The DICER Model: Methodological Issues and Initial Results

31 p.

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.

A Radial Basis Function Approach to Financial Time Series Analysis

Nonlinear multivariate statistical techniques on fast computers offer the potential to capture more of the dynamics of the high dimensional, noisy systems underlying financial markets than traditional models, while making fewer restrictive assumptions. This thesis presents a collection of practical techniques to address important estimation and confidence issues for Radial Basis Function networks arising from such a data driven approach, including efficient methods for parameter estimation and pruning, a pointwise prediction error estimator, and a methodology for controlling the "data mining'' problem. Novel applications in the finance area are described, including customized, adaptive option pricing and stock price prediction.

Financial modelling with 2-EPT probability density functions

The class of all Exponential-Polynomial-Trigonometric (EPT) functions is classical and equal to the Euler-d’Alembert class of solutions of linear differential equations with constant coefficients. The class of non-negative EPT functions defined on [0;1) was discussed in Hanzon and Holland (2010) of which EPT probability density functions are an important subclass. EPT functions can be represented as ceAxb, where A is a square matrix, b a column vector and c a row vector where the triple (A; b; c) is the minimal realization of the EPT function. The minimal triple is only unique up to a basis transformation. Here the class of 2-EPT probability density functions on R is defined and shown to be closed under a variety of operations. The class is also generalised to include mixtures with the pointmass at zero. This class coincides with the class of probability density functions with rational characteristic functions. It is illustrated that the Variance Gamma density is a 2-EPT density under a parameter restriction. A discrete 2-EPT process is a process which has stochastically independent 2-EPT random variables as increments. It is shown that the distribution of the minimum and maximum of such a process is an EPT density mixed with a pointmass at zero. The Laplace Transform of these distributions correspond to the discrete time Wiener-Hopf factors of the discrete time 2-EPT process. A distribution of daily log-returns, observed over the period 1931-2011 from a prominent US index, is approximated with a 2-EPT density function. Without the non-negativity condition, it is illustrated how this problem is transformed into a discrete time rational approximation problem. The rational approximation software RARL2 is used to carry out this approximation. The non-negativity constraint is then imposed via a convex optimisation procedure after the unconstrained approximation. Sufficient and necessary conditions are derived to characterise infinitely divisible EPT and 2-EPT functions. Infinitely divisible 2-EPT density functions generate 2-EPT Lévy processes. An assets log returns can be modelled as a 2-EPT Lévy process. Closed form pricing formulae are then derived for European Options with specific times to maturity. Formulae for discretely monitored Lookback Options and 2-Period Bermudan Options are also provided. Certain Greeks, including Delta and Gamma, of these options are also computed analytically. MATLAB scripts are provided for calculations involving 2-EPT functions. Numerical option pricing examples illustrate the effectiveness of the 2-EPT approach to financial modelling.

A study of the Hobson and Rogers volatility model

We firstly examine the model of Hobson and Rogers for the volatility of a financial asset such as a stock or share. The main feature of this model is the specification of volatility in terms of past price returns. The volatility process and the underlying price process share the same source of randomness and so the model is said to be complete. Complete models are advantageous as they allow a unique, preference independent price for options on the underlying price process. One of the main objectives of the model is to reproduce the `smiles' and `skews' seen in the market implied volatilities and this model produces the desired effect. In the first main piece of work we numerically calibrate the model of Hobson and Rogers for comparison with existing literature. We also develop parameter estimation methods based on the calibration of a GARCH model. We examine alternative specifications of the volatility and show an improvement of model fit to market data based on these specifications. We also show how to process market data in order to take account of inter-day movements in the volatility surface. In the second piece of work, we extend the Hobson and Rogers model in a way that better reflects market structure. We extend the model to take into account both first and second order effects. We derive and numerically solve the pde which describes the price of options under this extended model. We show that this extension allows for a better fit to the market data. Finally, we analyse the parameters of this extended model in order to understand intuitively the role of these parameters in the volatility surface.

A new proposition on the martingale representation theorem and on the approximate hedging of contingent claim in mean-variance criterion

In this work we revisit the problem of the hedging of contingent claim using mean-square criterion. We prove that in incomplete market, some probability measure can be identified so that becomes -martingale under .This is in fact a new proposition on the martingale representation theorem. The new results also identify a weight function that serves to be an approximation to the Radon-Nikodým derivative of the unique neutral martingale measure.

Long-term equity anticipation securities and stock market volatility dynamics

Recent empirical findings suggest that the long-run dependence in U.S. stock market volatility is best described by a slowly mean-reverting fractionally integrated process. The present study complements this existing time-series-based evidence by comparing the risk-neutralized option pricing distributions from various ARCH-type formulations. Utilizing a panel data set consisting of newly created exchange traded long-term equity anticipation securities, or leaps, on the Standard and Poor's 500 stock market index with maturity times ranging up to three years, we find that the degree of mean reversion in the volatility process implicit in these prices is best described by a Fractionally Integrated EGARCH (FIEGARCH) model. © 1999 Elsevier Science S.A. All rights reserved.

Latent Stick-Breaking Processes.

We develop a model for stochastic processes with random marginal distributions. Our model relies on a stick-breaking construction for the marginal distribution of the process, and introduces dependence across locations by using a latent Gaussian copula model as the mechanism for selecting the atoms. The resulting latent stick-breaking process (LaSBP) induces a random partition of the index space, with points closer in space having a higher probability of being in the same cluster. We develop an efficient and straightforward Markov chain Monte Carlo (MCMC) algorithm for computation and discuss applications in financial econometrics and ecology. This article has supplementary material online.

Numerical solutions of certain nonlinear models in European options on a distributed computing environment

Financial modelling in the area of option pricing involves the understanding of the correlations between asset and movements of buy/sell in order to reduce risk in investment. Such activities depend on financial analysis tools being available to the trader with which he can make rapid and systematic evaluation of buy/sell contracts. In turn, analysis tools rely on fast numerical algorithms for the solution of financial mathematical models. There are many different financial activities apart from shares buy/sell activities. The main aim of this chapter is to discuss a distributed algorithm for the numerical solution of a European option. Both linear and non-linear cases are considered. The algorithm is based on the concept of the Laplace transform and its numerical inverse. The scalability of the algorithm is examined. Numerical tests are used to demonstrate the effectiveness of the algorithm for financial analysis. Time dependent functions for volatility and interest rates are also discussed. Applications of the algorithm to non-linear Black-Scholes equation where the volatility and the interest rate are functions of the option value are included. Some qualitative results of the convergence behaviour of the algorithm is examined. This chapter also examines the various computational issues of the Laplace transformation method in terms of distributed computing. The idea of using a two-level temporal mesh in order to achieve distributed computation along the temporal axis is introduced. Finally, the chapter ends with some conclusions.

On the Viability of Microservers for Financial Analytics

Energy consumption and total cost of ownership are daunting challenges for Datacenters, because they scale disproportionately with performance. Datacenters running financial analytics may incur extremely high operational costs in order to meet performance and latency requirements of their hosted applications. Recently, ARM-based microservers have emerged as a viable alternative to high-end servers, promising scalable performance via scale-out approaches and low energy consumption. In this paper, we investigate the viability of ARM-based microservers for option pricing, using the Monte Carlo and Binomial Tree kernels. We compare an ARM-based microserver against a state-of-the-art x86 server. We define application-related but platform-independent energy and performance metrics to compare those platforms fairly in the context of datacenters for financial analytics and give insight on the particular requirements of option pricing. Our experiments show that through scaling out energyefficient compute nodes within a 2U rack-mounted unit, an ARM-based microserver consumes as little as about 60% of the energy per option pricing compared to an x86 server, despite having significantly slower cores. We also find that the ARM microserver scales enough to meet a high fraction of market throughput demand, while consuming up to 30% less energy than an Intel server

Iso-Quality of Service: Fairly Ranking Servers for Real-Time Data Analytics

We present a mathematically rigorous Quality-of-Service (QoS) metric which relates the achievable quality of service metric (QoS) for a real-time analytics service to the server energy cost of offering the service. Using a new iso-QoS evaluation methodology, we scale server resources to meet QoS targets and directly rank the servers in terms of their energy-efficiency and by extension cost of ownership. Our metric and method are platform-independent and enable fair comparison of datacenter compute servers with significant architectural diversity, including micro-servers. We deploy our metric and methodology to compare three servers running financial option pricing workloads on real-life market data. We find that server ranking is sensitive to data inputs and desired QoS level and that although scale-out micro-servers can be up to two times more energy-efficient than conventional heavyweight servers for the same target QoS, they are still six times less energy efficient than high-performance computational accelerators.

Methods and Metrics for Fair Server Assessment under Real-Time Financial Workloads

We present a rigorous methodology and new metrics for fair comparison of server and microserver platforms. Deploying our methodology and metrics, we compare a microserver with ARM cores against two servers with ×86 cores running the same real-time financial analytics workload. We define workload-specific but platform-independent performance metrics for platform comparison, targeting both datacenter operators and end users. Our methodology establishes that a server based on the Xeon Phi co-processor delivers the highest performance and energy efficiency. However, by scaling out energy-efficient microservers, we achieve competitive or better energy efficiency than a power-equivalent server with two Sandy Bridge sockets, despite the microserver's slower cores. Using a new iso-QoS metric, we find that the ARM microserver scales enough to meet market throughput demand, that is, a 100% QoS in terms of timely option pricing, with as little as 55% of the energy consumed by the Sandy Bridge server.

Influência do risco de incumprimento nos retornos de capital

Sempre foi do interesse das instituições financeiras de crédito determinar o risco de incumprimento associado a uma empresa por forma a avaliar o seu perfil. No entanto, esta informação é útil a todos os stakeholders de uma empresa, já que também estes comprometem uma parte de si ao interagirem com esta. O aumento do número de insolvências nos últimos anos tem reafirmado a necessidade de ampliar e aprofundar a pesquisa sobre o stress financeiro. A identificação dos fatores que influenciam a determinação do preço dos ativos sempre foi do interesse de todos os stakeholders, por forma a antecipar a variação dos retornos e agir em sua conformidade. Nesta dissertação será estudada a influência do risco de incumprimento sobre os retornos de capital, usando como indicador do risco de incumprimento a probabilidade de incumprimento obtida segundo o modelo de opções de Merton (1974). Efetuou-se esta análise durante o período de Fevereiro de 2002 a Dezembro de 2011, utilizando dados de empresas Portuguesas, Espanholas e Gregas. Os resultados evidenciam uma relação negativa do risco de incumprimento com os retornos de capital, que é devida a um efeito momentum e à volatilidade. A par disso, também se demonstra que o tamanho e o book-to-market não são representativos do risco de incumprimento na amostra aqui utilizada, ao contrário do que Fama & French (1992; 1996) afirmavam.

Essays on Applications of the Factor Model

Thesis (Ph.D.)--University of Washington, 2013

Three essays on the term structure of interest rates

A PhD Dissertation, presented as part of the requirements for the Degree of Doctor of Philosophy from the NOVA - School of Business and Economics