The market for interest rate derivatives has in recent decades grown considerably and the need for proper valuation models has increased. Interest rate derivatives are instruments that in some way are contingent on interest rates such as bonds and swaps and most financial transactions are in some way exposed to interest rate risk. Interest rate derivatives are commonly used to hedge this risk. This study focuses on the Black Derman & Toy model and its capability of pricing interest rate derivatives. The purpose was to simulate the model numerically using daily Euro-Bunds and options data to identify if the model can generate accurate prices. A second purpose was to simplify the theory of building a short rate binomial tree, since existing theory explains this step in a complex way. The study concludes that the BDT model have difficulties valuing the extrinsic value of options with longer maturities, especially out-of-the money options.

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

The aim of this study is to compare the performance of the four interest rate models (Vasicek Model, Cox Ingersoll Ross Model, Ho Lee Model and Black Der- man Toy Model) that are commonly used in pricing zero coupon bond options. In this study, 1{5 years US Treasury Bond daily data between the dates June 1, 1976 and December 31, 2007 are used. By using the four interest rate models, estimated option prices are compared with the real observed prices for the begin- ing work days of each months of the years 2004 and 2005. The models are then evaluated according to the sum of squared errors. Option prices are found by constructing interest rate trees for the binomial models based on Ho Lee Model and Black Derman Toy Model and by estimating the parameters for the Vasicek and the Cox Ingersoll Ross Models.