The Basel Committee on Banking Supervision (BCBS) designed the Internal Ratings Based (IRB) approach, which is based on a single risk factor model. This IRB approach was de-signed to determine banks’ regulatory capital for credit risk. The asymptotic single risk factor (ASRF) model they used makes use of prescribed asset correlations, which banks must use for their credit risk regulatory capital, in order to abide by the BCBS’s rules. Banks need to abide by these rules to reach an international standard of banking that promotes the health of the specific bank. To evaluate whether these correlations are as conservative as the BCBS intended, i.e. not too onerous or too lenient, empirical asset correlations embedded in gross loss data, spanning different economic milieus, were backed out of the regulatory credit risk model. A technique to extract these asset correlations from a Vasicek distribution of empirical loan losses was proposed and tested in international markets. This technique was used to extract the empirical asset correlation, and then compare the prescribed correlations for developed (US) and developing (South Africa) economies over the total time period, as well as a rolling time period. For the first analysis, the BCBS’s asset correlation was conservative when com-pared to South Africa and the US for all loan types. Comparing the empirical asset correlation over a seven-year rolling time period for South Africa and the BCBS, the specified asset cor-relation was found to be as conservative as the BCBS intended. Comparing the US empirical asset correlation for the same rolling period to that of the BCBS, it was found that for all loans, the BCBS was conservative, up until 2012. In 2012 the empirical asset correlation sur-passed that of the BCBS, and thus the BCBS was not as conservative as they had originally intended. / MCom (Risk Management), North-West University, Potchefstroom Campus, 2015

The Basel Committee on Banking Supervision (BCBS) designed the Internal Ratings Based (IRB) approach, which is based on a single risk factor model. This IRB approach was de-signed to determine banks’ regulatory capital for credit risk. The asymptotic single risk factor (ASRF) model they used makes use of prescribed asset correlations, which banks must use for their credit risk regulatory capital, in order to abide by the BCBS’s rules. Banks need to abide by these rules to reach an international standard of banking that promotes the health of the specific bank. To evaluate whether these correlations are as conservative as the BCBS intended, i.e. not too onerous or too lenient, empirical asset correlations embedded in gross loss data, spanning different economic milieus, were backed out of the regulatory credit risk model. A technique to extract these asset correlations from a Vasicek distribution of empirical loan losses was proposed and tested in international markets. This technique was used to extract the empirical asset correlation, and then compare the prescribed correlations for developed (US) and developing (South Africa) economies over the total time period, as well as a rolling time period. For the first analysis, the BCBS’s asset correlation was conservative when com-pared to South Africa and the US for all loan types. Comparing the empirical asset correlation over a seven-year rolling time period for South Africa and the BCBS, the specified asset cor-relation was found to be as conservative as the BCBS intended. Comparing the US empirical asset correlation for the same rolling period to that of the BCBS, it was found that for all loans, the BCBS was conservative, up until 2012. In 2012 the empirical asset correlation sur-passed that of the BCBS, and thus the BCBS was not as conservative as they had originally intended. / MCom (Risk Management), North-West University, Potchefstroom Campus, 2015

The short rate is central in the context of interest-rate markets as well as broader finance. As such, accurate modelling of this rate is of particular importance in the pricing of interest-rate options, especially during times of high volatility where increased demand is seen for simpler and lower risk investments. Recent interest has moved away from models of a pure continuous nature towards models that can account for discontinuities in the short rate. These are more representative of real world movements where the short rate is seen to jump due to current and scheduled market information. This dissertation examines this phenomenon in the context of a Vasicek short rate model and accounts for random-sized jumps at deterministic times following ideas similar to those introduced by Kim and Wright (2014). Finite difference methods are used successfully to find PDE solutions via backwards diffusion of the option value equation to its initial state. This procedure is implemented computationally and compared to Monte Carlo benchmark methods in order to assess its accuracy. In both non-jump and jump settings the method constructed was able to accurately price the call option specified and proved to be a viable means for pricing interest-rate options when stochastically-sized discontinuities are present at known times between inception and expiry. Furthermore the method showed that the stochastic discontinues in the short rate most notably affect the option price in the region around and just out of the money.

Affine term structure models (ATSMs) are one set of popular models for yield curve modeling. Given that the models forecast yields based on the speed of mean reversion, under what circumstances can we distinguish one ATSM from another? The objective of my dissertation is to quantify the benefit of knowing the “true” model as well as the cost of being wrong when choosing between ATSMs. In particular, I detail the power of out-of-sample forecasts to statistically distinguish one ATSM from another given that we only know the data are generated from an ATSM and are observed without errors. My study analyzes the power and size of affine term structure models (ATSMs) by evaluating their relative out-of-sample performance. Essay one focuses on the study of the oneactor ATSMs. I find that the model’s predictive ability is closely related to the bias of mean reversion estimates no matter what the true model is. The smaller the bias of the estimate of the mean reversion speed, the better the out-of-sample forecasts. In addition, my finding shows that the models' forecasting accuracy can be improved, in contrast, the power to distinguish between different ATSMs will be reduced if the data are simulated from a high mean reversion process with a large sample size and with a high sampling frequency. In the second essay, I extend the question of interest to the multiactor ATSMs. My finding shows that adding more factors in the ATSMs does not improve models' predictive ability. But it increases the models' power to distinguish between each other. The multiactor ATSMs with larger sample size and longer time span will have more predictive ability and stronger power to differentiate between models.

Empirical evidence indicates that the volatility in asset prices is not constant, but varies over time. However, many simple models for asset pricing rest on an assumption of constancy. In this thesis we analyse the zero-coupon bond price under a two-factor Vasicek model, where both the short rate and its volatility follow Ornstein-Uhlenbeck processes. Yield curves based on the two-factor model are then compared to those obtained from the standard Vasicek model with constant volatility. The simulated yield curves from the two-factor model exhibit "humps" that can be observed in the market, but which cannot be obtained from the standard model. / Det finns empiriska bevis som indikerar att volatiliteten i finansiella marknader inte är konstant, utan varierar över tiden. Dock så utgår många enkla modeller för tillgångsprisättning från ett antagande om konstans. I det här examensarbetet analyserar vi priset på nollkupongobligationer under en stokastisk Vasicekmodell, där både den korta räntan och dess volatilitet följer Ornstein-Uhlenbeck processer. De räntekurvor som tas fram genom två-faktormodellen jämförs sedan med de kurvor som erhålls genom den enkla Vasicekmodellen med konstant volatilitet. De simulerade räntekurvorna från två-faktormodellen uppvisar "pucklar" som kan urskiljas i marknaden, men som inte kan erhållas genom standardmodellen.

Esse estudo avalia a adequação dos requerimentos absolutos de capital no Brasil para bancos pequenos e grandes separadamente e investiga os requerimentos de capital mínimo para risco de crédito nas diferentes abordagens de Basiléia, em especial o impacto da adoção dos modelos dos ratings internos (IRB) conforme o Edital BCB n. 37/11. Além disso, propõe e avalia a abordagem padronizada dos ratings centralizados, CRBA, para cálculo do Capital Mínimo Exigido (CME) em bancos pequenos e que é baseada na abordagem padronizada em vigor na Europa, mas voltada para dados disponíveis nas Centrais de Risco. A CRBA pertence à família dos modelos internos e busca contribuir com as recentes discussões sobre a reforma regulatória bancária na Europa e nos Estados Unidos. Para os três objetivos mencionados, as metodologias adotadas foram: 1) o Valuet-at-Risk (VaR) não paramétrico de Crédito (CVaR) de Carey (2002) e o paramétrico Creditrisk+ para estimar o capital econômico do Sistema Bancário; seguido da 2) estimação amostral e avaliação do capital regulatório para bancos pequenos e grandes nas abordagens IRB, Basileia 1, abordagem padrão simplificada (SSA); além da 3) avaliação da abordagem proposta nesse estudo, a CRBA. A performance de todas essas abordagens é avaliada frente a cenários de stress ad hoc e durante a Crise de 2008-2009. Os dados utilizados foram exposições de crédito aleatórias colhidas da Nova Central de Risco do Banco Central do Brasil (SCR). Os principais resultados desse estudo são: 1) sugerir um capital regulatório total (Patrimônio de Referência mais provisão) para bancos grandes de 17,5% baseado no CVaR paramétrico de 99,9% e, para pequenos, de 15,31% baseado no CVaR de 99%; 2) sugerir que, de todas as abordagens de Basileia II, o IRB estimado conforme o Edital BCB n. 37/2011 e para as Probabilidade de Default (PDs) calculadas por matrizes de migração do SCR, é o mais conservador; 3) sugerir que a abordagem proposta seja mais sensível ao risco de crédito do que atual brasileira, especialmente no varejo, além de oferecer um nível proteção maior contra choques aleatórios de crédito. Na Crise de 2008-2009, os bancos pequenos e grandes apresentaram respostas muito distintas a choques diversos ou quando os \"estados da economia\" se deterioravam. Os bancos pequenos não atingem o grau de diversificação necessário para minimizar perdas extremas. Por outro lado, do ponto de vista do risco sistêmico, a falência dessas entidades tem impactos muito menores que a de conglomerados bancários de porte. Finalmente, a abordagem proposta CRBA é apresentada como uma alternativa à abordagem atual no Brasil e à abordagem padronizada (SA) nos demais países, em especial na Europa. No Brasil, a CRBA cumpriria o papel de aumentar a sensibilidade a risco de crédito do CME nos bancos pequenos criando incentivos para uma gestão de risco de crédito mais cautelosa e alinhando o nível de capital dos bancos pequenos ao seu risco efetivo. Nos demais países, a CRBA é uma alternativa à abordagem padronizada, que independe da opinião das Agências de Classificação de Risco (ACRs). A CRBA traz dois benefícios: o primeiro de ampliar o escopo dos modelos internos e eliminar a dependência regulatória na opinião das ACRs, diminuindo a oportunidade de arbitragem regulatória com ratings inflacionados e corrigindo incentivos para que as ACRs sejam apenas provedoras de opiniões isentas; e o segundo, de prover os organismos supervisores com um mecanismo de controle (tracking error) sobre a qualidade de gestão de risco dos bancos pequenos por meio das Centrais de Risco. / This work analyses capital requirements adequacy in Brazil both for small and big banks individually and evaluates the minimum capital requirements for credit risk in the different Basel II approaches, especially, the impacts of IRB adoption as stated on Edital BCB n.37/11. Besides, it proposes and evaluates the Centralized Standard Ratings Based Approach (CRBA) to calculate Minimum Capital Requirements (MCR) in small banks. It is inspired in the Basel II Standard Approach (SA) disseminated in Europe, but based on information from the Credit Registers. The CRBA is an internal model approach in line with recent discussions on regulatory reform in Europe and in the US. The methodology to address these three research goals is: the non-parametric credit Value-at-Risk (VaR) or CVaR of Carey(2002) and the parametric Creditrisk+ to estimate the economic capital for the banking system; to evaluate regulatory capital in small and big banks in the IRB, Basel 1 and the Simplified Standard Approach (SSA) on the sample; and to evaluate the CRBA, proposed in this study. The performance of these approaches is confronted with ad hoc stress scenarios and within the Credit Crisis of 2008-2009. The data is comprised of credit exposures available in the Brazilian Credit Register (SCR). This work main results are: 1) to suggest a total regulatory capital (capital and provision) of 17.5% to big banks based on a parametric CVaR (99.9%) and of 15.31% to small banks based on a CVaR (99%); 2) to suggest, based on all Basel II approaches, that the IRB, as stated on Edital BCB n.31/11 and calibrated with the probabilities of default (PD) estimated with transition matrixes from the SCR, is the most conservative approach; 3) to suggest that the proposed approach is more sensitive to credit risk especially in retail and is more effective against stress chocks. Small and big banks behave differently to adverse shocks. The small banks, for instance, have problems diversifying out extreme losses when the \"states of the economy\" deteriorate. On the other hand, considering systemic risk, the bankruptcies of these institutions are much less of a problem than the ones of a big bank. Finally, the CRBA is presented as an alternative to the current approach (SSA) in Brazil and to the Standard Approach (SA) in other countries, specifically in Europe. In Brazil, the CRBA would increase the risk sensitivity of MCR on smaller banks creating incentives to more careful risk management practices and aligning their capital and risk levels. On the other countries, the CRBA is an alternative to the Standard Approach (SA) that is not dependent on Credit Rating Agencies - CRAs\' opinions and brings two additional benefits. First, it is an internal model based approach eliminating regulatory dependence on CRAs\' opinions, minimizing opportunities to regulatory arbitrage with inflated ratings and allowing CRAs to be more of a trustworthy opinion provider. Second, it provides supervisors a tracking error mechanism to evaluate risk management in small banks using Credit Registers.

This thesis applies the concept of cost e ciency to the design of executive compensation. In a classical Black-Scholes framework, we are able to express the cost e cient counterpart of the Asian Executive Option explicitly, and design a payo that has the same distribution as the Asian Executive Indexed Option but comes at a cheaper price. The cost e cient counterpart of the latter option is not analytically tractable, but we are able to simulate its price. Furthermore, we extend the study of these two types of options in the presence of stochastic interest rates modeled by a Vasicek process. We are able to derive new closedform pricing formulas for these options. A framework for crafting the state price process is introduced. From here, an explicit expression for the state process is given and its distribution is derived. Using the pricing formulas and the state price process, we are then able to simulate the prices of the corresponding cost e cient counterparts in a stochastic interest rate environment. We conclude with some avenues for future research.

Preview:     SEB Investment Strategy is the function in SEB that supports business units SEB      Private Banking and SEB Retail with investment philosophy and investment            process. The framework of SEB Investment Strategy encompasses to manage a     structured investment philosophy and process to produce a range of investment                    options and portfolios for different target groups. From January 2006 to October        2009 forty “Proposal for fund portfolios” were produced each containing         writing on market condition and expectations plus portfolio recommendations.        Each time four portfolios consisting of six mutual funds was recommended,                    Fund Portfolio 30, 50, 70 and 100. Fund Portfolio 30 (FP30) contained           30% equity fund and 70% fixed-income funds. By same reasoning FP50           contains 50/50 equity- and fixed-income funds, FP70, 70% equity funds and         30% fixed-income funds and FP100 only equity funds.   Purpose:      The aim of this work is to evaluate these SEB Investment Strategy recommended       portfolios for private SEB Retail clients from January 2006 to December 2009.    Evaluation is done by comparing the performance of recommended portfolios       with portfolios produced by applying Vasicek´s Technique and simplified   optimization technique.   Method:     To allow work with Vasicek´s Technique in which we are dependent on a market        portfolio, I have created an Index which includes SEB Mutual Funds and their         share of the Index is determined from each fund´s total assets in relation to the    sum of the total assets under management of all funds inclusive in the Index.   Index consists of 40 mutual funds 2002-2007 and 37 mutual funds 2008         and 2009. The total supply of funds has been reduced to the above numbers by             the following criteria:   Clients must be able to invest in funds through conventional SEB Fund Account. No initiation fees or sales charges. Minimum historical Net Asset Value prices (NAV-prices) from 2nd January 2002. Daily trading and at least 300 million SEK in assets under management. No Fund-in-Fund products. Only SEB or SEB Choice funds.   The closing daily NAV-prices (time series) of these funds have been obtained from seb.se/fonder from 2nd January 2002 to 28th December 2009. With prices daily returns are calculated and used for estimation of historical and average values of variables needed for computing forecasted Alphas and Betas according to Vasicek´s Technique. Mutual funds are then ranked with respect to excess return over forecasted Beta given risk free rate equal to Swedish government 1 month treasury-bill (SSVX1M) at time for optimisation. Top six ranked funds are included in the optimization process. The first optimized portfolio given actual T-bill is then compared to FP100 recommended by SEB Investment Strategy. In order to find optimized solutions to other recommended portfolios premiums are added to actual T-bill rate.

Inflation-indexed instruments provide a real return and protect investors from the erosion of the purchasing power of money. Hence, inflation-indexed markets grow very fast day by day. In this thesis, we focus on pricing of the inflation-indexed swaps and swaptions which are the most liquid derivative products traded in the inflation-indexed markets. Firstly, we review the Hull-White extended Vasicek model in the HJM framework. Then, we use this model to price inflation-indexed swaps. Also, pricing of inflation-indexed swaptions is given using Black&rsquo / s market model.

This thesis applies the concept of cost e ciency to the design of executive compensation. In a classical Black-Scholes framework, we are able to express the cost e cient counterpart of the Asian Executive Option explicitly, and design a payo that has the same distribution as the Asian Executive Indexed Option but comes at a cheaper price. The cost e cient counterpart of the latter option is not analytically tractable, but we are able to simulate its price. Furthermore, we extend the study of these two types of options in the presence of stochastic interest rates modeled by a Vasicek process. We are able to derive new closedform pricing formulas for these options. A framework for crafting the state price process is introduced. From here, an explicit expression for the state process is given and its distribution is derived. Using the pricing formulas and the state price process, we are then able to simulate the prices of the corresponding cost e cient counterparts in a stochastic interest rate environment. We conclude with some avenues for future research.