Dynamic delta hedging of autocallables under a discrete rebalancing context

This work tests different delta hedging strategies for two products issued by Banco de Investimento Global in 2012. The work studies the behaviour of the delta and gamma of autocallables and their impact on the results when delta hedging with different rebalancing periods. Given its discontinuous payoff and path dependency, it is suggested the hedging portfolio is rebalanced on a daily basis to better follow market changes. Moreover, a mixed strategy is analysed where time to maturity is used as a criterion to change the rebalancing frequency.

Impact of Black-Scholes assumptions on Delta Hedging

In this work we are going to evaluate the different assumptions used in the Black- Scholes-Merton pricing model, namely log-normality of returns, continuous interest rates, inexistence of dividends and transaction costs, and the consequences of using them to hedge different options in real markets, where they often fail to verify. We are going to conduct a series of tests in simulated underlying price series, where alternatively each assumption will be violated and every option delta hedging profit and loss analysed. Ultimately we will monitor how the aggressiveness of an option payoff causes its hedging to be more vulnerable to profit and loss variations, caused by the referred assumptions.

Hedging de opções com ativos : base cujos preços seguem processos de difusão com salto

Na presente dissertação foi implementado um modelo para execução de hedging de mínima variância de opções de compra européias em mercados incompletos, considerando um espaço de tempo discreto e contínuo de estados. O desempenho foi medido de forma comparativa tomando como base a popular estratégia delta-hedging em um grande número de simulações, a partir de cenários definidos com o objetivo de submeter o modelo a diversas situações. A trajetória do preço do ativo objeto foi representada por um processo de difusão com saltos, composto por duas parcelas: (i) um processo de Wiener, cuja principal característica é ser uma função contínua e diferenciável em todos os pontos, e (ii) por um processo de Poisson, responsável por inserir descontinuidades na trajetória.

Uso de modelos econométricos en aseguramiento de portafolios

El aseguramiento de portafolio trae consigo unos costos de transacción asociados que son reconocidos por la teoría financiera pero que no han sido objeto de estudio de muchas aproximaciones empíricas. Mediante modelos econométricos de series de tiempo se puede pronosticar el número de rebalanceos necesarios para mantener un portafolio asegurado, así como el tiempo que debe transcurrir entre cada uno de estos. Para tal fin se usan modelos de Datos de Cuenta de Poisson Autorregresivos (ACP) modificados para captar las características de la serie y modelos de Duración Autorregresivos (ACD). Los modelos capturan la autocorrelación de las series y pronostican adecuadamente el costo de transacción asociado a los rebalanceos.

Precificação de opções de dólar no mercado brasileiro utilizando redes neurais e algoritmos genéticos

Esse trabalho comparou, para condições macroeconômicas usuais, a eficiência do modelo de Redes Neurais Artificiais (RNAs) otimizadas por Algoritmos Genéticos (AGs) na precificação de opções de Dólar à Vista aos seguintes modelos de precificação convencionais: Black-Scholes, Garman-Kohlhagen, Árvores Trinomiais e Simulações de Monte Carlo. As informações utilizadas nesta análise, compreendidas entre janeiro de 1999 e novembro de 2006, foram disponibilizadas pela Bolsa de Mercadorias e Futuros (BM&F) e pelo Federal Reserve americano. As comparações e avaliações foram realizadas com o software MATLAB, versão 7.0, e suas respectivas caixas de ferramentas que ofereceram o ambiente e as ferramentas necessárias à implementação e customização dos modelos mencionados acima. As análises do custo do delta-hedging para cada modelo indicaram que, apesar de mais complexa, a utilização dos Algoritmos Genéticos exclusivamente para otimização direta (binária) dos pesos sinápticos das Redes Neurais não produziu resultados significativamente superiores aos modelos convencionais.

The meaning of implied volatility in pricing stock options traded in options markets

Ph.D. in the Faculty of Business Administration

A Nonparametric Approach to Pricing and Hedging Derivative Securities via Learning Networks

We propose a nonparametric method for estimating derivative financial asset pricing formulae using learning networks. To demonstrate feasibility, we first simulate Black-Scholes option prices and show that learning networks can recover the Black-Scholes formula from a two-year training set of daily options prices, and that the resulting network formula can be used successfully to both price and delta-hedge options out-of-sample. For comparison, we estimate models using four popular methods: ordinary least squares, radial basis functions, multilayer perceptrons, and projection pursuit. To illustrate practical relevance, we also apply our approach to S&P 500 futures options data from 1987 to 1991.

Arbitragem estatística com opções utilizando modelo de volatilidade incerta e hedging estático

Com o objetivo de identificar oportunidades de arbitragem estatística no mercado de opções brasileiro, este trabalho utiliza o modelo de volatilidade incerta e o conceito de Hedging Estático, no apreçamento de um portfólio composto por diversas opções. São também incluídos os custos de transação relacionados a estruturação de um portfólio livre de risco, obtendo assim um modelo que pode ser facilmente implementado através da utilização do método de diferenças finitas explicito. Na aplicação do modelo ao mercado de opções sobre a ação preferencial da Petrobrás (PETR4), foi estabelecido um critério para estabelecer a frequência do ajuste do delta hedge do portfólio livre de risco de maneira a não incorrer em custos de transação elevados. Foi escolhido o período entre 19/05/08 e 20/01/14 para analisar o desempenho do modelo, selecionando-se em cada data de cálculo um conjunto de 11 opções de diferentes strikes e mesmo vencimento para compor o portfólio. O modelo apresentou um bom desempenho quando desconsiderados os custos de transação na apuração do resultado da estratégia de arbitragem, obtendo na maior parte dos casos resultados positivos. No entanto, ao incorporar os custos de transação, o desempenho obtido pelo modelo foi ruim, uma vez que na maior parte dos casos o resultado apresentado foi negativo.

Hedging options in a garch environment: testing the term structure of stochastic volatility models

This paper develops a methodology for testing the term structure of volatility forecasts derived from stochastic volatility models, and implements it to analyze models of S&P500 index volatility. U sing measurements of the ability of volatility models to hedge and value term structure dependent option positions, we fmd that hedging tests support the Black-Scholes delta and gamma hedges, but not the simple vega hedge when there is no model of the term structure of volatility. With various models, it is difficult to improve on a simple gamma hedge assuming constant volatility. Ofthe volatility models, the GARCH components estimate of term structure is preferred. Valuation tests indicate that all the models contain term structure information not incorporated in market prices.

Hepatitis B (HBV), Hepatitis C (HCV) and Hepatitis Delta (HDV) Viruses in the Colombian Population-How Is the Epidemiological Situation?

Background: Viral hepatitis B, C and delta still remain a serious problem worldwide. In Colombia, data from 1980s described that HBV and HDV infection are important causes of hepatitis, but little is known about HCV infection. The aim of this study was to determine the currently frequency of HBV, HCV and HDV in four different Colombian regions. Methodology/Principal Findings: This study was conducted in 697 habitants from 4 Colombian departments: Amazonas, Choco, Magdalena and San Andres Islands. Epidemiological data were obtained from an interview applied to each individual aiming to evaluate risk factors related to HBV, HCV or HDV infections. All samples were tested for HBsAg, anti-HBc, anti-HBs and anti-HCV markers. Samples that were positive to HBsAg and/or anti-HBc were tested to anti-HDV. Concerning the geographical origin of the samples, the three HBV markers showed a statistically significant difference: HBsAg (p = 0.033) and anti-HBc (p < 0.001) were more frequent in Amazonas and Magdalena departments. Isolated anti-HBs (a marker of previous vaccination) frequencies were: Choco (53.26%), Amazonas (32.88%), Magdalena (17.0%) and San Andres (15.33%) p < 0.001. Prevalence of anti-HBc increased with age; HBsAg varied from 1.97 to 8.39% (p = 0.033). Amazonas department showed the highest frequency for anti-HCV marker (5.68%), while the lowest frequency was found in San Andres Island (0.66%). Anti-HDV was found in 9 (5.20%) out of 173 anti-HBc and/or HBsAg positive samples, 8 of them from the Amazonas region and 1 from them Magdalena department. Conclusions/Significance: In conclusion, HBV, HCV and HDV infections are detected throughout Colombia in frequency levels that would place some areas as hyperendemic for HBV, especially those found in Amazonas and Magdalena departments. Novel strategies to increase HBV immunization in the rural population and to strengthen HCV surveillance are reinforced by these results.

X-ray diffraction data of tibolone Delta(4) isomer (isotibolone)

Tibolone is used for hormone reposition of postmenopause women and isotibolone is considered the major degradation product of tibolone. Isotibolone can also be present in tibolone API raw materials due to some inadequate synthesis. Its presence is then necessary to be identified and quantified in the quality control of both API and drug products. In this work we present the indexing of an isotibolone X-ray diffraction pattern measured with synchrotron light (lambda=1.2407 angstrom) in the transmission mode. The characterization of the isotibolone sample by IR spectroscopy, elemental analysis, and thermal analysis are also presented. The isotibolone crystallographic data are a=6.8066 angstrom, b=20.7350 angstrom, c=6.4489 angstrom, beta=76.428 degrees, V=884.75 angstrom(3), and space group P2(1), rho(o)= 1.187 g cm(-3), Z=2. (C) 2009 International Centre for Diffraction Data. [DOI: 10.1154/1.3257612]

Facies, delta(13)C, delta(15)N and C/N analyses in a late Quaternary compound estuarine fill, northern Brazil and relation to sea level

The present work integrates sedimentary facies, (14)C dating, delta(13)C, delta(15)N, and C/N with geologic and geomorphologic data available from literature. The aim was to characterize the depositional settings of a late Quaternary estuary in northeastern Marajo Island and analyze its evolution within the context of relative sea level fluctuations. The data derive from four continuous cores along a proximal-to-distal transect of a paleoestuary, previously recognized using remote sensing information. Fifteen sediment samples recorded ages ranging from 42,580 +/- 1430 to 3184 +/- 37 (14)C yr B.P. Fades analysis indicated fine- to coarse-grained sands with parallel lamination or cross stratification, massive or laminated muds and heterolithic deposits. delta(13)C (-28.1 parts per thousand to -19.7 parts per thousand, mean = -23.0 parts per thousand), delta(15)N (+ 14.8 parts per thousand to + 4.7 parts per thousand, mean = + 9.2 parts per thousand) and C/N (14.5 to 1.5, mean = 7.9) indicate mostly marine and freshwater phytoplankton sources for the organic matter. The results confirm a large late Quaternary paleoestuary in northeastern Marajo Island. The distribution of delta(13)C, delta(15)N, and C/N, together with fades associations, led to identify depositional settings related to fluvial channel, floodplain, tidal channel/tidal flat, central basin, tidal delta, and tidal inlet/sand barrier. These deposits are consistent with a wave-dominated estuary. Variations in stratigraphy and geochemistry are controlled by changes in relative sea level, revealing a main transgression from an undetermined time around 42,000 (14)C yr B.P. and 29,340 (+/- 200) (14)C yr B.P., which is synchronous to the overall drop in sea level after the last interglacial. Following this period, and probably until 9110 +/- 37 (14)C yr B.P., i.e., during a time interval encompassing two glacial episodes including the Last Glacial and the Younger Dryas, there was a pronounced drop in sea level, recorded by the development of a major erosional discontinuity due to valley re-incision. Sea level rose again until 5464 +/- 40 (14)C yr B.P, just before the main worldwide mid-Holocene transgressive peak. Mid to late Holocene coastal progradation ended the Marajo paleoestuarine history, and promoted the establishment of continental conditions throughout the island. The divergence comparing the Marajo sea level behavior with the eustatic curve allows hypothesizing that post-rifting tectonics along the Brazilian Equatorial margin influenced the sedimentary evolution of the studied paleoestuary. Considering that sedimentary facies in estuarine settings are highly variable both laterally and vertically, the present integration of facies with isotope and elemental analyses was crucial to provide a more precise interpretation of the Late Pleistocene and Holocene Marajo paleoestuary, and analyze its sea level history within the eustatic and tectonic context. (C) 2010 Elsevier B.V. All rights reserved.

Quaternary paleoenvironments and relative sea-level changes in Marajo Island (Northern Brazil): Facies, delta(13)C, delta(15)N and C/N

The reconstruction of physical environments of Amazonian areas is of great interest to determine the dynamic evolution of the Amazon drainage basin. However. few studies have emphasized the Quaternary deposits in this region. which is mostly due to the lack of natural exposures imposed by the low topography. This work integrates facies analysis. radiocarbon dating, delta(13)C, delta(15)N, and C/N of an 124 m-thick core from an area located at the mouth of the Amazon River. northeastern Amazonia. The study records deposits up to 50.795 (14)C yr B P. in age. which formed in a variety of depositional environments including fluvial channel, tidal flat, outer estuarine basin to shallow marine. inner estuarine basin, estuarine channel and lagoon. Facies interpretation was significantly improved with the inclusion of delta(13)C, delta(15)N, and C/N analyses of organic matter extracted from the sediments The obtained values conform to a transitional. mostly estuarine paleosetting evolved during successive relative sea-level fluctuations. The results suggest fluvial deposition between 40,950 (+/- 590) and 50.795 (14)C yr B P, with a rise in relative sea level that commenced between 35,567 (+/- 649) and 39,079 (+/- 1114) (14)C yr B P. An overall transgression took place until 29,340 (+/- 340) (14)C yr B P., after which the relative sea level dropped, favoring valley rejuvenation and incision. Following this time up to 10,479 (+/- 34) (14)C yr B.P. a rise in relative sea level filled up the valley with estuarine deposits After 10.479(+/- 34) (14)C yr B.P., the estuary was replaced by a lagoon At the end of the Holocene, the coastline prograided approximately 45 km northward, replaci ng the lagoon by a lake system Despite the influence of eustatic fluctuations. regional tectonics played a significant role to create new space where these Late Pleistocene and Holocene sediments accumulated. (C) 2009 Elsevier B V All rights reserved.

Ischaemic preconditioning improves proteasomal activity and increases the degradation of delta PKC during reperfusion

The response of the myocardium to an ischaemic insult is regulated by two highly homologous protein kinase C (PKC) isozymes, delta and epsilon PKC. Here, we determined the spatial and temporal relationships between these two isozymes in the context of ischaemia/reperfusion (I/R) and ischaemic preconditioning (IPC) to better understand their roles in cardioprotection. Using an ex vivo rat model of myocardial infarction, we found that short bouts of ischaemia and reperfusion prior to the prolonged ischaemic event (IPC) diminished delta PKC translocation by 3.8-fold and increased epsilon PKC accumulation at mitochondria by 16-fold during reperfusion. In addition, total cellular levels of delta PKC decreased by 60 +/- 2.7% in response to IPC, whereas the levels of epsilon PKC did not significantly change. Prolonged ischaemia induced a 48 +/- 11% decline in the ATP-dependent proteasomal activity and increased the accumulation of misfolded proteins during reperfusion by 192 +/- 32%; both of these events were completely prevented by IPC. Pharmacological inhibition of the proteasome or selective inhibition of epsilon PKC during IPC restored delta PKC levels at the mitochondria while decreasing epsilon PKC levels, resulting in a loss of IPC-induced protection from I/R. Importantly, increased myocardial injury was the result, in part, of restoring a delta PKC-mediated I/R pro-apoptotic phenotype by decreasing pro-survival signalling and increasing cytochrome c release into the cytosol. Taken together, our findings indicate that IPC prevents I/R injury at reperfusion by protecting ATP-dependent 26S proteasomal function. This decreases the accumulation of the pro-apoptotic kinase, delta PKC, at cardiac mitochondria, resulting in the accumulation of the pro-survival kinase, epsilon PKC.