Thesis (M.S.)--West Virginia University, 2005. / Title from document title page. Document formatted into pages; contains vii, 53 p. : ill. (some col.). Includes abstract. Includes bibliographical references (p. 52-53).

The use of forward-looking information from option prices attracted a lot of attention after the 2008 financial crisis, which highlighting the difficulty of using historical data to predict extreme events. Although a considerable number of papers investigate extraction of forward-information from cross-sectional option prices, Figlewski (2008) argues that it is still an open question and none of the techniques is clearly superior. This thesis focuses on getting information from option prices and investigates two broad topics: applying machine learning in extracting state price density and recovering natural probability from option prices. The estimation of state price density (often described as risk-neutral density in the option pricing litera- ture) is of considerable importance since it contains valuable information about investors' expectations and risk preferences. However, this is a non-trivial task due to data limitation and complex arbitrage-free constraints. In this thesis, I develop a more efficient linear programming support vector machine (L1-SVM) estimator for state price density which incorporates no-arbitrage restrictions and bid-ask spread. This method does not depend on a particular approximation function and framework and is, therefore, universally applicable. In a parallel empirical study, I apply the method to options on the S&P 500, showing it to be comparatively accurate and smooth. In addition, since the existing literature has no consensus about what information is recovered from The Recovery Theorem, I empirically examine this recovery problem in a continuous diffusion setting. Using the market data of S&P 500 index option and synthetic data generated by Ornstein-Uhlenbeck (OU) process, I show that the recovered probability is not the real-world probability. Finally, to further explain why The Recovery Theorem fails and show the existence of associated martingale component, I demonstrate a example bivariate recovery.

Thesis (Ph. D.)--West Virginia University, 2006. / Title from document title page. Document formatted into pages; contains v, 218 p. : ill. (some col.). Vita. Includes abstract. Includes bibliographical references.

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Yes / This paper compares several widely-used and recently-developed methods to extract risk-neutral densities (RND) from option prices in terms of estimation accuracy. It shows that positive convolution approximation method consistently yields the most accurate RND estimates, and is insensitive to the discreteness of option prices. RND methods are less likely to produce accurate RND estimates when the underlying process incorporates jumps and when estimations are performed on sparse data, especially for short time-to-maturities, though sensitivity to the discreteness of the data differs across different methods.

Inter-ocular suppression occurs when very different images are presented to each eye. Diplopia ensues if different images are superimposed and perceived. The brain removes this unfavourable viewing experience by suppressing one eye’s input to enable clear single vision. Inter-ocular suppression during visual development occurs in response to sufficiently disparate images caused by strabismus (misalignment of the visual axis) or anisometropia (uncorrected difference in refractive error), and if persistent may result in amblyopia. This is reduced visual sensitivity, usually in one eye, to a range of visual functions that cannot be corrected by refraction. Furthermore, binocular vision is reduced or absent. Depth and extent of suppression is measured across the central visual field in healthy participants with monocularly blurred vision, healthy participants with monocularly reduced luminance using neutral density (ND) filters, and participants with naturally disrupted binocular vision and/or amblyopia. Suppression of spatial stimuli defined by luminance (L) and luminancemodulated noise (LM) was compared to that measured for stimuli defined by contrast-modulated noise (CM), for which there is no change in mean luminance. For all stimuli suppression depth increased with increased imbalance of binocular input. Suppression was of a similar depth across the visual field with imposed blur and localised central suppression was found with ND filters. Microstrabismics showed central suppression, while strabismic amblyopes showed central in addition to hemifield suppression. Suppression for all participants was measured to be deeper for CM spatial stimuli than for LM spatial stimuli. This is suggested to be a result of CM stimuli engaging more binocular mechanisms of processing, than LM stimuli, thereby becoming more sensitive to disruptions of binocularity such as those produced in the participants in the present study. CM stimuli are therefore more sensitive to detecting suppression, which is associated with amblyopia.

The aim of the thesis is to present a robust conceptual framework for risk management of non-financial companies in order to improve decision making in the area of hedging with derivative instruments. Application of modern quantitative methods.

In this thesis, we study the estimation of the nonlinear conditionalrisk-neutral density function (RND) in discrete time. Specifically, weevaluate the extent to which the estimated nonlinear conditional RNDvaluable insights to answer relevant economic questions regarding to optionpricing, the measurement of invertors' preferences and portfolio choice.We make use of large dataset of options contracts written on the S&P 500index from 1996 to 2011, to estimate the parameters of the conditional RNDfunctions by minimizing the squared option pricing errors delivered by thenonlinear models studied in the thesis.In the first essay, we show that a semi-nonparametric option pricing modelwith GARCH variance outperforms several benchmarks models in-sample andout-of-sample. In the second essay, we show that a simple two-state regimeswitching model in volatility is not able to fully account for the pricingkernel and the risk aversion puzzle; however, it provides a reasonablecharacterisation of the time-series properties of the estimated riskaversion.In the third essay, we evaluate linear stochastic discount factormodels using an out-of-sample financial metric. We find that multifactormodels outperform the CAPM when this metric is used, and that modelsproducing the best fit in-sample are also those exhibiting the bestperformance out-of-sample.

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.

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.