As ruin theory evolves in recent years, there has been a variety of quantities pertaining to an insurer's bankruptcy at the centre of focus in the literature. Despite the fact that these quantities are distinct from each other, it was brought to our attention that many solution methods apply to nearly all ruin-related quantities. Such a peculiar similarity among their solution methods inspired us to search for a general form that reconciles those seemingly different ruin-related quantities. The stochastic approach proposed in the thesis addresses such issues and contributes to the current literature in three major directions. (1) It provides a new function that unifies many existing ruin-related quantities and that produces more new quantities of potential use in both practice and academia. (2) It applies generally to a vast majority of risk processes and permits the consideration of combined effects of investment strategies, policy modifications, etc, which were either impossible or difficult tasks using traditional approaches. (3) It gives a shortcut to the derivation of intermediate solution equations. In addition to the efficiency, the new approach also leads to a standardized procedure to cope with various situations. The thesis covers a wide range of ruin-related and financial topics while developing the unifying stochastic approach. Not only does it attempt to provide insights into the unification of quantities in ruin theory, the thesis also seeks to extend its applications in other related areas.

This thesis consists of a summary and five papers, dealing with financial applications of optimal stopping, optimal control and volatility. In Paper I, we present a method to recover a time-independent piecewise constant volatility from a finite set of perpetual American put option prices. In Paper II, we study the optimal liquidation problem under the assumption that the asset price follows a geometric Brownian motion with unknown drift, which takes one of two given values. The optimal strategy is to liquidate the first time the asset price falls below a monotonically increasing, continuous time-dependent boundary. In Paper III, we investigate the optimal liquidation problem under the assumption that the asset price follows a jump-diffusion with unknown intensity, which takes one of two given values. The best liquidation strategy is to sell the asset the first time the jump process falls below or goes above a monotone time-dependent boundary. Paper IV treats the optimal dividend problem in a model allowing for positive jumps of the underlying firm value. The optimal dividend strategy is of barrier type, i.e. to pay out all surplus above a certain level as dividends, and then pay nothing as long as the firm value is below this level. Finally, in Paper V it is shown that a necessary and sufficient condition for the explosion of implied volatility near expiry in exponential Lévy models is the existence of jumps towards the strike price in the underlying process.

欲透過流動性調整模型來探討流動性風險對或有償權的影響，但本篇研究著重於選擇權的分析。根據Feng (2014)，流動性折現因子由市場流動性與股價對市場流動性敏感度所構成，而且此流動性之動態過程具有均數復歸的特性。根據本篇研究結果，價內選擇權和價平選擇權的評價表現比傳統Black-Scholes好，如果進一步將流動性之跳躍性質引入模型，除了價內選擇權和價平選擇權之外，價外選擇權的評價表現亦呈現大幅度的改善。於探討模型評價表現優劣之餘，本篇文章欲更進一步探究市場不流動性對選擇權避險參數的影響。 / This study uses a liquidity-adjusted pricing model to discuss the impact of the liquidity risk on Contingent Claim. However, we focus on the analysis of option. The liquidity discount factor consists of market liquidity and the sensitivity of stock prices to market illiquidity. The dynamic process of market liquidity possesses mean-reversion. Our empirical results show the liquidity model will improve pricing performance for ITM and ATM options. After incorporating diffusive jumps in liquidity, marked improvements in pricing performance for OTM options are observed. In addition, we discuss the impacts of liquidity risk on hedging parameters.

<p>Diss. Stockholm : Handelshögskolan, 2013. Sammanfattning jämte 3 uppsatser.</p>

This dissertation is dedicated to study the design and utilization of financial contracts and pricing mechanisms for managing the demand/price risks in electricity markets and the price risks in carbon emission markets from different perspectives. We address the issues pertaining to the efficient computational algorithms for pricing complex financial options which include many structured energy financial contracts and the design of economic mechanisms for managing the risks associated with increasing penetration of renewable energy resources and with trading emission allowance permits in the restructured electric power industry. To address the computational challenges arising from pricing exotic energy derivatives designed for various hedging purposes in electricity markets, we develop a generic computational framework based on a fast transform method, which attains asymptotically optimal computational complexity and exponential convergence. For the purpose of absorbing the variability and uncertainties of renewable energy resources in a smart grid, we propose an incentive-based contract design for thermostatically controlled loads (TCLs) to encourage end users' participation as a source of DR. Finally, we propose a market-based approach to mitigate the emission permit price risks faced by generation companies in a cap-and-trade system. Through a stylized economic model, we illustrate that the trading of properly designed financial options on emission permits reduces permit price volatility and the total emission reduction cost.

經由愈來愈多的實證研究發現，的確在利率的變動過程中，除了包含連續性行為，即遵循”擴散”模式(diffusion process)，亦包含了不連續性行為，也就是有著跳躍(jump)的情形發生。因此顯示出假設利率隨機過程僅為連續性的擴散模型已是不足夠的，跳躍-擴散模型(Jump-diffusion model)顯然會比純粹擴散模型有著更好的解釋能力。而市場模型(LIBOR market model)的提出，則說明了遠期LIBOR利率模型較能描述市場實際的利率型態，並且可方便使用市場資訊，進行模型參數校準。 所以本研究旨在以LIBOR market model 加上跳躍過程，即遠期LIBOR利率的跳躍-擴散模型，分別針對歐洲美元期貨與利率結構型債券中的滾雪球式累息債券建立評價方法。由於所選用動態模型的複雜度，使得封閉解的求出不易，因此在文中，最後是採用蒙地卡羅模擬法，求兩商品的數值解。在後續研究上，本文還挑出了幾個最直接影響商品價值的因素，如殖利率、波動度、跳躍幅度等，進行各種情境下商品價值的敏感度分析，以提供投資人與發行商在考量風險因子所在時的一個參考。

Submitted by Renata Lopes (renatasil82@gmail.com) on 2016-05-04T13:32:38Z No. of bitstreams: 1 alexandreribeiroscarcioffolo.pdf: 4637086 bytes, checksum: cbb9a83bf6c45d454a12c1cc4deec75e (MD5) / Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2016-06-07T15:31:40Z (GMT) No. of bitstreams: 1 alexandreribeiroscarcioffolo.pdf: 4637086 bytes, checksum: cbb9a83bf6c45d454a12c1cc4deec75e (MD5) / Made available in DSpace on 2016-06-07T15:31:40Z (GMT). No. of bitstreams: 1 alexandreribeiroscarcioffolo.pdf: 4637086 bytes, checksum: cbb9a83bf6c45d454a12c1cc4deec75e (MD5) Previous issue date: 2015-05-13 / CAPES - Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Nesse estudo analisamos o caso de um projeto de parque eólico participante do mercado atacadista de compra e venda de eletricidade no Estado de Ohio (EUA) em dois cenários: (1) alugando o terreno de instalação do parque (prática atual) e (2) comprando o terreno de instalação visando a operação no mercado agrícola do milhono intuito de diminuir, pelo mecanismo da diversificação, os riscos da geração de receita pelo parque eólico, com a flexibilidade de esperar o melhor momento para investir, o que só irá acontecer nos cenários em que o valor presente dos fluxos de caixa for igual ou superior ao investimento inicial. Dois horizontes de operação (20 e 30 anos) serão considerados. A avaliação financeira foi baseada na Teoria das Opções Reais, que permite a consideração das flexibilidades gerenciais no valor do projeto. Uma importante inovação do trabalho consiste na incorporação de fatores sazonais nos saltos dos preços da eletricidade no Estado de Ohio, adaptando o processo estocástico de geração de preços para a realidade do mercado. Além disso, o presente estudo analisou uma nova possibilidade para os geradores eólicos, que consiste na compra do terreno de instalação visando a operação no mercado agrícola do milho. Foram consideradas como incertezas os preços da eletricidade um dia a frente do mercado atacadista no Estado de Ohio (LMP) e o preço do grão do milho recebido pelo produtor. Para o LMP, foi adotado o Modelo Geométrico de Reversão a Média com Saltos de Clewlow, Strickland e Kaminski (2000), com as devidas modificações sazonais, e para o preço do grão de milho foi utilizado o Modelo Geométrico de Reversão a Média 1 de Schwartz. Os resultados indicam que o projeto eólico no primeiro cenárioe em ambos os horizontes de operação não apresenta viabilidade financeira, sendo exercida a opção de espera por novas informações. Tal fato pode ser explicado pelo baixo valor do preço da eletricidade no mercado atacadista e pelo perfil ineficiente de geração da região, além da recente eliminação do subsídio PTC. Em relação ao segundo cenário, houve apenas um momento na simulação na qual houve níveis de preços capazes de gerar um projeto financeiramente viável em ambos os horizontes de operação. Contudo, mesmo a regra de decisão do segundo cenário apresentando um cenário com valor positivo, a opção de espera para realizar o investimento se apresenta como a melhor escolha do investidor, pois a probabilidade de ocorrência de tais níveis de preços são ínfimas. A comparação entre os dois cenários demonstrou que a incorporação do terreno pelo investidor é melhor que o aluguel, em ambos os horizontes de operação e em todos os momentos da simulação. Entretanto, ainda assim, a instalação de parques eólicos no norte do Estado de Ohio operando no mercado atacadista é financeiramente inviável, mesmo havendo um incremento na diversificação do projeto. Tal resultado sinaliza que o setor não está preparado para operar no mercado atacadista no norte do Estado de Ohio, havendo a necessidade de novos esforços para que isso ocorra, a despeito do governo americano vir trabalhando para aumentar a participação das renováveis na matriz energética americana (o principal programa adotado pelo Estado de Ohio, Renewable Portfolio Standards - RPS, pretende aumentar a partição das renováveis em 12,5% até o ano de 2024). / In this study we analyze the case of a wind energy generator’s project, which is a wholesale market participant in the Ohio electricity market in two scenarios: 1) renting the land of the turbines installation (usual practice), and 2) buying the land in order to commercialize the corn grain productionshortening the revenue risk by diversification mechanism. Both scenarios havea flexibility to wait the right moment to invest, in which it will happen when the present value of the cash flow is greater than the initial cost of installation. Two horizons of production, 20-years and 30-years, will be considerate in this study. The financial viability was based on Real Options Theory, which allows the consideration of managerial flexibility in the project value. An important innovation of the study consists in the incorporation of a seasonal factor of the spikes of Ohio electricity prices, adapting the stochastic process of generation prices to market reality. Also, the study analyzed a new possibility to the wind energy generator’s projects, in which the investor would buy the land of turbines installation in order to operate at the corn grain market. The electricity prices at the Ohio wholesale market, LMP, and the price of corn grain received by the farmers are the uncertainties considered in this study.The stochastic process to simulate LMP was the mean-reverting jump diffusion model of Clewlow, Strickland and Kaminski (2000), with seasonal changes, and the corn price uncertainty, was based on Schwartz 1 Mean Reversion Model. The results indicate that the wind energy generator’s project at the first scenario and at both production horizons, 20-years and 30-years, does not present financial viability, in which the flexibility of waiting the right moment to invest still on. It could be explained by the lower price levels of the electricity wholesale market, and the inefficient generation profile of the project region. In addition, the PTC elimination could affect the result. The second scenario provided a slightly different result. On the second scenario, there was only one moment at the price simulation, in which there were price levels capable of generating a financially viable project in both operating horizons. Yet, even the second scenario decision rule presented a scenario with a positive value, the wait option to carry out the investment itself is the best choice of the investor, because the likelihood of such price levels are negligible. The comparison between the two scenarios demonstrated that the incorporation of land by investor generated a positive value to the project, in which those results are greater than the first scenario at both production horizons, 20-years and 30-years, and at all price simulations. Therefore, the present study demonstrated that the wind energy generator’s project in Northern Ohio operating at the wholesale electricity market is cost-prohibitive, even with the increasing of diversification.This result indicates that the wind energy generators are not prepared to just operate at the wholesale electricity market in Northern Ohio, indicating the sector needs new efforts to make this a real possibility, despite the US government has been working to increase the share of renewable energy sources in the US (the main program adopted by the State of Ohio, renewable Portfolio Standards - RPS, aims to increase renewable partition by 12.5% by the year 2024).

Jump-diffusion processes often model financial time series as they can simulate the random jumps that they frequently exhibit. These jumps can be seen as anomalies and are essential for financial analysis and model building, making them vital to detect.The realized variation, realized bipower variation, and realized semi-variation were tested to see if one could use them to detect jumps in a jump-diffusion process and if anomaly detection algorithms can use them as features to improve their accuracy. The algorithms tested were Isolation Forest, Robust Random Cut Forest, and Isolation Forest Algorithm for Streaming Data, where the latter two use streaming data. This was done by generating a Merton jump-diffusion process with a varying jump-rate and tested using each algorithm with each of the features. The performance of each algorithm was measured using the F1-score to compare the difference between features and algorithms. It was found that the algorithms were improved from using the features; Isolation Forest saw improvement from using one, or more, of the named features. For the streaming algorithms, Robust Random Cut Forest performed the best for every jump-rate except the lowest. Using a combination of the features gave the highest F1-score for both streaming algorithms. These results show one can use these features to extract jumps, as anomaly scores, and improve the accuracy of the algorithms, both in a batch and stream setting. / Hopp-diffusionsprocesser används regelbundet för att modellera finansiella tidsserier eftersom de kan simulera de slumpmässiga hopp som ofta uppstår. Dessa hopp kan ses som anomalier och är viktiga för finansiell analys och modellbyggnad, vilket gör dom väldigt viktiga att hitta. Den realiserade variationen, realiserade bipower variationen, och realiserade semi-variationen är faktorer av en tidsserie som kan användas för att hitta hopp i hopp-diffusionprocesser. De används här för att testa om anomali-detektionsalgoritmer kan använda funktionerna för att förbättra dess förmåga att detektera hopp. Algoritmerna som testades var Isolation Forest, Robust Random Cut Forest, och Isolation Forest Algoritmen för Strömmande data, där de två sistnämnda använder strömmande data. Detta gjordes genom att genera data från en Merton hopp-diffusionprocess med varierande hoppfrekvens där de olika algoritmerna testades med varje funktion samt med kombinationer av funktioner. Prestationen av varje algoritm beräknades med hjälp av F1-värde för att kunna jämföra algoritmerna och funktionerna med varandra. Det hittades att funktionerna kan användas för att extrahera hopp från hopp-diffusionprocesser och även använda de som en indikator för när hopp skulle ha hänt. Algoritmerna fick även ett högre F1-värde när de använde funktionerna. Isolation Forest fick ett förbättrat F1-värde genom att använda en eller fler utav funktionerna och hade ett högre F1-värde än att bara använda funktionerna för att detektera hopp. Robust Random Cut Forest hade högst F1-värde av de två algoritmer som använde strömmande data och båda fick högst F1-värde när man använde en kombination utav alla funktioner. Resultatet visar att dessa funktioner fungerar för att extrahera hopp från hopprocesser, använda dem för att detektera hopp, och att algoritmernas förmåga att detektera hoppen ökade med hjälp av funktionerna.

An optimal dividend problem with investment opportunities, taking into consideration a source of strategic risk is being considered, as well as the effect of market frictions on the decision process of the financial entities. It concerns the problem of determining an optimal control of the dividend under debt constraints and investment opportunities in an economy with business cycles. It is assumed that the company is to be allowed to accept or reject investment opportunities arriving at random times with random sizes, by changing its outstanding indebtedness, which would impact its capital structure and risk profile. This work mainly focuses on the strategic risk faced by the companies; and, in particular, it focuses on the manager's problem of setting appropriate priorities to deploy the limited resources available. This component is taken into account by introducing frictions in the capital structure modification process. The problem is formulated as a bi-dimensional singular control problem under regime switching in presence of jumps. An explicit condition is obtained in order to ensure that the value function is finite. A viscosity solution approach is used to get qualitative descriptions of the solution. Moreover, a lending scheme for a system of interconnected banks with probabilistic constraints of failure is being considered. The problem arises from the fact that financial institutions cannot possibly carry enough capital to withstand counterparty failures or systemic risk. In such situations, the central bank or the government becomes effectively the risk manager of last resort or, in extreme cases, the lender of last resort. If, on the one hand, the health of the whole financial system depends on government intervention, on the other hand, guaranteeing a high probability of salvage may result in increasing the moral hazard of the banks in the financial network. A closed form solution for an optimal control problem related to interbank lending schemes has been derived, subject to terminal probability constraints on the failure of banks which are interconnected through a financial network. The derived solution applies to real bank networks by obtaining a general solution when the aforementioned probability constraints are assumed for all the banks. We also present a direct method to compute the systemic relevance parameter for each bank within the network. Finally, a possible computation technique for the Default Risk Charge under to regulatory risk measurement processes is being considered. We focus on the Default Risk Charge measure as an effective alternative to the Incremental Risk Charge one, proposing its implementation by a quasi exhaustive-heuristic algorithm to determine the minimum capital requested to a bank facing the market risk associated to portfolios based on assets emitted by several financial agents. While most of the banks use the Monte Carlo simulation approach and the empirical quantile to estimate this risk measure, we provide new computational approaches, exhaustive or heuristic, currently becoming feasible, because of both new regulation and the high speed - low cost technology available nowadays.

為了改進Black-Scholes模式的實證現象，許多其他的模型被建議有leptokurtic特性以及波動度聚集的現象。然而對於其他的模型分析的處理依然是一個問題。在本論文中，我們建議使用馬可夫跳躍擴散過程，不僅能整合leptokurtic與波動度微笑特性，而且能產生波動度聚集的與長記憶的現象。然後，我們應用Lucas的一般均衡架構計算選擇權價格，提供均衡下當跳躍的大小服從一些特別的分配時則選擇權價格的解析解。特別地，考慮當跳躍的大小服從兩個情況，破產與lognormal分配。當馬可夫跳躍擴散模型的馬可夫鏈有兩個狀態時，稱為轉換跳躍擴散模型，當跳躍的大小服從lognormal分配我們得到選擇權公式。使用轉換跳躍擴散模型選擇權公式，我們給定一些參數下研究公式的數值極限分析以及敏感度分析。 / To improve the empirical performance of the Black-Scholes model, many alternative models have been proposed to address the leptokurtic feature of the asset return distribution, and the effects of volatility clustering phenomenon. However, analytical tractability remains a problem for most of the alternative models. In this dissertation, we propose a Markov jump diffusion model, that can not only incorporate both the leptokurtic feature and volatility smile, but also present the economic features of volatility clustering and long memory. Next, we apply Lucas's general equilibrium framework to evaluate option price, and to provide analytical solutions of the equilibrium price for European call options when the jump size follows some specific distributions. In particular, two cases are considered, the defaultable one and the lognormal distribution. When the underlying Markov chain of the Markov jump diffusion model has two states, the so-called switch jump diffusion model, we write an explicit analytic formula under the jump size has a lognormal distribution. Numerical approximations of the option prices as well as sensitivity analysis are also given.