[pt] Na tentativa de melhor capturar fatos estilizados do comportamento dos preços de opções financeiras, em especial para tratar a questão do sorriso da volatilidade, modelos de volatilidade estocástica têm sido objeto de estudo em diversos mercados. Neste contexto, o principal objetivo deste trabalho é avaliar os modelos de volatilidade estocástica de Heston (1993), Bates (1996) e Double Heston (2009) junto ao método de Lewis (2000) para precificar opções de ações no mercado brasileiro de derivativos, caracterizados por serem de curto prazo. Para isto foram precificadas opções de compra da Petrobrás e Vale. Os modelos foram comparados de acordo com a qualidade do ajuste aos dados in-sample e a capacidade preditiva com dados out-of-sample. Ademais, buscou-se verificar a volatilidade implícita gerada por cada um dos modelos. Ao fim, identificou-se que considerar a volatilidade como estocástica, mesmo quando é descrita por apenas um processo estocástico, é a decisão mais importante a ser tomada a fim de melhorar o apreçamento das opções. Além disso, adicionar saltos a um modelo de volatilidade estocástica parece ser mais relevante do que adicionar um segundo processo estocástico para modelar a volatilidade na precificação de opções de curto prazo. / [en] In an attempt to better capture stylized facts about financial option prices behavior, especially to address the issue of volatility smile, stochastic volatility models have been the object of study in several markets. In this context, the main purpose of this work is to assess the stochastic volatility models of Heston (1993), Bates (1996) and Double Heston (2009) along with the Lewis method (2000) for stock option pricing in Brazilian derivative market, featured by being short-term. Therefore, Petrobrás and Vale s call options were priced. The models were compared according to the in-sample fit skill and the out-of-sample forecasting power. Furthermore, it was verified the implied volatility begot by each model. In the end, it was figured out that consider the volatility as stochastic even when it is described by only one stochastic process is the preeminent matter to do in order to improve option pricing. Plus, adding jumps in a stochastic volatility model seems to be more important than adding a second stochastic process to model the volatility in short-term option pricing.

<p>Condfidence in the future is a signicant factor for business development. However frequently, accurate and specific purposes are spread over the market environment influence.Thus,it is necessary to make an appropriate consideration of instability, which is peculiar to the dynamic development. Volatility, variance and standard deviation are used to</p><p>characterize the deviation of the investigated quantity from mean value.</p><p>Volatility is one of the main instruments to measure the risk of the asset.</p><p>The increasing availability of financial market data has enlarged volatility research potential but has also encouraged research into longer horizon volatility forecasts.</p><p>In this paper we investigate stock index volatility with respect to capitalization with help of GARCH-modelling.</p><p>There are chosen three indexes of OMX Nordic Exchange for our research. The Nordic list segment indexes comprising Nordic Large Cap,</p><p>Mid Cap and Small Cap are based on the three market capitalization groups.</p><p>We implement GARCH-modeling for considering indexes and compare our results in order to conclude which ones of the indexes is more volatile.</p><p>The OMX Nordic list indexis quiet new(2002)and reorganized as late as October 2006. The current value is now about 300 and no options do exist. In current work we are also interested in estimation of the Heston</p><p>model(SVmodel), which is popular in financial world and can be used in option pricing in the future.</p><p>The results of our investigations show that Large Cap Index is more volatile then Middle and Small Cap Indexes.</p>

<p>In this paper we investigate pricing of variance swaps contracts. The</p><p>literature is mostly dedicated to the pricing using replication with</p><p>portfolio of vanilla options. In some papers the valuation with stochastic</p><p>volatility models is discussed as well. Stochastic volatility is becoming</p><p>more and more interesting to the investors. Therefore we decided to</p><p>perform valuation with the Heston stochastic volatility model, as well</p><p>as by using replication strategy.</p><p>The thesis was done at SunGard Front Arena, so for testing the replica-</p><p>tion strategy Front Arena software was used. For calibration and testing</p><p>of the Heston model we used MatLab.</p>

Condfidence in the future is a signicant factor for business development. However frequently, accurate and specific purposes are spread over the market environment influence.Thus,it is necessary to make an appropriate consideration of instability, which is peculiar to the dynamic development. Volatility, variance and standard deviation are used to characterize the deviation of the investigated quantity from mean value. Volatility is one of the main instruments to measure the risk of the asset. The increasing availability of financial market data has enlarged volatility research potential but has also encouraged research into longer horizon volatility forecasts. In this paper we investigate stock index volatility with respect to capitalization with help of GARCH-modelling. There are chosen three indexes of OMX Nordic Exchange for our research. The Nordic list segment indexes comprising Nordic Large Cap, Mid Cap and Small Cap are based on the three market capitalization groups. We implement GARCH-modeling for considering indexes and compare our results in order to conclude which ones of the indexes is more volatile. The OMX Nordic list indexis quiet new(2002)and reorganized as late as October 2006. The current value is now about 300 and no options do exist. In current work we are also interested in estimation of the Heston model(SVmodel), which is popular in financial world and can be used in option pricing in the future. The results of our investigations show that Large Cap Index is more volatile then Middle and Small Cap Indexes.

In this paper we investigate pricing of variance swaps contracts. The literature is mostly dedicated to the pricing using replication with portfolio of vanilla options. In some papers the valuation with stochastic volatility models is discussed as well. Stochastic volatility is becoming more and more interesting to the investors. Therefore we decided to perform valuation with the Heston stochastic volatility model, as well as by using replication strategy. The thesis was done at SunGard Front Arena, so for testing the replica- tion strategy Front Arena software was used. For calibration and testing of the Heston model we used MatLab.

Thesis (Ph. D.)--University of Missouri-Columbia, 2003. / Typescript. Vita. Includes bibliographical references (leaves 390-404). Also available on the Internet.

Thesis (Ph. D.)--University of Missouri-Columbia, 2003. / Typescript. Vita. Includes bibliographical references (leaves 390-404). Also available on the Internet.

<p>The main idea of our work is the calibration parameters for the Heston stochastic volatility model. We make this procedure by using the OMXS30 index from the NASDAQ OMX Nordic Exchange Market. We separate our data into the stable period and high-volatility period on this Nordic Market. Deviation detection problem are solved using the Bayesian analysis of change-points. We estimate parameters of the Heston model for each of periods and make some conclusions.</p>

The main idea of our work is the calibration parameters for the Heston stochastic volatility model. We make this procedure by using the OMXS30 index from the NASDAQ OMX Nordic Exchange Market. We separate our data into the stable period and high-volatility period on this Nordic Market. Deviation detection problem are solved using the Bayesian analysis of change-points. We estimate parameters of the Heston model for each of periods and make some conclusions.

Thesis (doctoral)--Erasmus Universiteit Rotterdam, 2008.