We have also verified that the equilibrium price depends not only on the regulatory limits for obtaing a loan, but also on buyers reserve price and on sellers memory and sensitivity to changes in the demand. Sellers memory and sensitivity to changes in the demand can result in price oscillations above or below the equilibrium level, which is typical in bubble formation processes; or even in a Neimark-Sacker bifurcation, when the price has a stable oscillatory dynamics.

Many analysts believe that problems in the United States housing market initiated the 2007-2009 global financial crisis. In this regard, the subprime mortgage crisis (SMC) shook the foundations of the financial industry by causing the failure of many iconic Wall Street investment banks and prominent depository institutions. This crisis stymied credit extension to households and businesses thus creating credit crunches and, ultimately, a global recession. This thesis specifically discusses the SMC and its components, causes, consequences and cures in relation to subprime mortgage origination, data as well as bank bailouts. In particular, the SMC has highlighted the fact that risk, credit ratings, profit and valuation as well as capital regulation are important banking considerations. With regard to risk, the thesis discusses credit (including counterparty), market (including interest rate, basis, prepayment, liquidity and price), tranching (including maturity mismatch and synthetic), operational (including house appraisal, valuation and compensation) and systemic (including maturity transformation) risks. The thesis introduces the IDIOM hypothesis that postulates that the SMC was largely caused by the intricacy and design of subprime agents, mortgage origination that led to information problems (loss, asymmetry and contagion), valuation opaqueness and ineffective risk mitigation. It also contains appropriate examples, discussions, timelines as well as appendices about the main results on the aforementioned topics. Numerous references point to the material not covered in the thesis, and indicate some avenues for further research. In the sequel, the banks that we study are subprime interbank lenders (SILs), subprime originators (SORs), subprime dealer banks (SDBs) and their special purpose vehicles (SPVs) such as Wall Street investment banks and their special structures as well as subprime investing banks (SIBs). Furthermore, the primary subprime agents that we consider are house appraisers (HAs), mortgage brokers (MBs), mortgagors (MRs), servicers (SRs), trustees, underwriters and credit enhancement providers (CEPs). Also, the insurers involved in the subprime market are originator mortgage insurers (OMIs) and monoline insurers (MLIs). The main components of the SMC are MRs, the housing market, SDBs/hedge funds/money market funds/SIBs, the economy as well as the government (G) and central banks. Here, G either plays a regulatory, bailout or policymaking role. Most of the aforementioned banks and agents are assumed to be risk neutral with SOR being the exception since it can be risk (and regret) averse on occasion. The three main aspects of the SMC - subprime mortgage origination, data and bailouts - that we cover in this thesis and the chapters in which they are found are outlined below. In Chapter 2, we discuss the dynamics of SORs' capital, information, ratings, risk and valuation under mortgage origination. In particular, we model subprime mortgages that are able to fully amortize, voluntarily prepay or default and construct a discrete-time model for SOR risk and profit incorporating costs of funds and mortgage insurance as well as loan losses. Furthermore, a constrained optimal valuation problem for SORs under mortgage origination is solved. In addition, we show how high loan-to-value ratios curtailed the refinancing of subprime mortgages, while low ratios imply favorable house equity for subprime MRs. Chapter 2 also explores the relationship between Basel capital regulation and the SMC. This involves studying bank credit and capital under Basel regulation. Further issues dealt with are the quantity and pricing of subprime mortgages as well as credit ratings under Basel capital regulation. A key problem is whether Basel capital regulation exacerbated the SMC. Very importantly, the thesis answers this question in the affirmative. Chapter 3 contains subprime data not presented in Chapters 2. We present other mortgage data that also have connections with the main subprime issues raised. In Chapter 4, a troubled SOR's recapitalization by G via subprime bank bailouts is discussed. Our research supports the view that if SOR is about to fail, it will have an incentive not to extend low risk mortgages but rather high risk mortgages thus shifting risk onto its creditors. Here, for instance, we analyze the efficiency of purchasing toxic structured mortgage products from troubled SORs as opposed to buying preferred and common equity. In this regard, we compare the cases where SORs' on-balance sheet mortgages are fully amortizing, voluntarily prepaying (refinancing and equity extraction) and involuntarily prepaying (defaulting). If bailing out SORs considered to be too big to fail involves buying assets at above fair market values, then these SORs are encouraged ex-ante to invest in high risk mortgages and toxic structured mortgage products. Contrary to the policy employed by G, purchasing common (preferred) equity is always the most (least) ex-anteand ex-post-efficient type of capital injection. Our research confirms that this is true irrespective of whether SOR volunteers for recapitalization or not. In order to understand the key results in Chapters 2 to 4, a working knowledge of discrete-time stochastic modeling and optimization is required. The work presented in this thesis is based on a book (see [103]), 2 peer-reviewed international journal articles (see [51] and [105]), 2 peer-reviewed chapters in books (see [104] and [110]) and 4 peer-reviewed conference proceedings paper (see [23], [106], [107] and [109]). / Thesis (Ph.D. (Applied Mathematics))--North-West University, Potchefstroom Campus, 2011.

Many analysts believe that problems in the United States housing market initiated the 2007-2009 global financial crisis. In this regard, the subprime mortgage crisis (SMC) shook the foundations of the financial industry by causing the failure of many iconic Wall Street investment banks and prominent depository institutions. This crisis stymied credit extension to households and businesses thus creating credit crunches and, ultimately, a global recession. This thesis specifically discusses the SMC and its components, causes, consequences and cures in relation to subprime mortgage origination, data as well as bank bailouts. In particular, the SMC has highlighted the fact that risk, credit ratings, profit and valuation as well as capital regulation are important banking considerations. With regard to risk, the thesis discusses credit (including counterparty), market (including interest rate, basis, prepayment, liquidity and price), tranching (including maturity mismatch and synthetic), operational (including house appraisal, valuation and compensation) and systemic (including maturity transformation) risks. The thesis introduces the IDIOM hypothesis that postulates that the SMC was largely caused by the intricacy and design of subprime agents, mortgage origination that led to information problems (loss, asymmetry and contagion), valuation opaqueness and ineffective risk mitigation. It also contains appropriate examples, discussions, timelines as well as appendices about the main results on the aforementioned topics. Numerous references point to the material not covered in the thesis, and indicate some avenues for further research. In the sequel, the banks that we study are subprime interbank lenders (SILs), subprime originators (SORs), subprime dealer banks (SDBs) and their special purpose vehicles (SPVs) such as Wall Street investment banks and their special structures as well as subprime investing banks (SIBs). Furthermore, the primary subprime agents that we consider are house appraisers (HAs), mortgage brokers (MBs), mortgagors (MRs), servicers (SRs), trustees, underwriters and credit enhancement providers (CEPs). Also, the insurers involved in the subprime market are originator mortgage insurers (OMIs) and monoline insurers (MLIs). The main components of the SMC are MRs, the housing market, SDBs/hedge funds/money market funds/SIBs, the economy as well as the government (G) and central banks. Here, G either plays a regulatory, bailout or policymaking role. Most of the aforementioned banks and agents are assumed to be risk neutral with SOR being the exception since it can be risk (and regret) averse on occasion. The three main aspects of the SMC - subprime mortgage origination, data and bailouts - that we cover in this thesis and the chapters in which they are found are outlined below. In Chapter 2, we discuss the dynamics of SORs' capital, information, ratings, risk and valuation under mortgage origination. In particular, we model subprime mortgages that are able to fully amortize, voluntarily prepay or default and construct a discrete-time model for SOR risk and profit incorporating costs of funds and mortgage insurance as well as loan losses. Furthermore, a constrained optimal valuation problem for SORs under mortgage origination is solved. In addition, we show how high loan-to-value ratios curtailed the refinancing of subprime mortgages, while low ratios imply favorable house equity for subprime MRs. Chapter 2 also explores the relationship between Basel capital regulation and the SMC. This involves studying bank credit and capital under Basel regulation. Further issues dealt with are the quantity and pricing of subprime mortgages as well as credit ratings under Basel capital regulation. A key problem is whether Basel capital regulation exacerbated the SMC. Very importantly, the thesis answers this question in the affirmative. Chapter 3 contains subprime data not presented in Chapters 2. We present other mortgage data that also have connections with the main subprime issues raised. In Chapter 4, a troubled SOR's recapitalization by G via subprime bank bailouts is discussed. Our research supports the view that if SOR is about to fail, it will have an incentive not to extend low risk mortgages but rather high risk mortgages thus shifting risk onto its creditors. Here, for instance, we analyze the efficiency of purchasing toxic structured mortgage products from troubled SORs as opposed to buying preferred and common equity. In this regard, we compare the cases where SORs' on-balance sheet mortgages are fully amortizing, voluntarily prepaying (refinancing and equity extraction) and involuntarily prepaying (defaulting). If bailing out SORs considered to be too big to fail involves buying assets at above fair market values, then these SORs are encouraged ex-ante to invest in high risk mortgages and toxic structured mortgage products. Contrary to the policy employed by G, purchasing common (preferred) equity is always the most (least) ex-anteand ex-post-efficient type of capital injection. Our research confirms that this is true irrespective of whether SOR volunteers for recapitalization or not. In order to understand the key results in Chapters 2 to 4, a working knowledge of discrete-time stochastic modeling and optimization is required. The work presented in this thesis is based on a book (see [103]), 2 peer-reviewed international journal articles (see [51] and [105]), 2 peer-reviewed chapters in books (see [104] and [110]) and 4 peer-reviewed conference proceedings paper (see [23], [106], [107] and [109]). / Thesis (Ph.D. (Applied Mathematics))--North-West University, Potchefstroom Campus, 2011.