Estimating tail risk measures such as Value at Risk (VaR) and Conditional Tail Expectation (CTE) is a vital component in financial and actuarial risk management. The CTE is a preferred risk measure, due to coherence and a widespread acceptance in actuarial community. In particular we focus on the estimation of the CTE using both parametric and nonparametric approaches. In parametric case the conditional tail expectation and variance are analytically derived for the exponential distribution family and its transformed distributions. For small i.i.d. samples the exact bootstrap (EB) and the influence function are used as nonparametric methods in estimating the bias and the the variance of the empirical CTE. In particular, it is shown that the bias is corrected using the bootstrap for the CTE case. In variance estimation the influence function of the bootstrapped quantile is derived, and can be used to estimate the variance of any bootstrapped L-estimator without simulations, including the VaR and the CTE, via the nonparametric delta method. An industry model are provided by applying theoretical findings on the bias and the variance of the estimated CTE. Finally a new capital allocation method is proposed. Inspired by the allocation of the solvency exchange option by Sherris (2006), this method resembles the CTE allocation in its form and properties, but has its own unique features, such as managerbased decomposition. Through a numerical example the proposed allocation is shown to fail the no undercut axiom, but we argue that this axiom may not be aligned with the economic reality.

Estimating tail risk measures such as Value at Risk (VaR) and Conditional Tail Expectation (CTE) is a vital component in financial and actuarial risk management. The CTE is a preferred risk measure, due to coherence and a widespread acceptance in actuarial community. In particular we focus on the estimation of the CTE using both parametric and nonparametric approaches. In parametric case the conditional tail expectation and variance are analytically derived for the exponential distribution family and its transformed distributions. For small i.i.d. samples the exact bootstrap (EB) and the influence function are used as nonparametric methods in estimating the bias and the the variance of the empirical CTE. In particular, it is shown that the bias is corrected using the bootstrap for the CTE case. In variance estimation the influence function of the bootstrapped quantile is derived, and can be used to estimate the variance of any bootstrapped L-estimator without simulations, including the VaR and the CTE, via the nonparametric delta method. An industry model are provided by applying theoretical findings on the bias and the variance of the estimated CTE. Finally a new capital allocation method is proposed. Inspired by the allocation of the solvency exchange option by Sherris (2006), this method resembles the CTE allocation in its form and properties, but has its own unique features, such as managerbased decomposition. Through a numerical example the proposed allocation is shown to fail the no undercut axiom, but we argue that this axiom may not be aligned with the economic reality.

Thesis (Ph. D.)--UCLA, 2007. / Vita. Includes bibliographical references.

The risk capital has to be kept by insurance company to cover unexpected looses. In our thesis we focus on different approaches to calculation of risk capital. One part is concentrated on derivation of Solvency I regime, both for life and nonlife insurance. In addition, we characterize riders of life insurance that are avaliable on the Czech market. In next part of our thesis we set up our own model of risk capital calculation. We consider these risks: mortality, expense, lapse and interest rate risk. For numerical calculations we chose accidental death rider, so we included its risk also into our model.

Název práce: Metodiky Solvency II v životním pojištění Autor: Martina Benešová Katedra (ústav): Katedra pravděpodobnosti a matematické statistiky Vedoucí bakalářské práce: RNDr. Pavel Finfrle, Ph.D e-mail vedoucího: finfrle@generalippf.eu Abstrakt: Tato diplomová práce se zabývá problematikou solventnosti pojišťoven v souvislosti s konceptem regulatorního rámce Solvency II. Na začátku práce jsou shrnuté základní body o Solvency I, dále je větší pozornost věnovaná vlastnostem Solvency II a jednotlivým kategoriím rizik, jejichž správná kvantifikace je pro Solvency II klíčová. V další části jsou představeny metody na výpočet kapitálové dostatečnosti - interní a částečné interní modely a podrobněji pak standardní model. Klíčové dvě kapitoly práce se pak detailně zabývají rizikem storen v ži- votním pojištění. Rozebrána je standardní metodika výpočtu kapitálového poža- davku, a je navržen stochastický model, který ji rozšiřuje zahrnutím informace o diverzitě odbytových cest. Monte Carlo simulací je demonstrována nižší rizikovost pojišťovny s širším polem zprostředkovatelů. Klíčová slova: solventnost, Solvency II, kapitálové požadavky, riziko storen Title: The methods of Solvency II for life insurance Author: Martina Benešová Department: Department of Probability and Mathematical Statistics Supervisor: RNDr. Pavel...

Há distintos métodos matemáticos para o cálculo do capital mínimo de uma instituição financeira. A literatura relacionada ao tema os segrega essencialmente em duas formas. A primeira utiliza a volatilidade do valor dos ativos na determinação das potenciais perdas inesperadas e, conseqüentemente, do capital mínimo. Esse método está presente no pilar 1 do Novo Acordo de Capital da Basiléia. A segunda utiliza como base a volatilidade de resultados para determinar o montante de variação máxima negativa dessa variável para o cálculo do capital mínimo, a um determinado nível de probabilidade e em um horizonte de tempo. Esse montante de potencial variação máxima requer uma conversão para capital utilizando uma taxa livre de risco. Em outras palavras, o método com base na volatilidade de resultados procura determinar um capital mínimo que, investido a uma taxa livre de risco, seja capaz de cobrir a variação máxima de resultado esperada para a instituição financeira. Esse trabalho testa empiricamente as duas abordagens para os 50 maiores bancos presentes no mercado brasileiro. O objetivo é verificar afirmações presentes na literatura e relacionadas às diferenças entre as abordagens. / There are different methods for determining the minimum capital of a financial institution. The academic literature related to this subject essentially groups them into two approaches. The first uses asset volatility to obtain potential unexpected losses and, therefore, the minimum capital. This approach is present on the first pillar of the New Basel Capital Accord. The second approach uses earnings volatility to obtain the maximum negative change of this variable to calculate the minimum capital, given a confidence level and a time horizon. This potential maximum change must be translated into capital by using a risk-free rate. In other words, the earnings volatility approach aims to obtain a minimum capital which, invested in a risk-free rate, can generate a return to cover the potential maximum negative change in earnings. This research empirically tests the two approaches on the 50 biggest banks present in the Brazilian financial system. The objective is to verify statements present on the academic literature and related to the differences between the approaches.

We specify a class of non-linear and non-Gaussian models for which we estimate and forecast the conditional distributions with daily frequency. We use these forecasts to calculate VaR measures for three different equity markets (US, GB and Japan). These forecasts are evaluated on the basis of different statistical performance measures as well as on the basis of their economic costs that go along with the forecasted capital requirements. The results indicate that different performance measures generate different rankings of the models even within one financial market. We also find that for the three markets the improvement in the forecast by non-linear models over linear ones is negligible, while non-gaussian models significantly dominate the gaussian models. / Series: Report Series SFB "Adaptive Information Systems and Modelling in Economics and Management Science"

O presente trabalho estuda as alternativas de financiamento do processo de criação de valor de uma empresa, com ênfase na opção de capital de risco (venture capital). O estudo está dividido em três capítulos. O primeiro apresenta, com base nas teorias de finanças, o processo de tomada de decisão de financiamento, podendo este ser via capital próprio ou dívida, sendo apresentadas as principais opções destas duas modalidades gerais. O segundo capítulo aborda a evolução histórica, a forma de funcionamento e os principais mercados da indústria de capital de risco no mundo. O terceiro capítulo efetua análise de dados para um período de 15 anos de uma gestora privada, onde se avaliou, para uma amostra de 24 empresas de diversos setores, qual é a curva de maturação dos investimentos da gestora. Verificou-se que, principalmente para as pequenas e médias empresas, o processo de financiamento é um elemento de grande dificuldade na construção e crescimento das suas operações, com prazos mais longos de maturação. Ou seja, como principal resultado, o estudo dos dados dos investimentos realizados pela empresa gestora privada no Brasil sugere que o processo de criação de valor destas empresas demanda um tempo adicional ao que tradicionalmente se espera. Diante do crescimento da indústria de capital de risco no mundo, esta modalidade de financiamento pode apresentar maior disseminação e escolha por esta alternativa pelas pequenas e médias empresas, tendo em consideração a questão da curva de maturação mais dilatada. / The present research studies the financing alternatives of the process of creating value to a company, with emphasis on the option of venture capital. The study is divided into three chapters. The first presents, based on the theories of finance, the process of financing decision making, and it may be via equity or debt, presenting the main options of these two general procedures. The second chapter discusses the historical evolution, the form of operation and the main markets of the risk capital industry in the world. The third chapter performs data analysis for a period of 15 years of a private holding company, which evaluated, for a sample of 24 companies in various sectors, what is the maturation curve of the investments of the managing body. It was found that, especially for small and medium sized enterprises, the funding process is a key element of great difficulty in construction and growth of its operations, with longer deadlines of maturation. In other words, as main results, the study of the data of the investments made by the private company in Brazil suggests that the process of creation of value of these companies demand an additional time to which is traditionally expected. Before the growth of the venture capital industry in the world, this modality of financing may present greater dissemination and choice for this alternative by small and medium enterprises, taking into account the issue of maturation curve more dilated.

O sucesso alcançado pela indústria de Private Equity e Venture Capital (PE/VC) no fomento ao empreendedorismo e na dinamização do setor empresarial norte-americano encorajou diversos países a importar este modelo vencedor de intermediação financeira. Entretanto, a atividade de PE/VC foi criada para desempenhar sob o ambiente institucional norte-americano, fazendo com que estudiosos tais como Gompers e Lerner (1999) levantassem dúvida sobre o sucesso na implantação deste modelo em outros países. Para verificar como a atividade de PE/VC se molda segundo o ambiente, este trabalho conduz um estudo empírico com todas as 65 organizações gestoras de PE/VC com escritórios no Brasil. A pesquisa foi realizada ao final de 2004 e obteve 100% de resposta. A análise foca no tamanho e a na macroestrutura da indústria. Os resultados são plenamente representativos e revelam um setor de PE/VC com tamanho modesto, bastante limitado pelo ambiente econômico-institucional, que prejudica a realização de negócios, embora ofereça oportunidades de investimento que supram as insuficiências do país em termos de infra-estrutura, segurança etc. Como principal resultado, o trabalho identifica similaridades e diferenças do modelo brasileiro de PE/VC em relação ao modelo vigente nos EUA. Os principais pontos em comum são: (i) predominam as organizações independentes que gerenciam recursos de investidores institucionais; (ii) o capital é concentrado regionalmente e em poucas organizações gestoras; (iii) os investimentos tendem a ser feitos próximos às organizações gestoras; (iv) os setores de software e TI são os mais procurados; (v) a qualificação dos gestores é similar a de seus pares internacionais. Por sua vez, as diferenças sugerem que o modelo tenha se adaptado ao novo ambiente institucional: (i) há tendência de investimento em empresas mais maduras, o que é compatível com o baixo nível de empreendedorismo de crescimento e elevada informalidade das pequenas empresas; (ii) O baixo numero de LBOs é compatível com a escassez e o alto custo do crédito; (iii) baixo grau de especialização dos gestores sugere poucas oportunidades de investimento em cada setor; (iv) concentração das organizações no centro financeiro do país sugere a busca de parceiros comerciais e compradores estratégicos para as empresas do portfolio (IPO é um mecanismo raramente utilizado); (v) a regulamentação reconhece o baixo grau de proteção dos investidores e obriga a utilização da arbitragem. Entre as diferenças encontradas, a pouca confiança que os investidores depositam nos gestores tende a se alterar conforme o setor adquire experiência e os gestores adquirem reputação. / The outstanding success attained by Private Equity and Venture Capital (PE/VC) in fostering the U.S. entrepreneurial sector has encouraged several countries to import it. However, PE/VC was tailored to perform in the American institutional environment. As Gompers and Lerner (1999) state, the degree to which the U.S. venture model will - or can - be successfully adapted to other countries is a particularly interesting question. To answer this question we conduct an empirical study with all the 65 PE/VC management firms with offices in Brazil. The survey was conducted at the end of 2004 and attained a response rate of 100%. For this reason the results are fully representative. The analysis aims at the industry's size and structure. Relates them to institutional factors. It reveals a PE/VC industry whose size is heavily limited by the Brazilian institutional idiosyncrasies. At the same time, Brazil's lack of transportation, energy and telecommunications' infrastructure and security provides opportunities for PE/VC type of investments. As a main finding, this work identifies differences and similarities between the American and the Brazilian PE/VC models. The similarities are: (i) PE/VC firms are mainly independent and manage capital from institutional investors; (ii) capital is heavily concentrated regionally as well as in few management firms; (iii) investments are made within a close range from management firms; (iv) software and IT are the preferred sectors; and (v) managers are highly qualified. The main differences suggest that the model has adapted to the new environment: (i) in line with a lack of high-expectation entrepreneurship, there is a tendency to invest in more advanced stages; (ii) since credit is scarce, few LBOs take place; (iii) lack of sector specialization suggests few opportunities within each sector; (iv) management firms concentration in the financial cluster suggest a quest for commercial partners and strategic buyers for portfolio companies (IPO is a quite rare exit mechanism); and (v) Brazilian PE/VC regulation recognizes the inefficiency of the legal system and obliges the use of arbitration. Among the differences, the lack of trust between investors and managers should change as the industry evolves and managers gain reputation.

<p>Avsikten med denna studie är att undersöka vilka motiv, påverkande faktorer och synsätt små IT-företag har när de väljer att ta in riskkapital som finansiering. Vi har utgått från tidigare forskning inom området för att identifiera vilka motiv och påverkande faktorer som kan förekomma och utifrån dessa byggt upp grunden för vår studie. Kapitaltillskott är det som naturligt känns som det mest primära motivet, vilket även vår studie har visat men det finns ändå en önskan om annan värdetillförsel i form av affärskompetens, nätverk och kontakter. Dessa önskemål har dock inte varit några huvudsakliga motiv för att inleda samarbete med riskkapitalisterna utan de kan mer ses som positiva sekundära motiv. </p><p>Motiven kapitaltillskott och tillförsel av affärskompetens samt nätverk och kontakter blir i sin tur påverkade av ett antal faktorer såsom företagets och produktens livscykelfas, ägande och kontroll, produkt och marknad samt ledningens erfarenhet och kompetens. Alla dessa både inre och yttre faktorer är mer eller mindre sammankopplade med varandra och påverkar beslutsfattarnas val om de ska ta in riskkapital eller välja någon annan form av externt kapital. Studien omfattar fyra små IT-företag och trots att företagen utifrån sett är lika genom att de alla har en eller flera unika IT-produkter, så har de ändå delvis olika synsätt på nyttan och effekten av finansiering med riskkapital. Två av företagen är totalt sett mer negativa medan två av dem är mer positiva. Av de två som är positiva är det bara det ena som idag har riskkapital och detta beror då på att alla ägarna inte har haft samma synsätt.</p>