The purpose of this study is to investigate the pricing of variable annuity embedded derivatives in a Lévy process setting. This is one of the practical issues that continues to face life insurers in the management of derivatives embedded within these products. It also addresses how such providers can protect themselves against adverse scenarios through a hedging framework built from the pricing framework. The aim is to comparatively consider the price differentials of a life insurer that prices its variable annuity guarantees under the more actuarially accepted regime-switching framework versus the use of a Lévy framework. The framework should address the inadequacies of conventional deterministic pricing approaches used by life insurers given the increasing complexity of the option-like products sold. The study applies finance models in the insurance context given the similarities in payoff structure of the products offered while taking into account the differences that may exist. The underlying Lévy process used in this study is the Variance-Gamma (VG) process. This process is useful in option pricing given its ability to model higher moments, skewness and kurtosis, and also incorporate stochastic volatility. The research results compare well with the regime-switching framework besides the added merit in the use of a more refined model for the underlying that captures most of the observed market dynamics. / Dissertation (MSc)--University of Pretoria, 2014. / tm2015 / Mathematics and Applied Mathematics / MSc / Unrestricted

Submitted by Mario Lopes (mariosilvalopes@gmail.com) on 2011-11-17T22:51:02Z No. of bitstreams: 1 DissertaçãoMSLFinal.pdf: 2601229 bytes, checksum: 8dd97b22637c4e3c6b2b47dfcab63218 (MD5) / Approved for entry into archive by Gisele Isaura Hannickel (gisele.hannickel@fgv.br) on 2011-11-18T10:41:59Z (GMT) No. of bitstreams: 1 DissertaçãoMSLFinal.pdf: 2601229 bytes, checksum: 8dd97b22637c4e3c6b2b47dfcab63218 (MD5) / Made available in DSpace on 2011-11-18T10:43:55Z (GMT). No. of bitstreams: 1 DissertaçãoMSLFinal.pdf: 2601229 bytes, checksum: 8dd97b22637c4e3c6b2b47dfcab63218 (MD5) Previous issue date: 2011-10-24 / O funcionamento dos bancos comerciais implica no sucesso de suas estratégias de captação de depósitos a prazo. O Certificado de Depósito Bancário (CDB) é um dos instrumentos mais utilizados para este fim. 95% dos CDBs são flutuantes e atrelados ao CDI, sendo que grande parte destes CDBs tem data de carência pré-definida para o resgate. Esta característica é responsável pela opção implícita de resgate oferecida ao investidor. Ou seja, o investidor tem a prerrogativa de resgatar seu investimento entre a data de carência e o vencimento do CDB sem que seja penalizado por isso. Este trabalho apresenta um método de apreçamento da opção de resgate implícita no CDB utilizando o modelo de Black Derman Toy. A técnica empregada inova ao considerar o nível da estrutura a termo de taxa de juros tanto em relação à curva de CDBs observada no mercado, quanto a sua volatilidade. Entretanto, a volatilidade é preservada e, por isso, não é contaminada pelas oscilações da estrutura a termo. No procedimento foram utilizados os CDBs do banco de dados da Cetip com valores maiores que quinhentos mil reais emitidos entre 2007 e 2009. Assumiu-se que todos os investidores eram racionais e não precisaram recorrer aos seus investimentos, portanto só resgataram seus recursos após o fim do prazo de carência. Com o intuito de verificar a validade dos preços calculados através do modelo Black Derman Toy, foi aplicada a técnica da simulação de Monte Carlo com a criação de dez mil trajetórias para o preço do ativo. Os resultados obtidos através do modelo proposto foram confirmados quando confrontados com a simulação de Monte Carlo. / The functioning of commercial banks relies on the success of their strategies to attract deposits. Time Deposits (TD) are one of the most used for this purpose. 95% of TDs have floating rates linked to Interbank Certificate of Deposits (CDI) and most of them have a pre-set grace date to the withdrawal. This feature is responsible for the embedded option offered to the investor. That is, the investor has the right to withdrawal their investment between the grace date and the TD maturity without being penalized. This paper presents a method of pricing withdrawal implied options in TDs using Black Derman Toy model. The innovative technique considers the level of the interest rates term structure in relation to TDs curve observed on the market, as well as its volatility. However, volatility is preserved, and therefore is not contaminated by term structure oscillations. In the procedure were used TDs (Cetip database) with amounts greater than five hundred thousand Reais issued between 2007 and 2009. It was assumed that all investors were rational and did not need to rely on their investments, so only withdrew them after their grace period. In order to verify the validity of the calculated prices by Black Derman Toy Model, Monte Carlo simulation technique was applied with the creation of ten thousand asset trajectories. Results obtained by the proposed model were confirmed when confronted with Monte Carlo simulation

Submitted by Daniel Loureiro da Silva (danloux@hotmail.com) on 2018-01-26T14:38:47Z No. of bitstreams: 1 Opção em Debêntures.pdf: 1582205 bytes, checksum: 6007183ecaa2252dd077e1fb1902f4f9 (MD5) / Approved for entry into archive by GILSON ROCHA MIRANDA (gilson.miranda@fgv.br) on 2018-01-26T18:34:06Z (GMT) No. of bitstreams: 1 Opção em Debêntures.pdf: 1582205 bytes, checksum: 6007183ecaa2252dd077e1fb1902f4f9 (MD5) / Made available in DSpace on 2018-01-30T13:02:17Z (GMT). No. of bitstreams: 1 Opção em Debêntures.pdf: 1582205 bytes, checksum: 6007183ecaa2252dd077e1fb1902f4f9 (MD5) Previous issue date: 2017-12-28 / On June 24, 2011, Law 12.431/11 was introduced, which granted a reduction of the Income Tax rate on bonds issued with the purpose of financing infrastructure projects. Since then, the so-called "Infrastructure Bonds" have increased their importance as a funding mechanism to companies in this sector. Since the publication of the Resolution of the Central Bank of Brazil (Bacen) No. 4.476, of 4 November 2016, it was allowed to include early redemption clauses at the discretion of the issuing company. Considering the peculiarities of these bonds, the methodologies already developed for pricing call options on bonds are not applicable. In this way, this work intends to develop a methodology for pricing the existence of an early redemption clause in an Infrastructure Bond covered by Law 12.431/11, considering the term structure of Brazilian interest rates and the costs of issuing bonds. / Em 24.06.2011, foi lançada a Lei n° 12.431/11, que concedeu uma redução da alíquota de Imposto de Renda (IR) em debêntures emitidas com o objetivo de financiar projetos de infraestrutura. Desde então, as chamadas “Debêntures de Infraestrutura” têm aumentado a sua importância como mecanismo de captação das empresas desse setor. A partir da publicação da Resolução do Banco Central do Brasil (Bacen) nº 4.476, de 11.04.2016, foi permitida a inclusão de cláusulas de regaste antecipado a exclusivo critério da empresa emissora. Tendo em vista as peculiaridades desses títulos, as metodologias já desenvolvidas para precificação de opções de recompra em debêntures não são aplicáveis. Desta forma, o trabalho proposto pretende desenvolver uma metodologia para precificar a existência de uma cláusula de resgate antecipado em uma debênture de infraestrutura abrangida pela Lei n° 12.431/11, considerando a estrutura a termo das taxas de juros brasileiras e os custos de emissão de debêntures.