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This paper has two researches direction, one is in the pricing and application of a probation option, the other is in the pricing and application of an American option. In the research of a probation option, this paper used the concept of the marketing strategy to be the source of financial innovation, and therefore decision a new exotic option. We call this option is a probation option. We introduce the application of this option, and further more to device the value of this option. Beside, this option also can apply to the field of marketing, and to calculate the cost of marketing strategy. In the research of an American, this paper proposes a new method- the implied belief model, to obtain a closed-form solution of the value of the American option. We analyze the value of the American option through the view point of the sellers of the options. By adopting this method, we derive the upper bound for the value of an American option. Then we define the belief value of seller to obtain a closed-form solution of the value of an American option. Finally, we apply the method to S&P 100 American option and deduce the implied belief value.

In this thesis I discuss the method of time-change and its applications in quantitative finance. I mainly consider the time change by writing a continuous diffusion process as a Brownian motion subordinated by a subordinator process. I divide the time change method into two cases: deterministic time change and stochastic time change. The difference lies in whether the subordinator process is a deterministic function of time or a stochastic process of time. Time-changed Brownian motion with deterministic time change provides a new viewpoint to deal with option pricing under stochastic interest rates and I utilize this idea in pricing various exotic options under stochastic interest rates. Time-changed Brownian motion with stochastic time change is more complicated and I give the equivalence in law relation governing the ``original time" and the ``new stochastic time" under different clocks. This is readily applicable in pricing a new product called ``timer option". It can also be used in pricing barrier options under the Heston stochastic volatility model. Conclusion and further research directions in exploring the ideas of time change method in other areas of quantitative finance are in the last chapter.

In this thesis I discuss the method of time-change and its applications in quantitative finance. I mainly consider the time change by writing a continuous diffusion process as a Brownian motion subordinated by a subordinator process. I divide the time change method into two cases: deterministic time change and stochastic time change. The difference lies in whether the subordinator process is a deterministic function of time or a stochastic process of time. Time-changed Brownian motion with deterministic time change provides a new viewpoint to deal with option pricing under stochastic interest rates and I utilize this idea in pricing various exotic options under stochastic interest rates. Time-changed Brownian motion with stochastic time change is more complicated and I give the equivalence in law relation governing the ``original time" and the ``new stochastic time" under different clocks. This is readily applicable in pricing a new product called ``timer option". It can also be used in pricing barrier options under the Heston stochastic volatility model. Conclusion and further research directions in exploring the ideas of time change method in other areas of quantitative finance are in the last chapter.

Submitted by William Lopes Nascimento (william.math@gmail.com) on 2015-01-27T11:43:05Z No. of bitstreams: 1 Hedge em Carteiras de Opções Exóticas no Brasil.pdf: 1014311 bytes, checksum: 362a78f0f2246da796f4cacd181453e3 (MD5) / Rejected by JOANA MARTORINI (joana.martorini@fgv.br), reason: Willian, boa tarde. Por gentileza ligar no telefone 3799-7892 Joana on 2015-01-27T15:09:12Z (GMT) / Submitted by William Lopes Nascimento (william.math@gmail.com) on 2015-01-27T15:29:24Z No. of bitstreams: 1 Hedge em Carteiras de Opções Exóticas no Brasil.pdf: 1012800 bytes, checksum: 487bfc3073181afbade0c9113a05f638 (MD5) / Approved for entry into archive by JOANA MARTORINI (joana.martorini@fgv.br) on 2015-01-27T15:56:37Z (GMT) No. of bitstreams: 1 Hedge em Carteiras de Opções Exóticas no Brasil.pdf: 1012800 bytes, checksum: 487bfc3073181afbade0c9113a05f638 (MD5) / Made available in DSpace on 2015-01-27T16:58:19Z (GMT). No. of bitstreams: 1 Hedge em Carteiras de Opções Exóticas no Brasil.pdf: 1012800 bytes, checksum: 487bfc3073181afbade0c9113a05f638 (MD5) Previous issue date: 2015-01-16 / The goal of this work is to assess the empirical performance of some hedging strategies in the Brazilian derivative market. In particular, we entertain a portfolio of exotic options with knock-in and knock-out barriers. Apart from the traditional static and dynamic hedging, we also employ a hybrid strategy that combines both static and dynamic features. The empirical results show that all strategies perform statistically well, though the hybrid hedging is more efficient for it combines the accuracy of the dynamic hedging with the reduced transaction costs of the static hedging. / O objetivo do trabalho é efetuar uma análise empírica de estratégias de hedge no mercado brasileiro de derivativos. Em particular, consideramos uma carteira de opções exóticas com barreira do tipo knock-in e knock-out. Além das tradicionais estratégias de hedge estático e dinâmico, propomos também uma abordagem alternativa definida por uma estratégia híbrida de hedge. Os resultados apontam que todas as estratégias são eficazes do ponto de vista estatístico, porém a abordagem híbrida é a mais eficiente, combinando a precisão da dinâmica com os menores custos da estática.

Public-private partnerships (PPPs) have become a significant global phenomenon and governments are utilizing them more frequently to deliver projects that satisfy increasing societal demands in infrastructure sectors such as highways. Compared to traditional project delivery approaches, PPPs are long-term contracts between the public and the private sectors, where the private sector is engaged in more project tasks and accepts more risks. However, due to their long-term and complex nature, PPP contracts face many issues. Consequently, each project's contract becomes vital to project success because it: allocates risks, governs project relationships, and can align parties' interests. This dissertation examined 21 project contracts in the US highway PPP market to investigate risk allocation; contract designs and risk sharing mechanisms; and revenue risk guarantees. Using a content analysis framework, the allocation of 31 risks associated with highway PPPs was determined. These risks were mostly transferred to the private sector or shared between public and private parties, and project context had a significant influence on risk allocation. Assessment of contract designs indicated that the public sector imposes extensive monitoring and retains a majority of the decision rights to preclude opportunistic actions by the private sector; further, risk sharing mechanisms were complex and largely dependent on resolution during project implementation, which likely increases ex post transaction costs. Finally, revenue guarantees, commonly structured as standard options to mitigate revenue risk, were redesigned to incorporate exotic option features; quantitative analysis revealed that exotic structures can better serve chief PPP stakeholders' interests through increased robustness and flexibility. / Ph. D.

由於現今市場上的新金融商品種類仍不能滿足各種避險者的需要，鑒於台灣目前仍沒有數位選擇權(digital option)的相關產品，且數位選擇權能為避險者減低避險成本的特性是值得被重視的，因此本論文對於另一個新奇選擇權：C-Brick進行較詳細的討論與實證分析。C-Brick是數位選擇權的一種，C-Brick有兩個標的資產，是一個多元數位選擇權，它能提供給擁有兩檔標的股票的投資者較低成本的避險管道。 本文將對C-Brick的價格行為、特質做進一步的研究，討論股價、波動度、相關係數等與C-Brick價格的關係。另外對delta做更詳細的分析。 在實證分析方面，利用建構避險部位的方式對C-Brick進行避險績效的分析，以聯電與台積電、南亞與台塑、合發與台積電為例子進行分析。為了探討避險績效之優劣本文將股價走勢分為上升、盤整、下降等三類探討股價變動對於避險績效的影響。同時也探討波動度對避險績效之關係。 最後，我們將C-Brick做較不同的變化：同時發行數個不同到期日、不同履約價的C-Brick，這樣除了讓這項商品更具吸引力外，我們也對此發行方法在避險考量上，做了可行與否的討論。

<p>In the Black-Scholes model, the volatility considered being deterministic and it causes some</p><p>inefficiencies and trends in pricing options. It has been proposed by many authors that the</p><p>volatility should be modelled by a stochastic process. Heston Model is one solution to this</p><p>problem. To simulate the Heston Model we should be able to overcome the correlation</p><p>between asset price and the stochastic volatility. This paper considers a solution to this issue.</p><p>A review of the Heston Model presented in this paper and after modelling some investigations</p><p>are done on the applet.</p><p>Also the application of this model on some type of options has programmed by MATLAB</p><p>Graphical User Interface (GUI).</p>

In the Black-Scholes model, the volatility considered being deterministic and it causes some inefficiencies and trends in pricing options. It has been proposed by many authors that the volatility should be modelled by a stochastic process. Heston Model is one solution to this problem. To simulate the Heston Model we should be able to overcome the correlation between asset price and the stochastic volatility. This paper considers a solution to this issue. A review of the Heston Model presented in this paper and after modelling some investigations are done on the applet. Also the application of this model on some type of options has programmed by MATLAB Graphical User Interface (GUI).

Basic motive for the work comes out of the hypothesis of growing need of non-financial Czech companies to manage foreign exchange risk, which is demonstrated by foreign trade development. In the work, there are also specified basic species of entrepreneurial risks. Main attention of the writing is paid to currency hedging by finance derivatives, like futures, forwards, swaps and options. Single chapters are dedicated to their basic characteristics and to their function logic and, above all, to alternatives of their usage for currency hedging in different situations at Czech nonfinancial companies.