No description available.

Thesis (Ph. D.)--Florida State University, 2002. / Advisor: Dr. Dennis Moore, Florida State University, College of Arts and Sciences, Dept. of English. Title and description from dissertation home page (viewed Sept. 29, 2003). Includes bibliographical references.

Thesis (Ph. D.)--University of Texas at Austin, 1998. / Vita. Includes bibliographical references (leaves 257-269). Available also in a digital version from Dissertation Abstracts.

Universiẗat, Habil.-Schr., 1998--Stuttgart.

No description available.

O Objetivo deste trabalho é usar uma ferramenta matemática conhecida como expansão de Edgeworth em conjunto com a moderna teoria de análise de derivativos financeiros que utilizam o método de precificação neutra ao risco. Tal expansão permite obter uma função densidade de probabilidade com assimetria e curtose arbitrárias a partir de uma densidade normal. Desta forma, podemos usar esta nova distribuição como a state price density do ativo-objeto procurando corrigir o sorriso da volatilidade através da definição de funções de probabilidade com assimetrias positivas ou negativas e curtose maior de que três. Além disso esperamos também chegar a uma nova maneira de realizar o delta hedge de uma carteira de replicação de modo mais eficiente do que a de Black-Scholes. / There is a well-developed framework, the Black?Scholes theory, for the pricing of contracts based on the future prices of certain assets, called options. This theory assumes that the probability distribution of the returns of the underlying asset is a Gaussian distribution. However, it is observed in the market that this hypothesis is 2awed, leading to the introduction of a fudge factor, the so-called volatility smile. Therefore, it would be interesting to explore extensions of the Black?Scholes theory to non-Gaussian distributions. In this paper, we provide an explicit formula for the price of an option when the distributions of the returns of the underlying asset is parametrized by an Edgeworth expansion, which allows for the introduction of higher independent moments of the probability distribution, namely skewness and kurtosis. We test our formula with options in the Brazilian and American markets, showing that the volatility smile can be reduced. We also check whether our approach leads to more e6cient hedging strategies of these instruments.

Zur Approximation der Dichte von linearen Integralfunktionalen schwach korrelierter Prozesse mit Korrelationslänge wurden bisher Gram-Charlier-Reihen benutzt. In diesem Artikel werden weitere Verfahren zur Dichteapproximation "integraler" Zufallsgrößen beschrieben und untersucht, ob sie sinnvoll auf das Dichteapproximationsproblem bei linearen Integralfunktionalen angewendet werden können.

被廣泛應用在選擇權定價的Black-Scholes 模型[3] 時常在深價內與深價外 的選擇權價格有錯價的現象，也就是理論價格估計實際市場價格的偏差。藉由 Black-Scholes 評價公式所反推出的隱含波動度往往不像我們所期待的在不同履約價格具有一致性，這種現象被稱為波動度的微笑曲線。在這份論文裡，我們參考Jarrow and Rudd [13] 提出的方法，將Edgeworth展開式套用在Black-Scholes模型作延伸應用，進而推導出偏態峰態修正後的的評價公式，再利用台指選擇權的市場資料作實證分析並與Filho and Rosenfeld [1] 的研究作比較。我們發現從台指選擇權的實證結果得到非常態分配的隱含偏態和隱含峰態。此外，理論價格的估計偏誤比例顯著的被新的模型改善且隱含波動度的微笑曲線也變的較為平坦，這個方法提供我們一個有效的方法，利用標的資產的偏態峰態得到該資產的近似分配。 / The Black-Scholes [3] option pricing model widely applied in option contracts frequently misprices deep-in-the-money and deep-out-of-the-money options. The implied volatilities computed by the Black-Scholes formula are not identical on each strike price as we expect. This phenomenon is called the volatility smile or skew. In this thesis, we derived a skewness- and kurtosis-adjusted option pricing model using an Edgeworth expansion constructed by Jarrow and Rudd [13] to an investigation of TAIEX option prices and compare the results with those in Filho and Rosenfeld [1]. We found that non-normal skewness and kurtosis are implied by TAIEX option returns. Moreover, the magnitude of price deviations were signicantly corrected and the volatility skew is attened. This approach provides an useful way to derive an approximate distribution of a underlying security with its skewness and kurtosis.

O Objetivo deste trabalho é usar uma ferramenta matemática conhecida como expansão de Edgeworth em conjunto com a moderna teoria de análise de derivativos financeiros que utilizam o método de precificação neutra ao risco. Tal expansão permite obter uma função densidade de probabilidade com assimetria e curtose arbitrárias a partir de uma densidade normal. Desta forma, podemos usar esta nova distribuição como a state price density do ativo-objeto procurando corrigir o sorriso da volatilidade através da definição de funções de probabilidade com assimetrias positivas ou negativas e curtose maior de que três. Além disso esperamos também chegar a uma nova maneira de realizar o delta hedge de uma carteira de replicação de modo mais eficiente do que a de Black-Scholes. / There is a well-developed framework, the Black?Scholes theory, for the pricing of contracts based on the future prices of certain assets, called options. This theory assumes that the probability distribution of the returns of the underlying asset is a Gaussian distribution. However, it is observed in the market that this hypothesis is 2awed, leading to the introduction of a fudge factor, the so-called volatility smile. Therefore, it would be interesting to explore extensions of the Black?Scholes theory to non-Gaussian distributions. In this paper, we provide an explicit formula for the price of an option when the distributions of the returns of the underlying asset is parametrized by an Edgeworth expansion, which allows for the introduction of higher independent moments of the probability distribution, namely skewness and kurtosis. We test our formula with options in the Brazilian and American markets, showing that the volatility smile can be reduced. We also check whether our approach leads to more e6cient hedging strategies of these instruments.

This dissertation is a study of error in long haul optical fiber systems and how to coupe with them. First we characterize error events occurring during transmission, then we determine lower bounds on information capacity (achievable information rates) and at the end we propose coding schemes for these systems.Existing approaches for obtaining probability density functions (PDFs) for pulse energy in long-haul optical fiber transmission systems rely on numerical simulations or analytical approximations. Numerical simulations make far tails of the PDFs difficult to obtain, while existing analytic approximations are often inaccurate, as they neglect nonlinear interaction between pulses and noise.Our approach combines the instanton method from statistical mechanics to model far tails of the PDFs, with numerical simulations to refine the middle part of the PDFs. We combine the two methods by using an orthogonal polynomial expansion constructed specifically for this problem. We demonstrate the approach on an example of a specific submarine transmission system.Once the channel is characterized estimating achievable information rates is done by a modification of a method originally proposed by Arnold and Pfitser. We give numerical results for the same optical transmission system (submarine system at transmission rate 40Gb/s).The achievable information rate varies with noise and length of the bit patterns considered (among other parameters). We report achievable numerical rates for systems with different noise levels, propagation distances and length of the bit patterns considered.We also propose two iterative decoding schemes suitable for high-speed long-haul optical transmission. One scheme is a modification of a method, originally proposed in the context of magnetic media, which incorporates the BCJR algorithm (to overcomeintersymbol interference) and Low-Density Parity-Check (LDPC) codes for additional error resilience. This is a ``soft decision scheme" -meaning that the decoding algorithm operates with probabilities(instead of binary values). The second scheme is ``hard decision" -it operates with binary values. This scheme is based on the maximum likelihood sequence detection-Viterbi algorithm and a hard decision"Gallager B" decoding algorithm for LDPC codes.