This PhD thesis investigates the pricing of a corporate loan according to the credit risk, the liquidity cost and the embedded prepayment option. A loan contract issued by a bank for its corporate clients is a financial agreement that often comes with more flexibility than a retail loan contract. These options are designed to meet clients' expectations and can include e.g., a prepayment option (which entitles the client, if he desires so, to pay all or a fraction of its loan earlier than the maturity). The prepayment is the main option and it will be study in this thesis. In order to decide whether the exercise of the option is worthwhile the borrower compares the remaining payments with the outstanding amount of the loan. If the remaining payments exceed the nominal value then it is optimal for the borrower to refinance his debt at a lower rate. For a bank, the prepayment option is essentially a reinvestment risk, i.e. the risk that the borrower decides to repay earlier his/her loan and that the bank cannot reinvest his/her excess of cash in a new loan with same characteristics.The valuation problem of the prepayment option can be modelled as an embedded compound American option on a risky debt owned by the borrower. We choose in this thesis to price a loan and its prepayment option by resolving the associated PDE instead of binomial trees (time-consuming) or Monte Carlo techniques (slow to converge).

The interest rate dynamics is an important fundamental for valuation more complex structures of interest rate derivatives. The goal of this diploma thesis is to describe the use of models of interest rate for interest rate option pricing. The paper could be logically divided into two parts, the theoretical one and practical one. In the first part the essentials for pricing theory are introduced as risk neutrality, martingales, stochastic differential calculus, and theory of arbitrage. On their basis four basic yield curve models are derived, Vasicek model, model Cox-Ingersoll-Ross , Black-Derman-Toy and two factor Heath-Jarrow-Morton model. Second part provides the analysis of yields of U.S. Treasury bonds with different maturity. At the end CIR model and BDT binomial tree are used for valuation of option on 10 years yield.

The Almost-Exact Scheme (AES), as proposed by Oosterlee and Grzelak, has been applied to the Heston stochastic volatility model to show improved error convergence for small time-steps, as opposed to the classical Euler-Maruyama (EM) scheme, in European option pricing. This idea has been extended to the double Heston stochastic volatility model, to show similar improved results for Bermudan options. In this thesis, we extend this idea even further and develop an Almost-Exact Scheme to the Gatheral double mean reverting (DMR) model, to show improved error convergence for American put options. We illustrate that, because of the complexity of the dynamics of our model, a direct application of the AES is not possible, and therefore derive a diffusion trick, so we can instead use a partial implementation of the AES. Our partial implementation has two variants. In the first variant, we implement the AES on the long-run mean process combined with the Milstein scheme on the variance process. In the second variant, the Milstein scheme is replaced by a second order refinement. We name these two schemes AEMS and AEMS-SOR respectively. We conduct extensive simulation studies to evaluate the proposed schemes. The results indicate improved error convergence of the proposed scheme for small time-steps when time-to-maturity is equal to half a year, but does not seem to differ much from the EM scheme for a shorter time-to-maturity.

Made available in DSpace on 2015-04-14T13:35:42Z (GMT). No. of bitstreams: 1 449052.pdf: 589111 bytes, checksum: 854eb80219f2ea6775b8336257985625 (MD5) Previous issue date: 2013-03-22 / Objective: To determine the risk factors related to the development of stroke in patients undergoing cardiac surgery. Methods: A historical cohort study. We included 4626 patients aged &#8805; 18 years who underwent coronary artery bypass surgery, heart valve replacement surgery alone or combined with CABG between January 1996 and December 2011. The relationship between risk predictors and stroke was assessed by logistic regression model with a significance level of 0.05. Results: The incidence of stroke was 3% in the overall sample. After logistic regression found the following risk predictors for stroke: age 50-65 years (OR=2.11 95% CI 1.05-4.23 p=0.036) and age &#8805;66 years (OR=3.22 95% CI 1.6-6.47 p=0.001), urgent and emergency surgery (OR=2.03 95% CI 1.20-3.45 p=0.008), aortic valve disease (OR=2.32 95% CI 1.18-4.56 p=0.014), atrial fibrillation (OR=1.88 95% CI 1.05-3.34 p=0.032), peripheral artery disease (OR=1.81 95% CI 1.13-2.92 p=0.014), history of stroke (OR=3.42 95% CI 2.19-5.35 p<0.001) and cardiopulmonary bypass time >110 minutes (OR=1.71 95% CI 1.16-2.53 p=0.007). The mortality was 31.9% in the stroke group and 8.5% in the control group (OR=5.06 95% CI 3.5-7.33 p<0.001). Conclusion: The study identified the following risk predictors for stroke after cardiac surgery: age, urgent and emergency surgery, aortic valve disease, atrial fibrillation, peripheral artery disease, history of cerebrovascular disease and cardiopulmonary bypass time> 110 minutes. / Objetivos: Determinar os preditores de risco relacionados ao desenvolvimento de acidente vascular cerebral em pacientes que realizaram cirurgia card?aca. M?todos: Estudo de coorte hist?rico. Inclu?mos 4626 pacientes com idade &#8805; 18 anos submetidos ? cirurgia de revasculariza??o do mioc?rdio, cirurgia card?aca valvar isolada ou cirurgia valvar associada com revasculariza??o do mioc?rdio, de janeiro de 1996 e dezembro de 2011. A rela??o entre os preditores de risco e o acidente vascular cerebral, foi avaliada por modelo de regress?o log?stica com n?vel de signific?ncia de 0,05. Resultados: A incid?ncia de acidente vascular cerebral foi 3% na amostra total. A an?lise multivariada identificou como preditores de risco para o acidente vascular cerebral: idade 50-65 anos (OR=2,11 95% IC 1,05-4,23 p=0,036) e idade &#8805; 66 anos (OR=3,22 95% IC 1,6-6,47 p=0,001), cirurgia de urg?ncia/emerg?ncia (OR=2,03 95% IC 1,20-3,45 p=0,008), valvulopatia a?rtica (OR=2,32 95% IC 1,18-4,56 p=0,014), fibrila??o atrial (OR=1,88 95% IC 1,05-3,34 p=0,032), doen?a arterial obstrutiva perif?rica (OR=1,81 95% IC 1,13-2,92 p=0,014), hist?ria de doen?a cerebrovascular (OR=3,42 95% IC 2,19-5,35 p<0,001) e tempo de circula??o extracorp?rea >110 minutos (OR=1,71 95% IC 1,16-2,53 p=0,007). A mortalidade foi 31,9% nos pacientes que sofreram AVC e 8,5% nos sem AVC (OR=5,06 95% IC 3,5-7,33 p<0,001). Conclus?o: Idade, cirurgia de urg?ncia/emerg?ncia, doen?a de valva a?rtica, fibrila??o atrial, doen?a arterial obstrutiva perif?rica, hist?ria de doen?a cerebrovascular e tempo de circula??o extracorp?rea >110 minutos foram preditores independentes para o desenvolvimento de AVC intra-hospitalar, em pacientes submetidos ? cirurgia card?aca.

Submitted by Setor de Tratamento da Informa??o - BC/PUCRS (tede2@pucrs.br) on 2016-12-09T10:53:50Z No. of bitstreams: 1 TES_ELLEN_HETTWER_MAGEDANZ_COMPLETO.pdf: 2253745 bytes, checksum: 9b7bd256f9791fbf0115519d7f1d704d (MD5) / Made available in DSpace on 2016-12-09T10:53:50Z (GMT). No. of bitstreams: 1 TES_ELLEN_HETTWER_MAGEDANZ_COMPLETO.pdf: 2253745 bytes, checksum: 9b7bd256f9791fbf0115519d7f1d704d (MD5) Previous issue date: 2016-08-24 / Introduction: Stroke is a complication responsible for high morbidity and mortality after cardiac surgery, affecting 1.3 to 4.3% and mortality between 13% and 41%. Several models have been proposed to assess the risk of mortality after cardiac surgery. However, most of these models doesn?t evaluate the postoperative morbidity. Objective: To develop a risk score model for postoperative stroke in patients undergoing cardiac surgery (coronary artery bypass surgery, valve replacement surgery and combined - CABG + valve replacement), with cardiopulmonary bypass (CPB). Methods: The study sample included data from 4,862 adult patients who underwent cardiac surgery between January 1996 to December 2012, at the Hospital S?o Lucas. Logistic regression was used to evaluate the relationship between risk factors and the development of stroke. After univariate and multivariate analysis, data from 3,258 patients were used to develop the model. Its performance has been validated in the remaining patients (n = 1,604). The final model was constructed with the total sample, remaining the same variables. The accuracy of the model was tested using the area under the ROC curve. Results: The estimated incidence for stroke in the postoperative period was 3% (149). Among patients who developed stroke, 59.1% were male, 51% were aged ? 66 years and 31.5% died. The mean age of the study population was 58.9 ? 12 years. In multivariate analysis, five variables remained independent predictors for the outcome: age, urgent / emergency surgery, peripheral arterial occlusive disease (PAOD), history of cerebrovascular disease (CVD) and cardiopulmonary bypass (CPB) time> 110 minutes. The area under the ROC curve obtained was 0.71 (95% CI 0.66 to .75). Conclusion: The risk score allows to establish the calculation of the incidence of stroke after cardiac surgery using clinical and surgical variables (age, surgical priority, PAD, CVD history and CPB time). From these variables, it was possible to construct a risk score that classifies patients as low, medium, high and very high operative risk for cerebrovascular stroke. / Introdu??o: O acidente vascular cerebral (AVC) ? uma complica??o respons?vel por alta morbi-mortalidade no p?s-operat?rio de cirurgia card?aca, com incid?ncia de 1,3 a 4,3% e mortalidade entre 13% e 41%. V?rios modelos foram propostos para avaliar risco de mortalidade ap?s cirurgia card?aca. Entretanto, a maioria desses modelos n?o avalia a morbidade p?s-operat?ria. Objetivo: Desenvolver um modelo de escore de risco para AVC p?s-operat?rio de pacientes submetidos ? cirurgia card?aca (cirurgia de revasculariza??o do mioc?rdio, troca valvar e cirurgia combinada - CRM + troca valvar), com circula??o extracorp?rea (CEC). M?todos: A amostra do estudo incluiu dados de 4.862 pacientes adultos que realizaram cirurgia card?aca entre janeiro de 1996 a dezembro de 2012 no Hospital S?o Lucas da PUCRS. Regress?o log?stica foi utilizada para avaliar a rela??o entre fatores de risco e o desenvolvimento de AVC. Dados de 3.258 pacientes foram utilizados para desenvolver o modelo, ap?s an?lises uni e multivariada. Seu desempenho foi validado nos demais pacientes (n=1.604). O modelo final foi constru?do com a amostra total, permanecendo as mesmas vari?veis. A acur?cia do modelo foi testada utilizando-se a ?rea sob a curva ROC. Resultados: A incid?ncia estimada para AVC no p?s-operat?rio foi de 3% (149). Dentre os pacientes que desenvolveram o desfecho, 59,1% eram do sexo masculino, 51% tinham idade ? 66 anos e 31,5% evolu?ram para ?bito. Na an?lise multivariada, cinco vari?veis permaneceram preditoras independentes para o desfecho: idade avan?ada, cirurgia de urg?ncia/emerg?ncia, doen?a arterial obstrutiva perif?rica (DAOP), hist?ria de doen?a cerebrovascular (DCV) e tempo de circula??o extracorp?rea (CEC) > 110 minutos. A ?rea sob a curva ROC obtida foi de 0,71 (IC 95% 0,66 ? 0,75), Conclus?o: O escore de risco constru?do permite estabelecer c?lculo da incid?ncia de AVC ap?s cirurgia card?aca, utilizando vari?veis cl?nicas e cir?rgicas (idade, prioridade cir?rgica, DAOP, hist?ria de DCV e tempo de CEC). A partir dessas vari?veis, foi poss?vel construir um escore de risco que classifica o paciente como de baixo, m?dio, elevado e muito elevado risco operat?rio para o evento cerebrovascular AVC.

In this thesis study, joint frequency offset and channel estimation methods for single-input single-output (SISO) systems are examined. The performance of maximum likelihood estimate of the parameters are studied for different training sequences. Conventionally training sequences are designed solely for the channel estimation purpose. We present a numerical comparison of different training sequences for the joint estimation problem. The performance comparisons are made in terms of mean square estimation error (MSE) versus SNR and MSE versus the total training energy metrics. A novel estimation scheme using complementary sequences have been proposed and compared with existing schemes. The proposed scheme presents a lower estimation error than the others in almost all numerical simulations. The thesis also includes an extension for the joint channel-frequency offset estimation problem to the multi-input multi-output systems and a brief discussion for multiple frequency offset case is also given.

Different diversity techniques such as Maximal-Ratio Combining (MRC), Equal-Gain Combining (EGC) and Selection Combining (SC) are described and analyzed. Two branches (N=2) diversity systems that are used for pre-detection combining have been investigated and computed. The statistics of carrier to noise ratio (CNR) and carrier to interference ratio (CIR) without diversity assuming Rayleigh fading model have been examined and then measured for diversity systems. The probability of error (p_e) vs CNR and (p_e) versus CIR have also been obtained. The fading dynamic range of the instantaneous CNR and CIR is reduced remarkably when diversity systems are used [1]. For a certain average probability of error, a higher valued average CNR and CIR is in need for non-diversity systems [1]. But a smaller valued of CNR and CIR are compared to diversity systems. The overall conclusion is that maximal-ratio combining (MRC) achieves the best performance improvement compared to other combining methods. Diversity techniques are very useful to improve the performance of high speed wireless channel to transmit data and information. The problems which considered in this thesis are not new but I have tried to organize, prove and analyze in new ways.

Este trabalho tem por objetivo principal aplicar o modelo de precificação de opções de taxas de juros proposto por Barbachan e Ornelas (2003), com base nos modelos de taxa de juro e avaliação de opções de Cox, Ingerssol e Ross (1985), para avaliação de opções de compra sobre o Índice de Taxa Média de Depósitos Interfinanceiros de Um Dia (IDI), negociadas na BM&FBovespa. Para estimação dos parâmetros deste modelo, foi empregado o método de Máxima Verossimilhança. Neste contexto, também fez-se uso da fórmula de precificação de opções proposta por Black (1976), adaptada para o mercado de derivativos brasileiros, conforme implementação verificada no trabalho de Gluckstern et al. (2002). Tal aplicação torna-se interessante, pois este modelo é amplamente utilizado pelo mercado brasileiro para avaliação de opções sobre o IDI. De forma a verificar a aderência dos preços teóricos gerados pelos modelos, em comparação aos preços de mercado, métricas de erro foram empregadas. De forma geral, nossos resultados mostraram que ambos os modelos apresentam erros sistemáticos de precificação, onde o modelo CIR subavalia os prêmios das opções e o modelo de Black superprecifica. No entanto, bons resultados foram encontrados ao avaliarmos opções in-the-money e out-of-money com o modelo de Black. / This work aims to apply the interest rate option pricing model proposed by Barbachan and Ornelas (2003), based on the interest rate model and option pricing model developed by Cox, Ingersoll and Ross (1985), to evaluate call options on the 1 day Brazilian Interfinancial Deposits Index - IDI, traded at BM&FBovespa. The Maximum Likelihood method was applied to estimate the model parameters. In this context, the option pricing formula proposed by Black (1976), adapted for the Brazilian derivative Market, was also used, according implementation verified in Gluckstern et al. (2002). This application becomes interesting because this model is widely used by the Brazilian Market to evaluate options on IDI. In order to verify the adherence of theoretical prices generated by the models, in comparison to the Market prices, error metrics were applied. In general, our results pointed out that both models presented systematic pricing errors, in which the CIR model underestimates the option prices and Black’s model overestimates. However, good results were found on the evaluation of options in-the-money and out-of-money with the Black’s Model.

Este trabalho tem por objetivo principal aplicar o modelo de precificação de opções de taxas de juros proposto por Barbachan e Ornelas (2003), com base nos modelos de taxa de juro e avaliação de opções de Cox, Ingerssol e Ross (1985), para avaliação de opções de compra sobre o Índice de Taxa Média de Depósitos Interfinanceiros de Um Dia (IDI), negociadas na BM&FBovespa. Para estimação dos parâmetros deste modelo, foi empregado o método de Máxima Verossimilhança. Neste contexto, também fez-se uso da fórmula de precificação de opções proposta por Black (1976), adaptada para o mercado de derivativos brasileiros, conforme implementação verificada no trabalho de Gluckstern et al. (2002). Tal aplicação torna-se interessante, pois este modelo é amplamente utilizado pelo mercado brasileiro para avaliação de opções sobre o IDI. De forma a verificar a aderência dos preços teóricos gerados pelos modelos, em comparação aos preços de mercado, métricas de erro foram empregadas. De forma geral, nossos resultados mostraram que ambos os modelos apresentam erros sistemáticos de precificação, onde o modelo CIR subavalia os prêmios das opções e o modelo de Black superprecifica. No entanto, bons resultados foram encontrados ao avaliarmos opções in-the-money e out-of-money com o modelo de Black. / This work aims to apply the interest rate option pricing model proposed by Barbachan and Ornelas (2003), based on the interest rate model and option pricing model developed by Cox, Ingersoll and Ross (1985), to evaluate call options on the 1 day Brazilian Interfinancial Deposits Index - IDI, traded at BM&FBovespa. The Maximum Likelihood method was applied to estimate the model parameters. In this context, the option pricing formula proposed by Black (1976), adapted for the Brazilian derivative Market, was also used, according implementation verified in Gluckstern et al. (2002). This application becomes interesting because this model is widely used by the Brazilian Market to evaluate options on IDI. In order to verify the adherence of theoretical prices generated by the models, in comparison to the Market prices, error metrics were applied. In general, our results pointed out that both models presented systematic pricing errors, in which the CIR model underestimates the option prices and Black’s model overestimates. However, good results were found on the evaluation of options in-the-money and out-of-money with the Black’s Model.

Este trabalho tem por objetivo principal aplicar o modelo de precificação de opções de taxas de juros proposto por Barbachan e Ornelas (2003), com base nos modelos de taxa de juro e avaliação de opções de Cox, Ingerssol e Ross (1985), para avaliação de opções de compra sobre o Índice de Taxa Média de Depósitos Interfinanceiros de Um Dia (IDI), negociadas na BM&FBovespa. Para estimação dos parâmetros deste modelo, foi empregado o método de Máxima Verossimilhança. Neste contexto, também fez-se uso da fórmula de precificação de opções proposta por Black (1976), adaptada para o mercado de derivativos brasileiros, conforme implementação verificada no trabalho de Gluckstern et al. (2002). Tal aplicação torna-se interessante, pois este modelo é amplamente utilizado pelo mercado brasileiro para avaliação de opções sobre o IDI. De forma a verificar a aderência dos preços teóricos gerados pelos modelos, em comparação aos preços de mercado, métricas de erro foram empregadas. De forma geral, nossos resultados mostraram que ambos os modelos apresentam erros sistemáticos de precificação, onde o modelo CIR subavalia os prêmios das opções e o modelo de Black superprecifica. No entanto, bons resultados foram encontrados ao avaliarmos opções in-the-money e out-of-money com o modelo de Black. / This work aims to apply the interest rate option pricing model proposed by Barbachan and Ornelas (2003), based on the interest rate model and option pricing model developed by Cox, Ingersoll and Ross (1985), to evaluate call options on the 1 day Brazilian Interfinancial Deposits Index - IDI, traded at BM&FBovespa. The Maximum Likelihood method was applied to estimate the model parameters. In this context, the option pricing formula proposed by Black (1976), adapted for the Brazilian derivative Market, was also used, according implementation verified in Gluckstern et al. (2002). This application becomes interesting because this model is widely used by the Brazilian Market to evaluate options on IDI. In order to verify the adherence of theoretical prices generated by the models, in comparison to the Market prices, error metrics were applied. In general, our results pointed out that both models presented systematic pricing errors, in which the CIR model underestimates the option prices and Black’s model overestimates. However, good results were found on the evaluation of options in-the-money and out-of-money with the Black’s Model.