Submitted by Jorge Silva (jorgelmsilva@ufrrj.br) on 2018-05-17T18:14:26Z No. of bitstreams: 1 2013 - Marcus Vinicius Silva de Oliveira.pdf: 4662898 bytes, checksum: aa288711b207b66ed5c2b8d76c26db6f (MD5) / Made available in DSpace on 2018-05-17T18:14:26Z (GMT). No. of bitstreams: 1 2013 - Marcus Vinicius Silva de Oliveira.pdf: 4662898 bytes, checksum: aa288711b207b66ed5c2b8d76c26db6f (MD5) Previous issue date: 2013-09-30 / CAPES / This paper seeks to highlight the importance of teaching financial mathematics, capitalization and amortization in high school. For this we admitted him to educators who advocate the idea of using mathematics as a provider of citizenship and legal aspects that discourse on Financial Mathematics and its importance for the development of citizenship. We also conduct a survey of mathematics teachers of Basic Education, a qualitative, in order to investigate how and to which topic is the teaching that content. Finally, we propose a class on capitalization and amortization, with the use of technological resources for high school. / Esse trabalho procura destacar a import?ncia do ensino de Matem?tica Financeira, capitaliza??o e amortiza??o no Ensino M?dio. Para isso nos amparamos em educadores que defendem a id?ia do uso da matem?tica como provedora da cidadania e em aspectos legais que discorrem sobre a Matem?tica Financeira e sua import?ncia para o desenvolvimento da cidadania. Realizamos tamb?m uma pesquisa junto a professores de matem?tica da Educa??o B?sica, de cunho qualitativo, a fim de investigar como e at? qual t?pico ocorre o ensino desse conte?do. Por fim, propomos uma aula sobre Capitaliza??o e Amortiza??o, com uso de recursos tecnol?gicos, para o Ensino M?dio.

<p>An article of Zariphopoulou and Musiela "An example of indifference prices under exponential preferences", was background of our work.</p>

<p>In this work we consider the methods of pricing and hedging an option on the forward commodity market described by the multi-factor diffusion model. In the previous research there were presented explicit valuation formulas for standard European type options and simulation schemes for other types of options. However, hedging strategies were not developed in the available literature. Extending known results this work gives analytical formulas for the price of American, Asian and general European options. Moreover, for all these options hedging strategies are presented. Using these results the dynamics of the portfolio composed of options on futures with different maturities is studied on a commodity market.</p>

In this work we consider the methods of pricing and hedging an option on the forward commodity market described by the multi-factor diffusion model. In the previous research there were presented explicit valuation formulas for standard European type options and simulation schemes for other types of options. However, hedging strategies were not developed in the available literature. Extending known results this work gives analytical formulas for the price of American, Asian and general European options. Moreover, for all these options hedging strategies are presented. Using these results the dynamics of the portfolio composed of options on futures with different maturities is studied on a commodity market.

In this thesis we focus mainly on special finite differences and finite volume methods and apply them to the pricing of barrier options.The structure of this work is the following: in Chapter 1 we introduce the definitions of options and illustrate some properties of vanilla European options and exotic options.Chapter 2 describes a classical model used in the financial world, the  Black-Scholes model. We derive theBlack-Scholes formula and show how stochastic differential equations model financial instruments prices.The aim of this chapter is also to present the initial boundary value problem and the maximum principle.We discuss boundary conditions such as: the first boundary value problem, also called  Dirichlet problem that occur in pricing ofbarrier options and European options. Some kinds of put options lead to the study of a second boundary value problem (Neumann, Robin problem),while the Cauchy problem is associated with one-factor European and American options.Chapter 3 is about finite differences methods such as theta, explicit, implicit and Crank-Nicolson method, which are used forsolving partial differential equations.The exponentially fitted scheme is presented in Chapter 4. It is one of the new classesof a robust difference scheme that is stable, has good convergence and does not produce spurious oscillations.The stability is also advantage of the box method that is presented in Chapter 5.In the beginning of the Chapter 6 we illustrate barrier options and then we consider a novel finite volume discretization for apricing the above options.Chapter 7 describes discretization of the Black-Scholes equation by the fitted finite volume scheme. In  Chapter 8 we present and describe numerical results obtained by using  the finite difference methods illustrated in the previous chapters.

Since the liberalisation of the energy market in Europe in the early 1990s, much opportunity to trade electricity as a commodity has arisen. One significant consequence of this movement is that market prices have become more volatile instead of its tradition constant rate of supply. Spot price markets have also been introduced, affecting the demand of electricity as companies now have the option to not only produce their own supply but also purchase this commodity from the market. Following the liberalisation of the energy market, hence creating a greater demand for trading of electricity and other types of energy, various types of options related to the sales, storage and transmission of electricity have consequently been introduced. Particularly, swing options are popular in the electricity market. As we know, swing-type derivatives are given in various forms and are mainly traded as over-the-counter (OTC) contracts at energy exchanges. These options offer flexibility with respect to timing and quantity. Traditionally, the Geometric Brownian Motion (GBM) model is a very popular and standard approach for modelling the risk neutral price dynamics of underlyings. However, a limitation of this model is that it has very few degrees of freedom, as it does not capture the complex behaviour of electricity prices. In short the GBM model is inefficient in the pricing of options involving electricity. Other models have subsequently been used to bridge this inadequacy, e.g. spot price models, futures price models, etc. To model risk-neutral commodity prices, there are basically two different methodologies, namely spot and futures or so-called term structure models. As swing options are usually written on spot prices, by which we mean the current price at which a particular commodity can be bought or sold at a specified time and place, it is important for us to examine these models in order to more accurately inculcate their effect on the pricing of swing options. Monte Carlo simulation is also a widely used approach for the pricing of swing options in the electricity market. Theoretically, Monte Carlo valuation relies on risk neutral valuation and the technique used is to simulate as many (random) price paths of the underlying(s) as possible, and then to average the calculated payoff for each path, discounted to today's prices, giving the value of the desired derivative. Monte Carlo methods are particularly useful in the valuation of derivatives with multiple sources of uncertainty or complicated features, like our electricity swing options in question. However, they are generally too slow to be considered a competitive form of valuation, if any analytical techniques of valuation exist. In other words, the Monte Carlo approach is, in a sense, a method of last resort. In this thesis, we aim to examine a numerical method involved in the pricing of swing options in the electricity market. We will consider an existing and widely accepted electricity price process model, use the finite volume method to formulate a numerical scheme in order to calibrate the prices of swing options and make a comparison with numerical solutions obtained using the theta-scheme. Further contributions of this thesis include a comparison of results and also a brief discussion of other possible methods.

In this thesis we investigate the case of monitoring of stocks havingjust been introduced for public trading on the nancial market. Theempirical distribution of the change-point for 20 assets for 60 days was calculated to check the support for the assumption that the priceinitially drop or rise to some steady level.The price process X = {Xt : t in Z} is assumed to be an AR(1) process with a shift in the mean value from a slope to a constant. The Shiryaev-Roberts, Shewhart, EWMA, Likelihood ratio and CUSUM proceduresfor detecting a change-point in such a process are derived. The expecteddelay of the motivated alarm according to these methods is achievedunder the assumptions of a Poisson, uniform, binomial and geometric distributed by means of simulations.

An article of Zariphopoulou and Musiela "An example of indifference prices under exponential preferences", was background of our work.

Modelling defaultable contingent claims has attracted a lot of interest in recent years, motivated in particular by the Late-2000s Financial Crisis. In several papers various approaches on the subject have been made. This thesis tries to summarize these results and derive explicit formulas for the prices of financial derivatives with credit risk. It is divided into two main parts. The first one is devoted to the well-known theory of modelling the default risk while the second one presents the results concerning pricing of the defaultable models that we obtained ourselves.

In this paper we examine energy derivatives pricing. The previous studies considered the same source of uncertainty for the spot and the futures prices. We investigate the problem of futures pricing with two independent sources of risk. In general the structure of the oil and gas futures markets is closely related to some stock indices. Therefore, we develop a model for the futures market and compound derivatives with pricing in accordance with the correspondent index. We derive a framework for energy derivatives pricing, compute the price of the European call option on futures and corresponding hedging strategy. We calculate the price of the European call option adjusted for an index level, study the American put option on futures and corresponding hedging strategies.