Problemas inversos em engenharia financeira: regularização com critério de entropia

Esta dissertação aplica a regularização por entropia máxima no problema inverso de apreçamento de opções, sugerido pelo trabalho de Neri e Schneider em 2012. Eles observaram que a densidade de probabilidade que resolve este problema, no caso de dados provenientes de opções de compra e opções digitais, pode ser descrito como exponenciais nos diferentes intervalos da semireta positiva. Estes intervalos são limitados pelos preços de exercício. O critério de entropia máxima é uma ferramenta poderosa para regularizar este problema mal posto. A família de exponencial do conjunto solução, é calculado usando o algoritmo de Newton-Raphson, com limites específicos para as opções digitais. Estes limites são resultados do princípio de ausência de arbitragem. A metodologia foi usada em dados do índice de ação da Bolsa de Valores de São Paulo com seus preços de opções de compra em diferentes preços de exercício. A análise paramétrica da entropia em função do preços de opções digitais sínteticas (construídas a partir de limites respeitando a ausência de arbitragem) mostraram valores onde as digitais maximizaram a entropia. O exemplo de extração de dados do IBOVESPA de 24 de janeiro de 2013, mostrou um desvio do princípio de ausência de arbitragem para as opções de compra in the money. Este princípio é uma condição necessária para aplicar a regularização por entropia máxima a fim de obter a densidade e os preços. Nossos resultados mostraram que, uma vez preenchida a condição de convexidade na ausência de arbitragem, é possível ter uma forma de smile na curva de volatilidade, com preços calculados a partir da densidade exponencial do modelo. Isto coloca o modelo consistente com os dados do mercado. Do ponto de vista computacional, esta dissertação permitiu de implementar, um modelo de apreçamento que utiliza o princípio de entropia máxima. Três algoritmos clássicos foram usados: primeiramente a bisseção padrão, e depois uma combinação de metodo de bisseção com Newton-Raphson para achar a volatilidade implícita proveniente dos dados de mercado. Depois, o metodo de Newton-Raphson unidimensional para o cálculo dos coeficientes das densidades exponenciais: este é objetivo do estudo. Enfim, o algoritmo de Simpson foi usado para o calculo integral das distribuições cumulativas bem como os preços do modelo obtido através da esperança matemática.

Self-licensing and financial rewards: is morality for sale?

This paper studies the impact of financially rewarding good deeds on self-licensing. We run a between-subjects experiment comprised of an adapted dictator game preceded by paid and unpaid pro-environmental tasks. We find that prefacing the dictator game with an unpaid good deed seems to establish a 'moral rectitude' which licenses subsequent selfish behaviour, whereas a paid good deed dampens this effect. Interestingly, the nature of the initial task has more of an effect on the binary option (give vs. not give) than on the amount donated.

Classification with a reject option using a hinge loss

We consider the problem of binary classification where the classifier can, for a particular cost, choose not to classify an observation. Just as in the conventional classification problem, minimization of the sample average of the cost is a difficult optimization problem. As an alternative, we propose the optimization of a certain convex loss function φ, analogous to the hinge loss used in support vector machines (SVMs). Its convexity ensures that the sample average of this surrogate loss can be efficiently minimized. We study its statistical properties. We show that minimizing the expected surrogate loss—the φ-risk—also minimizes the risk. We also study the rate at which the φ-risk approaches its minimum value. We show that fast rates are possible when the conditional probability P(Y=1|X) is unlikely to be close to certain critical values.

Role of corporate governance in mitigating the selective disclosure of executive stock option information

We examine the nature and extent of statutory executive stock option (ESO) disclosures by Australian listed companies over the 2001 to 2004 period, and the influence of corporate governance mechanisms on these disclosures. Our results show a progressive increase in overall compliance from 2001 to 2004. However, despite the improved compliance, the results reveal managements’ continued reluctance to disclose more sensitive ESO information. Factors associated with good internal governance, including board independence, audit committee independence and effectiveness, and compensation committee independence and effectiveness are found to contribute to improved compliance. Similarly, certain external governance factors are associated with improved disclosure, including external auditor quality, shareholder activism (as proxied by companies identified as poor performers by the Australian Shareholders’ Association), and regulatory intervention.

The relationship between implied and realized volatility : evidence from the Australian stock index option market

This paper examines the relationship between the volatility implied in option prices and the subsequently realized volatility by using the S&P/ASX 200 index options (XJO) traded on the Australian Stock Exchange (ASX) during a period of 5 years. Unlike stock index options such as the S&P 100 index options in the US market, the S&P/ASX 200 index options are traded infrequently and in low volumes, and have a long maturity cycle. Thus an errors-in-variables problem for measurement of implied volatility is more likely to exist. After accounting for this problem by instrumental variable method, it is found that both call and put implied volatilities are superior to historical volatility in forecasting future realized volatility. Moreover, implied call volatility is nearly an unbiased forecast of future volatility.

Don’t judge a superannuation default investment option by its name

With the massive decline in savings arising from the Global Financial Crisis (GFC), it is timely to review superannuation fund investment and disclosure strategies in the lead-up to the crisis. Accordingly, this study examines differences among superannuation funds’ default investment options in terms of naming and framing over three years from 2005 to 2007, as presented in product disclosure statements (PDSs). The findings indicate that default options are becoming more alike regardless of their name, and consequently, members may face increasing difficulties in distinguishing between balanced and growth-named default options when comparing them across superannuation funds. Comparability is also likely to be constrained by variations in the framing of default options presented in investment option menus in PDSs. These findings highlight the need for standardisation of default option definitions and disclosures to ensure descriptive accuracy, transparency and comparability.

Assignment of reversion on put option contained in a lease : what is the effect?

Justice Mullins of the Queensland Supreme Court recently considered the status of a put option contained in a registered lease in circumstances where there was an assignment of the reversion. The matter arose for determination in Denham Bros Ltd v W Freestone Leasing Pty Ltd [2002] QSC 307. The decision is of interest as a lease containing a put option, exercisable by a landlord, is perhaps less commonly encountered than a lease containing a call option, exercisable by a tenant.

Design of experiments for bivariate binary responses modelled by Copula functions

Optimal design for generalized linear models has primarily focused on univariate data. Often experiments are performed that have multiple dependent responses described by regression type models, and it is of interest and of value to design the experiment for all these responses. This requires a multivariate distribution underlying a pre-chosen model for the data. Here, we consider the design of experiments for bivariate binary data which are dependent. We explore Copula functions which provide a rich and flexible class of structures to derive joint distributions for bivariate binary data. We present methods for deriving optimal experimental designs for dependent bivariate binary data using Copulas, and demonstrate that, by including the dependence between responses in the design process, more efficient parameter estimates are obtained than by the usual practice of simply designing for a single variable only. Further, we investigate the robustness of designs with respect to initial parameter estimates and Copula function, and also show the performance of compound criteria within this bivariate binary setting.