This thesis establishes an information system which combines three credit risk models through Service-Oriented Architecture (SOA). The system requires the bank user inputting finance-related data and selecting options to generate a series of credit risk related results, including the probabilities of default, the recovery rates, the expected market value of assets, the volatilities of the expected market value of assets, the default points, the default distances, and four indexes from principal components analyses. In addition to exhibiting the numerical results, graphical results are also available for the user. Three credit risk models joining this system are the Moody¡¦s KMV Model with Default Point Modified, the Risk-Neutral Probability Measure Model, and the Time-Varying Jointly Estimated Model. Several previous researches have demonstrated the validity of these credit risk models, hence the purpose of this study is not to examine the practicability of these models, but to see if these models are capable of connecting each other effectively and eventually establishing a process to evaluate the credit risk of enterprises and industries by the use of testing samples. Testing samples are data from Taiwan Small and Medium Enterprise Credit Guarantee Fund. The finance-related data includes the loan amounts, the book value of assets, the data used to calculate the default point threshold (such as the short-term debt and the long-term debt), and the financial ratios with regard to growth ability (such as the revenue growth rate and the profit growth rate before tax), operation ability (such as the accounts receivable turnover rate and the inventory turnover rate), liability-paying ability (such as the current ratio and the debt ratio), and profitability (such as the return on assets and the return on equity). In addition to inputting the finance-related data, the system also require the user selecting the industrial category, the default point threshold, the way data being weighted, the data period, and the borrowing rates from the option page for every enterprise in order to acquire the results. Among the computing process, user is required to select weighted average method, either weighted by loan amounts or weighted by market value of assets, to obtain ¡§the weighted average probability of default of the industry¡¨ and ¡§the weighted average recovery rate of the industry¡¨ which are both used by the Time-Varying Jointly Estimated Model. This study also makes use of quartiles to simulate the situation when the user is near the bottom and top of the business cycle. Furthermore, the ¡§Supremum Strategy¡¨ and the ¡§Infimum Strategy¡¨ are added to this study to let the user realize the best condition and the worse condition of the ¡§Time-Varying Industrial Marginal Probabilities of Default¡¨.

Build-Operate-Transfer (BOT) is a form of Public-Private Partnerships that is commonly used to close the growing gap between the cost of developing and modernizing transportation infrastructure systems and the financial resources available to governments. When assessing the feasibility of a BOT project, private investors consider revenue risk - which is stemmed from the uncertainty about future traffic demand - as a critical factor. A potential approach to mitigating the revenue risk is the offering of revenue risk sharing mechanisms such as Minimum Revenue Guarantee options by the government. In addition to Minimum Revenue Guarantee options, a mechanism known as Traffic Revenue Cap options may also be negotiated, which makes the government entitled to a share of revenue when it grows beyond a specified threshold. Financial valuation of investments in BOT projects should take into account uncertainty about future traffic demand, as well as Minimum Revenue Guarantee and Traffic Revenue Cap options. The conventional valuation methods including Net Present Value (NPV) analysis are not capable of integrating the uncertainty about future traffic demand in the valuation of BOT projects and properly pricing Minimum Revenue Guarantee and Traffic Revenue Cap options. Real options analysis can be used as an alternative approach to valuation of investments in transportation projects under uncertainties. However, the appropriate application of real options analysis to valuation of investments in transportation projects is conditioned upon overcoming specific theoretical challenges. Current real options models do not provide a systematic method for estimating the project volatility, which measures the variability of investment value. Existing models do not provide a method for calculating the market value of Minimum Revenue Guarantee and Traffic Revenue Cap options. Also, current models are not able to characterize the impact of Minimum Revenue Guarantee and Traffic Revenue Cap options on private investors' financial risk profile. The overarching objective of this research is to apply the real options theory in order to price Minimum Revenue Guarantee and Traffic Revenue Cap options under the uncertainty about future traffic demand. To achieve this objective, a real options model is created that characterizes the long-term traffic demand uncertainty in BOT projects and determines investors' financial risk profile under uncertainty about future traffic demand. This model presents a novel method for estimating the project volatility for real options analysis. This model devises a market-based option pricing approach to determine the correct value of Minimum Revenue Guarantee and Traffic Revenue Cap options. An appropriate procedure is created for characterizing the impact of Minimum Revenue Guarantee and Traffic Revenue Cap options on the investors' financial risk profile. The proposed real options model is applied to a BOT project to illustrate the valuation process. The limitations of the proposed real options model, as well as the barriers to its implementation, are identified and recommendations for future research are offered. This research contributes to the state of knowledge by presenting a new method for estimating the project volatility, which is required for the real options analysis of transportation investments. It also introduces a risk-neutral valuation method for pricing the market value of Minimum Revenue Guarantee and Traffic Revenue Cap options in BOT projects. The research also contributes to the state of practice by introducing a novel class of assessment tools for decision makers that characterize the investors' financial risk profile under uncertainty about future traffic demand. Proper methods for pricing of Minimum Revenue Guarantee and Traffic Revenue Cap options are useful to public and private investors, in order to avoid wasting capital in transportation projects.

http://orcid.org/0000-0002-1641-5388 / Pricing options quickly and accurately is a well known problem in finance. Quantum computing is being researched with the hope that quantum computers will be able to price options more efficiently than classical computers. This research extends the quantum binomial option pricing model proposed by Zeqian Chen to European put options and to Barrier options and develops a quantum algorithm to price them. This research produced three key results. First, when Maxwell-Boltzmann statistics are assumed, the quantum binomial model option prices are equivalent to the classical binomial model. Second, options can be priced efficiently on a quantum computer after the circuit has been built. The time complexity is O((N − τ)log(N − τ)) and it is in the BQP quantum computational complexity class. Finally, challenges extending the quantum binomial model to American, Asian and Bermudan options exist as the quantum binomial model does not take early exercise into account. / May 2009

<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>

Pricing options quickly and accurately is a well known problem in finance. Quantum computing is being researched with the hope that quantum computers will be able to price options more efficiently than classical computers. This research extends the quantum binomial option pricing model proposed by Zeqian Chen to European put options and to Barrier options and develops a quantum algorithm to price them. This research produced three key results. First, when Maxwell-Boltzmann statistics are assumed, the quantum binomial model option prices are equivalent to the classical binomial model. Second, options can be priced efficiently on a quantum computer after the circuit has been built. The time complexity is O((N − τ)log(N − τ)) and it is in the BQP quantum computational complexity class. Finally, challenges extending the quantum binomial model to American, Asian and Bermudan options exist as the quantum binomial model does not take early exercise into account.

Submitted by Kym Marcel Martins Ardison (kymmarcel@gmail.com) on 2015-04-06T19:04:20Z No. of bitstreams: 1 Tail Risk - Original.pdf: 817189 bytes, checksum: 02561a6a7cb94d1480a4f78933486df4 (MD5) / Approved for entry into archive by BRUNA BARROS (bruna.barros@fgv.br) on 2015-04-28T12:21:10Z (GMT) No. of bitstreams: 1 Tail Risk - Original.pdf: 817189 bytes, checksum: 02561a6a7cb94d1480a4f78933486df4 (MD5) / Approved for entry into archive by Marcia Bacha (marcia.bacha@fgv.br) on 2015-05-04T12:33:49Z (GMT) No. of bitstreams: 1 Tail Risk - Original.pdf: 817189 bytes, checksum: 02561a6a7cb94d1480a4f78933486df4 (MD5) / Made available in DSpace on 2015-05-04T12:37:02Z (GMT). No. of bitstreams: 1 Tail Risk - Original.pdf: 817189 bytes, checksum: 02561a6a7cb94d1480a4f78933486df4 (MD5) Previous issue date: 2015-02-12 / This paper proposes a new novel to calculate tail risks incorporating risk-neutral information without dependence on options data. Proceeding via a non parametric approach we derive a stochastic discount factor that correctly price a chosen panel of stocks returns. With the assumption that states probabilities are homogeneous we back out the risk neutral distribution and calculate five primitive tail risk measures, all extracted from this risk neutral probability. The final measure is than set as the first principal component of the preliminary measures. Using six Fama-French size and book to market portfolios to calculate our tail risk, we find that it has significant predictive power when forecasting market returns one month ahead, aggregate U.S. consumption and GDP one quarter ahead and also macroeconomic activity indexes. Conditional Fama-Macbeth two-pass cross-sectional regressions reveal that our factor present a positive risk premium when controlling for traditional factors.

Submitted by Laura Simonsen Leal (arula@fgvmail.br) on 2016-06-22T12:59:34Z No. of bitstreams: 1 laura_tese14(final).pdf: 1036208 bytes, checksum: eac8007047195b00593f30884e72a3e2 (MD5) / Approved for entry into archive by GILSON ROCHA MIRANDA (gilson.miranda@fgv.br) on 2016-06-22T13:18:16Z (GMT) No. of bitstreams: 1 laura_tese14(final).pdf: 1036208 bytes, checksum: eac8007047195b00593f30884e72a3e2 (MD5) / Approved for entry into archive by Marcia Bacha (marcia.bacha@fgv.br) on 2016-06-29T13:38:50Z (GMT) No. of bitstreams: 1 laura_tese14(final).pdf: 1036208 bytes, checksum: eac8007047195b00593f30884e72a3e2 (MD5) / Made available in DSpace on 2016-06-29T13:39:56Z (GMT). No. of bitstreams: 1 laura_tese14(final).pdf: 1036208 bytes, checksum: eac8007047195b00593f30884e72a3e2 (MD5) Previous issue date: 2016-03-21 / The main purpose of this paper is to propose a methodology to obtain a hedge fund tail risk measure. Our measure builds on the methodologies proposed by Almeida and Garcia (2015) and Almeida, Ardison, Garcia, and Vicente (2016), which rely in solving dual minimization problems of Cressie Read discrepancy functions in spaces of probability measures. Due to the recently documented robustness of the Hellinger estimator (Kitamura et al., 2013), we adopt within the Cressie Read family, this specific discrepancy as loss function. From this choice, we derive a minimum Hellinger risk-neutral measure that correctly prices an observed panel of hedge fund returns. The estimated risk-neutral measure is used to construct our tail risk measure by pricing synthetic out-of-the-money put options on hedge fund returns of ten specific categories. We provide a detailed description of our methodology, extract the aggregate Tail risk hedge fund factor for Brazilian funds, and as a by product, a set of individual Tail risk factors for each specific hedge fund category.

Esta tese promove uma integração entre Finanças e Teoria de Informação para criação de um ambiente alternativo para a determinação do preço racional da opção européia simples ordinária sobre ação e ativo de renda fixa (bond). Uma das características deste novo ambiente de determinação de preço racional é poder continuar utilizando o cálculo newtoniano em vez do estocástico. Cria uma notação matemática precisa e completa para a Teoria da Informação e a integra com a teoria de Finanças em condições de incerteza. Integra as abordagens entrópicas de determinação do preço racional da opção européia simples ordinária de Gulko (1998 e 1998a) e de Yang (1997). Define precisamente o mundo com preço da incerteza neutralizado (risk-neutral world), o mundo martingale, o mundo informacionalmente eficiente e o mundo entrópico e suas implicações para a Ciência do Investimento e, mais especificamente, para a determinação do preço racional de ativos básicos e derivativos. Demonstra detalhadamente a fórmula do preço racional da opção européia simples ordinária de Black-Scholes-Merton, melhorando a notação matemática, simplificando (eliminando a abordagem martingale) e complementando a demonstração feita por Baxter & Rennie (1998). Interrompe uma sucessão de trabalhos que estabelecem uma forma equivocada de calcular o preço da opção européia simples ordinária. Esse erro teve sua origem, muito provavelmente, numa edição de Brealey & Myers, que equivocadamente utilizou um resultado de Cox & Rubinstein (1985); esse resultado facilitava o cálculo do preço racional da opção européia simples ordinária por meio de uma tabela que evita o uso direto da fórmula de Black-Scholes-Merton. Brealey & Myers (desde a quarta edição de 1991), Luehrman (nos seus dois artigos da HBR de 1998 e um caso de 1995 pela HBS) e Edleson (caso publicado em 1994 pela HBS) ensinam que o valor percentual encontrado nessa tabela deve ser multiplicado pelo preço do valor mobiliário, quando deveria ser multiplicado pelo valor presente do preço de exercício. Os resultados mais importantes desta tese para Finanças são: (i) desenvolvimento de um método alternativo, robusto e parcimonioso, baseado no princípio da máxima entropia da Teoria da Informação e do Sistema de Distribuições de Pearson para obtenção de uma única medida de probabilidade neutralizadora do preço da incerteza (risk-neutral probability), (ii) obtenção de fórmula prática para a determinação do preço racional da opção européia simples ordinária para ação, (iii) validação da fórmula de Black-Scholes-Merton para ação, (iv) obtenção de uma fórmula adequada para a determinação do preço racional da opção européia simples ordinária sobre um título de renda fixa (bond), (v) estimação da volatilidade implícita entrópica do preço do valor mobiliário e (vi) definição e estimação do valor em risco (value at risk) entrópico. Há ainda dois resultados importantes para a Teoria da Informação e Economia: (i) distinção mais precisa entre incerteza e risco e (ii) desenvolvimento da medida de ganho informacional da previsão aprimorando o resultado de Theil (1967) e Benish (1999) pela utilização do conceito de divergência de Kullback-Leibler. / This thesis integrates Finance and Information Theory in order to create an alternative environment to the calculation of the rational price of the simple ordinary European option over stocks and bonds. One of the features of this new environment is to allow us to continue using the Newtonian calculus instead of the stochastic one. It creates a precise and complete mathematical notation for the Information Theory and integrates it with the Finance Theory under uncertainty conditions. It integrates Gulko’s (1998 and 1998a) and Yang’s (1997) entropic approaches to the calculation of the rational price of the simple ordinary European option. It precisely defines the uncertainty-price-neutral world (risk-neutral world), the martingale world, the informationally efficient world and the entropic world and their implications to the Investment Science and, more specifically, to the calculation of the rational price of ordinary assets and derivatives. It demonstrates with details the Black-Scholes-Merton formula of the rational price of the simple ordinary European option, improves the mathematical notation, simplifies it (by eliminating the martingale approach) and completes the demonstration done by Baxter & Rennie (1998). It breaks a succession of works that established a mistaken way to calculate the price of the simple ordinary European option. This mistake had its origin, much probably, in an edition of Brealey & Myers, who erroneously used a result from Cox & Rubinstein (1985). This result facilitates the calculation of the rational price of the simple ordinary European option by using a table that avoids the direct usage of the Black-Scholes-Merton formula. Brealey & Myers (since the 1991 fourth edition), Luehrman (in his two 1998 articles in HBR and in a 1995 case in HBS) and Edleson (1994 case published in HBS) teach that the percentage value found in this table must be multiplied by the price of the asset, when in reality it should have been multiplied by the present value of the strike price. The most important results of this thesis for Finance are: (i) development of a robust and economic alternative method, based on the maximum-entropy principle of the Information Theory and on Pearson’s Distribution System, to the calculation of a unique uncertainty-price-neutral probability measure (risk-neutral probability), (ii) achievement of a practical formula to the calculation of the rational price of the simple ordinary European option on stocks, (iii) validation of the Black-Scholes-Merton formula on stocks, (iv) achievement of an adequate formula to the calculation of the rational price of the simple ordinary European option on bonds, (v) estimation of the implied entropic volatility of the price of an asset and (vi) definition and estimation of the entropic value-at-risk. There are still two important results to the Information Theory and to Economics: (i) a more precise distinction between uncertainty and risk and (ii) development of the forecast informational gain, an enhancement of the result of Theil (1967) and Benish (1999) by using the Kullback-Leibler divergence concept.

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

Implied volatility obtained from market option prices is widely regarded as an efficient predictor of future realised volatility. Implied volatility can be thought of as market's expectation of future realised volatility. We distinguish between volatility-changing events with respect to expectations - scheduled events (such as information releases) and unscheduled events. We propose a method of testing the information content of option-implied risk-neutral moments prior to volatility-changing events. Using the method introduced by Bakshi, Kapadia & Madan (2003) we extract implied volatility, skewness and kurtosis from S&P 500 options market prices and apply the proposed method in four case studies. Two are concerned with scheduled events - United Kingdom European Union membership referendum, 2016 and United States presidential election, 2016, two are concerned with unscheduled events - flash crash of August 24, 2015 and flash crash of October 15, 2014. Implied volatility indicates a rise in future realised volatility prior to both scheduled events. We find a significant rise in implied kurtosis during the last three days prior to the presidential election of 2016. Prior to unscheduled events, we find no evidence of implied moments indicating a rise in future realised volatility.