A European option is a contract in which the seller of the option grants the buyer the right, but not the obligation, to purchase from or sell to the seller the underlying asset at pre-specified price at maturity date. Herewith the buyer should pay out a premium for the value of flexibility that he was granted. Such premium as the compensation to the seller was provides in close form by Black and Scholes (1973) and Merton (1973). Even since then the option pricing methodology, or otherwise known as ¡§contingent claim analysis¡¨ has found its application in many prospects. Otherwise known as the real option analysis first induced by Myers (1977) and the structure form model of the credit risk analysis first induced by Merton (1974). In the thesis, we consider the application of the optional pricing methodology to the rationality and valuation of penalty in a contract and extent the penalty to the money back guarantee. In the former, we provide the general form solution to illustrate the both parties all hold the right to default the contract, and prove the existence of the optimal penalty is a policy to protect the disadvantaged minority such as to make the trade contract to be fair. In the latter, we prove the suitable way to evaluate that the consumer buy a good and long a MBG is the call option but the put by reviewing the final cash flow of the replicated strategy and the put-call parity at firstly, and then we find out the better way to grant the consumer to return the good to the vendor is penalty if the good is normal and the utility function of the consumer is concave. In sum, we integrate the penalty and in the MBG with the contingent claim analysis in this thesis, we find out we can use the uncomplicated model to explain the real world. Herewith we consider the option pricing model as another methodology to illustrate the social environment.

Neste trabalho, apresentamos uma Teoria de Mercados Financeiros com custos de penalidade. Os custos de penalidade sao atribuídos a posicoes vendidas a descoberto. Estes custos diferem dos custos de transacao, pois nao dependem de mudancas nas estrategias de negociacao. No caso da venda de acoes a descoberto, o agente aluga a ação e depois realiza a venda; nesse caso, o custo de penalidade representa o custo do aluguel. Para o caso do título livre de risco, o custo de penalidade representa o diferencial ou spread no custo para o agente tomador de recursos (credito). O trabalho e desenvolvido em um espaco de estados discreto e finito; a matematica envolvida e a mesma dos textos tradicionais de finanças e envolve conceitos de algebra linear, programacao linear e calculo estocastico discreto. A utilizacao dessa estrutura vem ao encontro dos objetivos deste trabalho que consistem em introduzir uma nova teoria sem perder a intuicao financeira ou a capacidade de implementação computacional, ou seja a aplicacao pratica dos conceitos desenvolvidos. Iniciamos o estudo para o caso Uni-Período e em seguida estendemos os resultados para o caso Multi-Período. Em particular, apresentamos as condicoes necessarias e suficientes para a nao existencia de arbitragem; vale notar que essas condicoes se tornam as mesmas do modelo tradicional quando os custos sao nulos. Mostramos ainda que a condicao necessaria e suficiente para que o modelo seja completo e a mesma no modelo com penalidade e tradicional. A introducao do custo de penalidade implica na existencia de uma diferenca no valor da estrategia replicante do título contingente -X e X; os precos iniciais destas estrategias serao denominados preco de compra e preco de venda, respectivamente. Por fim, mostramos que sob certas condicoes podemos construir um algoritmo para calcular uma estrategia maxima que replica um título contingente de forma consistente, ou seja, podemos calcular os precos de venda e compra de um título contingente sem que exista arbitragem. / In this work we present a financial theory with penalty costs on short selling positions. Penalty costs differ from transaction costs for they do not depend on changes on trading positions (strategies). In the case of short selling in stocks, the investor borrows and then sells the position; in this case, the penalty costs are associated with the borrowing rate. For the risk free asset the penalty costs are associated with the spread between the credit and deposit rates. The work is developed in a discrete and finite framework; the mathematics involved is the same found in traditional financial literature; roughly, it runs through concepts of linear algebra, linear programming and discrete stochastic calculus. This framework is aligned with the objectives of this work which consist of developing a new theory without losing its financial intuition or the computational feasibility to implement solutions; in other words, the ability to apply the theory in practical applications. We begin by studding the Single-Period case and then extend the results to the Multi-Period case. In particular we present the necessary and sufficient conditions for the non existence of arbitrage, these conditions become the same as in the traditional model if the penalty costs are zero. Also, we show that the necessary and sufficient conditions for the model to be complete are the same in both cases. The introduction of penalty costs induces a difference in the costs of replicating the contingent claims -X and X; the replicating prices will be denominated bid and ask prices, respectively. To finish, we show that under certain conditions we can build an algorithm to calculate the maximal replicating strategy in a consistent manner, that is, we can calculate the bid and ask prices free of arbitrage.

Neste trabalho, apresentamos uma Teoria de Mercados Financeiros com custos de penalidade. Os custos de penalidade sao atribuídos a posicoes vendidas a descoberto. Estes custos diferem dos custos de transacao, pois nao dependem de mudancas nas estrategias de negociacao. No caso da venda de acoes a descoberto, o agente aluga a ação e depois realiza a venda; nesse caso, o custo de penalidade representa o custo do aluguel. Para o caso do título livre de risco, o custo de penalidade representa o diferencial ou spread no custo para o agente tomador de recursos (credito). O trabalho e desenvolvido em um espaco de estados discreto e finito; a matematica envolvida e a mesma dos textos tradicionais de finanças e envolve conceitos de algebra linear, programacao linear e calculo estocastico discreto. A utilizacao dessa estrutura vem ao encontro dos objetivos deste trabalho que consistem em introduzir uma nova teoria sem perder a intuicao financeira ou a capacidade de implementação computacional, ou seja a aplicacao pratica dos conceitos desenvolvidos. Iniciamos o estudo para o caso Uni-Período e em seguida estendemos os resultados para o caso Multi-Período. Em particular, apresentamos as condicoes necessarias e suficientes para a nao existencia de arbitragem; vale notar que essas condicoes se tornam as mesmas do modelo tradicional quando os custos sao nulos. Mostramos ainda que a condicao necessaria e suficiente para que o modelo seja completo e a mesma no modelo com penalidade e tradicional. A introducao do custo de penalidade implica na existencia de uma diferenca no valor da estrategia replicante do título contingente -X e X; os precos iniciais destas estrategias serao denominados preco de compra e preco de venda, respectivamente. Por fim, mostramos que sob certas condicoes podemos construir um algoritmo para calcular uma estrategia maxima que replica um título contingente de forma consistente, ou seja, podemos calcular os precos de venda e compra de um título contingente sem que exista arbitragem. / In this work we present a financial theory with penalty costs on short selling positions. Penalty costs differ from transaction costs for they do not depend on changes on trading positions (strategies). In the case of short selling in stocks, the investor borrows and then sells the position; in this case, the penalty costs are associated with the borrowing rate. For the risk free asset the penalty costs are associated with the spread between the credit and deposit rates. The work is developed in a discrete and finite framework; the mathematics involved is the same found in traditional financial literature; roughly, it runs through concepts of linear algebra, linear programming and discrete stochastic calculus. This framework is aligned with the objectives of this work which consist of developing a new theory without losing its financial intuition or the computational feasibility to implement solutions; in other words, the ability to apply the theory in practical applications. We begin by studding the Single-Period case and then extend the results to the Multi-Period case. In particular we present the necessary and sufficient conditions for the non existence of arbitrage, these conditions become the same as in the traditional model if the penalty costs are zero. Also, we show that the necessary and sufficient conditions for the model to be complete are the same in both cases. The introduction of penalty costs induces a difference in the costs of replicating the contingent claims -X and X; the replicating prices will be denominated bid and ask prices, respectively. To finish, we show that under certain conditions we can build an algorithm to calculate the maximal replicating strategy in a consistent manner, that is, we can calculate the bid and ask prices free of arbitrage.

Contingent Claim Pricing with Applications to Financial Risk Management By Hua Chen 2008 Committee Chair: Samuel H. Cox and Shaun Wang Major Academic Unit: Department of Risk Management and Insurance This is a multi-essay dissertation designed to explore the contingent claim pricing theory with non-tradable underlying assets, with emphasis on its applications to insurance and risk management. In the first essay, I apply the real option pricing theory and dynamic programming methods to address problems in the area of operational risk management. Particularly, I develop a two-stage model to help firms determine optimal switching triggers in the event of an influenza epidemic. In the second essay, I examine mortality securitization in an incomplete market framework. I build a jump-diffusion process into the original Lee-Carter model and explore alternative model with transitory versus permanent jump effects. I discuss pricing difficulties of the Swiss Re mortality bond (2003) and use the Wang transform to account for correlations of the mortality index over time. In the third essay, I study the valuation of the non-recourse provision in reverse mortgages. I model the various risks embedded in the HECM program and apply the conditional Esscher transform to price the non-recourse provision. I further examine the premium structure of HECM loans and investigate whether insurance premiums are adequate to cover expected claims.

We quantify the effects on contingent claim valuation of using an estimator for the volatility of a geometric Brownian motion (GBM) process. That is, we show what difficulties can arise when failing to account for estimation risk. Our working problem uses a direct estimator of volatility based on the sample standard deviation of increments from the underlying Brownian motion. After substituting into the GBM the direct volatility estimator for the true, but unknown, value of the parameter sigma, we derive the resulting marginal distribution of the approximated GBM. This allows us to derive post-estimation distributions and valuation formulae for an assortment of European contingent claims that are in accord with the basic properties of the underlying risk-neutral process. Next we extend our work to the contingent claim sensitivities associated with an assortment of European option portfolios that are based on the direct estimator of the volatility of the GBM process. Our approach to the option sensitivities - the Greeks - uses the likelihood function technique. This allows us to obtain computable results for the technically more-complicated formulae associated with our post-estimation process. We discuss an assortment of difficulties that can ensue when failing to account for estimation risk in valuation and hedging formulae.

<p>The present mini-thesis seeks to explore and investigate the mathematical theory and concepts that underpins the valuation of derivative securities, particularly European plainvanilla options. The main argument that we emphasise is that novel models of option pricing, as is suggested by Hull and White (1987) [1] and others, must account for the discrepancy observed on the implied volatility &ldquo / smile&rdquo / curve. To achieve this we also propose that market volatility be modeled as random or stochastic as opposed to certain standard option pricing models such as Black-Scholes, in which volatility is assumed to be constant.</p>

<p>The present mini-thesis seeks to explore and investigate the mathematical theory and concepts that underpins the valuation of derivative securities, particularly European plainvanilla options. The main argument that we emphasise is that novel models of option pricing, as is suggested by Hull and White (1987) [1] and others, must account for the discrepancy observed on the implied volatility &ldquo / smile&rdquo / curve. To achieve this we also propose that market volatility be modeled as random or stochastic as opposed to certain standard option pricing models such as Black-Scholes, in which volatility is assumed to be constant.</p>

Magister Scientiae - MSc / The present mini-thesis seeks to explore and investigate the mathematical theory and concepts that underpins the valuation of derivative securities, particularly European plainvanilla options. The main argument that we emphasise is that novel models of option pricing, as is suggested by Hull and White (1987) [1] and others, must account for the discrepancy observed on the implied volatility curve. To achieve this we also propose that market volatility be modeled as random or stochastic as opposed to certain standard option pricing models such as Black-Scholes, in which volatility is assumed to be constant. / South Africa

鑑於近年來中國大陸經濟高度成長，當地金融市場在其內需市場強勁，以及均富水準普遍提升下，更顯得朝氣蓬勃，本論文係以分析過去外資金融機構在中國大陸相關佈局模式及進行相關實證研究，並續以剖析臺灣銀行業未來佈局中國大陸市場策略，以作為現階段國內高度競爭金融環境下，拓展另片藍海空間之策略與方向。 本論文首先說明外資金融機構於近年來在高度發展中國大陸金融市場所扮演的角色與目標，並應用Cox比例強度存活模型，分析採行參股策略方式進入中國大陸銀行之動機與機率強度，並以主成份分析進行資料萃取及最大概似法估計模型參數。再者，藉由此參股機率估計值進而求得外資金融機構最適參股機率強度門檻，可作為日後金融機構（含臺灣銀行業）參股動機之衡量指標。實證研究顯示，過去外資金融機構採行參股策略之目的主要在於創造被參股對象市場價值，以增加其參股投資報酬。對於獲利能力及資產品質較佳之外資金融機構，以及資產品質較佳之中國大陸銀行，則往往具有較高的參股與被參股潛在動機。 再者，為進一步探討外資金融機構採行參股策略後之風險與報酬關係，本論文係以或有求償權之模式，同時納入參股外資金融機構與被參股中國大陸銀行之個別資產價值，以及匯率波動等三項動態因子，在股東權益價值極大化為目標，及因應風險性資產所導向之資本管制，據以剖析外資金融機構經參股後之資產價值風險及其影響因素，並以靜態分析所對應之最適參股比例變化情形。其數值分析研究發現：當參股外資金融機構資產價值遞增、負債比率降低，以及所面臨法定風險權數增加時，對於其參股後之整體資產組合風險將有所降低。同時，對於具有高資產品質、獲利佳及多元化幣別資產組合之外資金融機構，以及面臨資產品質佳且著重本土金融開發之被參股中國大陸銀行，將有助於提高外資金融機構之最適參股比例。 針對臺灣銀行業參股模式方面，以投資中國大陸股份制商業銀行之動機強度為最高，其中泛公股銀行相對民營銀行更具有條件優勢，並以具備綠色通道優惠之大西部地區為佳。研究亦顯示，在外資金融機構已著墨中國大陸金融市場些許時日下，對於身為追隨性金融機構的臺灣銀行業而言，在當地金融服務未臻飽和、初始投資成本降低，以及台商業務平均需求成長趨勢下，將有助於降低其進入門檻。同時，研究中也採行模型論證，對於現階段臺灣銀行業實務上多以先行成立代表人辦事處後升格分行，並儘速於合規範內取得人民幣業務承做資格方式，以深根當地金融市場之經營方向，同時研究亦指出臺灣銀行業應具備創新化業務與利基性策略，方能提高採行成立獨資子銀行或參股之進入動機。 / In recent years China has experienced rapid economic growth that enables the advancement of the local financial industry, which benefited from the strong domestic consumption as well as improvement in average income per capita. The purpose of this paper is to point out an alternative direction for Taiwanese banks by mapping out the future China market expansion strategy, as the Taiwanese banks are facing prolong highly competitive domestic market. This paper applies Cox’s proportional-hazard survival model to analyze the strategic decisions of foreign financial institutions about acquiring equity stakes in Chinese banks. Based on principal component analysis, we extract significant independent variables from Cox’s model and employ a maximum likelihood method to estimate parameters. With the probability of equity stake acquisition, we obtain the optimal probability hazard threshold and treat it as a criterion for the foreign financial institutions to conduct equity stakes acquisition. Our empirical results confirm that the decisions of foreign financial institutions about equity stake acquisitions are to increase the profitability and market values of the target Chinese banks. In general, financial institutions with higher earning ability and better asset quality have stronger motives to take part in the acquisition or disposal of equity stakes. The contingent claim model is applied in this paper to examine the risk and return of foreign financial institutions after acquiring equity stakes of a Chinese bank. The model considers dynamic factors such as individual asset value and exchange rates to achieve the goal of maximizing shareholder value. In addition to analyzing the asset value and factors associated with risk after participation, this paper evaluates the optimal acquiring equity stakes proportion with numerical analyses under capital control. For China banking sector, we discover the overall portfolio risk of foreign financial institution will decrease after acquiring equity stakes when the asset value increases, the debt ratio decreases, and the required risk-weighted asset increases. Overall, these foreign financial institutions have well-diversified currency portfolio and enjoy a better asset quality and surplus earning; therefore, they will likely increase their optimal acquiring equity stakes proportion if the invested Chinese banks are with good assets quality and focused on local business. For the analysis of equity stake acquisition in China banks by Taiwanese banks, invested in the joint-stock commercial banks exists the higher intensity than others, and pan-government-owned Taiwanese bank also stands on the better vantage point than private banks. Under the possession of policy advantage for its green channels, the Western China Region is the best district in China for Taiwanese banks. This paper also examines the appropriate time and method to enter the market in China by applying the real options model. Being the market follower, Taiwan banking industry would need to find the right timing when ready entering China sine the market is pretty much laid out by many other foreign financial institutions. Therefore, the paper discovered some salubrious circumstances for Taiwan banking industry to enter the market, for example, the local financial service has not saturated, and initial investment cost is lower or Taiwan businessman demands more service gradually. The paper also confirms the current practice, which is to establish a representative office first and then promote it to a branch, seems to be practical for Taiwanese banks enter the market. Once meet the standard requests and acquire the license to operate RMB business, Taiwanese banks can establish wholly-owned subsidiary bank or take ownership stakes by having the innovation and business strategy in the local financial market.

Submitted by Paula Magalhães (paulakmagalhaes@gmail.com) on 2017-05-24T17:25:55Z No. of bitstreams: 1 Paula Magalhaes Dissertacao.pdf: 437299 bytes, checksum: 5ee7ce9b3eb164a2bd2068b1d47f4c92 (MD5) / Approved for entry into archive by Suzinei Teles Garcia Garcia (suzinei.garcia@fgv.br) on 2017-05-24T19:26:49Z (GMT) No. of bitstreams: 1 Paula Magalhaes Dissertacao.pdf: 437299 bytes, checksum: 5ee7ce9b3eb164a2bd2068b1d47f4c92 (MD5) / Made available in DSpace on 2017-05-25T12:11:52Z (GMT). No. of bitstreams: 1 Paula Magalhaes Dissertacao.pdf: 437299 bytes, checksum: 5ee7ce9b3eb164a2bd2068b1d47f4c92 (MD5) Previous issue date: 2017-05-11 / Este artigo trata do papel do Fundo Monetário Internacional como um agente sênior, fato observado empiricamente. Um agente soberano sujeito a um choque estocástico deve tomar emprestado para suavizar seu consumo. O mercado financeiro internacional oferece seus fundos, contudo cobra um prêmio por dividir o risco sobre o choque com o governo. O FMI, embora sênior, empresta a uma taxa menor. Encontramos as condições sob as quais a presença do FMI em tal mercado é relevante e positiva ao agente emprestador. Tais condições dependerão do tamanho do prêmio de risco cobrado, que em nossa análise é dado exogenamente. / This paper addresses the role of the International Monetary Fund in the international monetary economy as a senior agent, as observed empirically. A sovereign agent subject to a stochastic shock must borrow to smooth out consumption. The international financial market offers fund, however it charges a premium for sharing the risk over the shock with the government. The IMF, however senior, lends at a lower rate. Hence, the sovereign government must choose its borrower. We find conditions under which the IMF presence in such market is relevant and positive to the borrowing agent. Such conditions will depend on the size of the risk premium charged, which in our analysis will be exogenously given