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In the first part of this article, we discuss the time and the probability for the barrier option to become effective, and then employ the risk neutral assumption to derive the pricing formula of the barrier option. Our pricing formula is a closed form solution, and we may calculate the price of the barrier option without considering the Binomial tree of the underlying asset. We also calculate the traditional option price by our pricing formula, and compare the result to the value that is calculated by Binomial pricing formula. Both of them give the same value about the tradition option, and thus we may regard the tradition option as the special case of the barrier option. In the second part of this article, we employ the pricing formula of the barrier to derive the value of the National Finance Stabilization Fund, and then analyze the impact of the NFSF to the market. Our results reveal that when the benchmark market is not shifted by the bad news, then the NFSF may advance and stabilize the stock price index. In fact, many new style derivatives have the characteristics like barrier option, for example, a convertible bond with forced convert clause, which is a up-and-out call. Other course like bankruptcy costs, agency problems, and contingent liabilities etc, which can all be solved by the pricing formula in our discussion. We hope that results and the process in this article are helpful in solving above questions.

Barrier options are the most popular and traded derivatives in the financial market because of their lower prices. Many studies have been conducted to develop the methods of pricing barrier options. Barrier option prices can be calculated using the classical binomial tree method, but it is time-consuming when we have a large number of time periods. Muroi and Yamada have developed a new fast algorithm to obtain the prices of barrier options by using the spectral expansion approach. We implement and check this algorithm by doing more extensive numerical experimental studies and showing that the same prices calculated using the binomial tree method can also be obtained using the spectral binomial tree approach with a higher computational speed.

The diploma thesis is focused on robotic proces automation of sending financial contracts for barrier option product. Thesis also deals with proces mapping and process improvement thanks to implementation of SWIFT systém and automatic data routing to all systems.

This dissertation studies the pricing of Outside barrier call options, when their activation starts at a hitting time. The pricing of Outside barrier options when their activation starts at time zero, and the pricing of standard barrier options when their activation starts at a hitting time of a pre speci ed barrier level, have been studied previously (see [21], [24]). The new work that this dissertation will do is to price Outside barrier call options, where they will be activated when the triggering asset crosses or hits a pre speci ed barrier level, and also the pricing of Outside barrier call options where they will be activated when the triggering asset crosses or hits a sequence of two pre specifed barrier levels. Closed form solutions are derived using Girsanov's theorem and the re ection principle. Existing results are derived from the new results, and properties of the new results are illustrated numerically and discussed. / Mathematical Sciences / M. Sc. (Applied Mathematics)

This dissertation studies the pricing of Outside barrier call options, when their activation starts at a hitting time. The pricing of Outside barrier options when their activation starts at time zero, and the pricing of standard barrier options when their activation starts at a hitting time of a pre speci ed barrier level, have been studied previously (see [21], [24]). The new work that this dissertation will do is to price Outside barrier call options, where they will be activated when the triggering asset crosses or hits a pre speci ed barrier level, and also the pricing of Outside barrier call options where they will be activated when the triggering asset crosses or hits a sequence of two pre specifed barrier levels. Closed form solutions are derived using Girsanov's theorem and the re ection principle. Existing results are derived from the new results, and properties of the new results are illustrated numerically and discussed. / Mathematical Sciences / M. Sc. (Applied Mathematics)

本文研究最近在市面上常見的結構型債券，利用Martingale評價方法以及數值方法求出結構型商品的理論價格以及利用情境分析來推估期末可能的報酬，提供投資人與券商對於結構型商品特性與風險的了解，並且提供發行商避險的參考。然而結構型商品的複雜程度往往是來自於隱含的新奇選擇權，本文亦分析商品內含的新奇選擇權，使得投資人更了解結構型商品的組成，發行商也可藉以由組成的概念進而設計新的結構型商品。

本文主要評價與分析兩種結構型債券：一為目標贖回雪球型利率連動債、一為雙匯率連動債。 第一個商品利率連動債券為十年期、每季付息債券，其指標利率為三個月期LIBOR利率。本文以BGM市場模型進行評價，同時考慮40個遠期三個月期LIBOR利率的動態過程，而每個動態過程之間的相關係數為一40維度的方陣，為了加速計算速度採用Weigel(2004)運用線性代數降秩的方法，使原本相關係數矩陣由「秩40」降為「秩11」後，不僅可以加快運算速度又不會使原本相關係數矩陣失真。以蒙地卡羅模擬利率路徑評價後並進行敏感性分析。 第二個商品雙匯率連動債券連結到兩個匯率指標：歐元兌日圓及美元兌新台幣。其中連結歐元兌日圓匯率的報酬型態為雙界限出局二元選擇權，而連結美元兌新台幣匯率的報酬型態為下出界選擇權。本文利用Ritchken(1995)三元樹分別建構兩個匯率界限選擇權的評價，並發現歐元兌日圓匯率界限選擇權的價值佔債券面額的比例極小，故之後只針對美元兌新台幣匯率界限選擇權進行敏感性分析。

[pt] Com o objetivo de reduzir o efeito estufa e atender a alta demanda de energia elétrica, muitos países desenvolvidos e emergentes têm optado pelo uso de energias essencialmente de origem renovável, incluindo energia eólica, biomassa e solar fotovoltaica. Para determinar a viabilidade econômica dos projetos de energias renováveis é necessário capturar as variáveis de maior interesse. As opções reais ao considerar a dinâmica e incertezas, típicas dos mercados de eletricidade, surgem como uma alternativa para a tomada de decisões neste tipo de projetos. Este trabalho aplica a técnica tradicional de avaliação de projetos através do fluxo de caixa descontado (FCD) e a teoria de opções reais (TOR) para avaliação de um parque eólico. A flexibilidade foi incluída ao considerar a opção de fazer um investimento em retrofit para atualizar a tecnologia das turbinas eólicas e estender o contrato de operação. A opção real analisada é análoga a uma opção de compra europeia, seu valor é calculado através de uma árvore binomial recombinante com barreira no preço da energia eólica, principal fonte de incerteza do modelo. Realizaram-se análises de sensibilidade para avaliar o comportamento do preço da opção frente às mudanças em alguns parâmetros do modelo. Conclui-se a viabilidade econômica de estender a operação do parque eólico através de um investimento em retrofit, utilizando a TOR, uma vez que o seu valor é muito superior frente ao calculado pelo FCD, apesar do valor da opção ter uma forte correlação com o limite da barreira e a volatilidade do preço. / [en] In order to reduce the greenhouse effect and meet the high demand of electricity, many developed and emerging countries have opted for the use of renewable energies, for example, wind energy, biomass and solar photovoltaic. To determine the economic viability of renewable energy projects it is necessary to capture the most relevant variables that suggest greater interest. Real options allows to consider the dynamic and uncertainties present in the power markets, therefore it is an attractive tool for decision-making in this kind of markets. In this work we apply the traditional technique of project evaluation, the discounted cash flow (DCF), as well as the real real options theory (ROT) for the financial evaluation of a wind farm. The flexibility is the option of making a retrofit investment that allows upgrading the wind turbines technology in order to extend the operating contract. The real option analyzed is analogous to a european call option and its value was calculated through a recombinant binomial tree with barrier in the wind energy price, considered the main source of uncertainty in the model. Sensitivity analyzes were performed to assess the option price behavior when some parameters of the model change. We finally conclude for the economic viability of extending the operation of the wind farm through an investment in retrofit, using the ROT, since its value is much higher than the calculated by the DCF, even though the option value is strongly dependent on the barrier and the volatility of electricity prices.

傳統上，對於選擇權的評價模型，大抵可分為封閉解與數值分析兩大類。封閉解計算的速度快，但卻十分缺乏彈性，譬如無法求得美式解，相反的數值分析相當具有彈性，評價時卻比較耗時，譬如障礙選擇權。本文針對上面的問題，提出一個以數值分析中的樹狀模型為基礎，輔以封閉解來維持應有的彈性，並提高計算的速度，我們將此方法稱之為分解結合法。 由於樹狀模型用來評價重設型選擇權必須考慮消除重設界限所導致的非線性誤差，在本文中，主要是以Boyle and Lau(1994)的二元樹模型及Ritchken(1995)的三元樹模型作為主要的架構，搭配分解結合法來針對重設型選擇權進行研究。就本文分析的結果顯示，利用分解結合法不但能夠提高計算的速度，同時對於某些條件下的選擇權，還能夠減少其評價的波動度，效果相當的顯著。 本文主要針對單點單價式與整段時間單價式的重設型選擇權，推導適用分解結合法的方法。以此兩種基本的重設型選擇權為基礎，我們將相同的概念推廣至其他更複雜的重設型選擇權上。此外在選取結合的方式上，我們也可以充分利用已經推導出的重設型選擇權封閉解，應用在更複雜的重設條件上，無形中，增加了封閉解的應用彈性，也減少了樹狀模型的評價時間，所以具有一舉兩得的效果。此外，本文也針對分解結合法的評價速度，作一完整的比較。並在最後，本文也針對分解結合法下避險比率的計算以及重設型選擇權避險所特有的現象：Delta Jump、Negative Delta，這兩種情形發生的原因及可能的影響與因應之道進行分析。