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Maj, Mateusz. "Essays in risk management: conditional expectation with applications in finance and insurance." Doctoral thesis, Universite Libre de Bruxelles, 2012. http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/209668.
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In this work we study two problems motivated by Risk Management: the optimal design of financial products from an investor's point of view and the calculation of bounds and approximations for sums involving non-independent random variables. The element that interconnects these two topics is the notion of conditioning, a fundamental concept in probability and statistics which appears to be a useful device in finance. In the first part of the dissertation, we analyse structured products that are now widespread in the banking and insurance industry. These products typically protect the investor against bearish stock markets while offering upside participation when the markets are bullish. Examples of these products include capital guaranteed funds commercialised by banks, and equity linked contracts sold by insurers. The design of these products is complex in general and it is vital to examine to which extent they are actually interesting from the investor's point of view and whether they cannot be dominated by other strategies. In the academic literature on structured products the focus has been almost exclusively on the pricing and hedging of these instruments and less on their performance from an investor's point of view. In this work we analyse the attractiveness of these products. We assess the theoretical cost of inefficiency when buying a structured product and describe the optimal strategy explicitly if possible. Moreover we examine the cost of the inefficiency in practice. We extend the results of Dybvig (1988a, 1988b) and Cox & Leland (1982, 2000) who in the context of a complete, one-dimensional market investigated the inefficiency of path-dependent pay-offs. In the dissertation we consider this problem in one-dimensional Levy and multidimensional Black-Scholes financial markets and we provide evidence that path-dependent pay-offs should not be preferred by decision makers with a fixed investment horizon, and they should buy path-independent structures instead. In these market settings we also demonstrate the optimal contract that provides the given distribution to the consumer, and in the case of risk- averse investors we are able to propose two ways of improving the design of financial products. Finally we illustrate the theory with a few well-known securities and strategies e.g. dollar cost averaging, buy-and-hold investments and widely used portfolio insurance strategies. The second part of the dissertation considers the problem of finding the distribution of a sum of non- independent random variables. Such dependent sums appear quite often in insurance and finance, for instance in case of the aggregate claim distribution or loss distribution of an investment portfolio. An interesting avenue to cope with this problem consists in using so-called convex bounds, studied by Dhaene et al. (2002a, 2002b), who applied these to sums of log-normal random variables. In their papers they have shown how these convex bounds can be used to derive closed-form approximations for several of the risk measures of such a sum. In the dissertation we prove that unlike the log-normal case the construction of a convex lower bound in explicit form appears to be out of reach for general sums of log-elliptical risks and we show how we can construct stop-loss bounds and we use these to construct mean preserving approximations for general sums of log-elliptical distributions in explicit form.Doctorat en Sciences
info:eu-repo/semantics/nonPublished
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Nuugulu, Samuel Megameno. "Fractional black-scholes equations and their robust numerical simulations." University of the Western Cape, 2020. http://hdl.handle.net/11394/7612.
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Philosophiae Doctor - PhDConventional partial differential equations under the classical Black-Scholes approach have been extensively explored over the past few decades in solving option pricing problems. However, the underlying Efficient Market Hypothesis (EMH) of classical economic theory neglects the effects of memory in asset return series, though memory has long been observed in a number financial data. With advancements in computational methodologies, it has now become possible to model different real life physical phenomenons using complex approaches such as, fractional differential equations (FDEs). Fractional models are generalised models which based on literature have been found appropriate for explaining memory effects observed in a number of financial markets including the stock market. The use of fractional model has thus recently taken over the context of academic literatures and debates on financial modelling.
2023-12-02
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Nilsson, Oscar, and Okumu Emmanuel Latim. "Does Implied Volatility Predict Realized Volatility? : An Examination of Market Expectations." Thesis, Uppsala universitet, Nationalekonomiska institutionen, 2014. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-218792.
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The informational content of implied volatility and its prediction power is evaluated for time horizons of one month. The study covers the period of November 2007 to November 2013 for the two indices S&P500 and OMXS30. The findings are put in relation to the corresponding results for past realized volatility. We find results supporting that implied volatility is an efficient, although biased estimator of realized volatility. Our results support the common notion that implied volatility predicts realized volatility better than past realized volatility, and that it also subsumes most of the informational content of past realized volatility.
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Alston, Rowan Gilbert. "The efficiency of the South African market for rights issues: an application of the Black-Scholes model." Master's thesis, University of Cape Town, 1996. http://hdl.handle.net/11427/14414.
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Bibliography: leaves 87-93.Capital market efficiency is an important aspect of modern financial theory. This is because in an efficient capital market, scarce resources are optimally allocated to productive investments in a way that is beneficial to market participants. Yet there appears to be a dearth of research into the market efficiency of rights issues in South Africa, despite the fact that the majority of equity issues on the JSE are via a rights issue. The problem is that if the market is inefficient it is failing in its role of being an efficient allocator of scarce resources. The objective of this study is to establish whether the South African market for rights issues is efficient.
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TEIXEIRA, THIAGO CARDOSO. "COMPARING BLACK-SCHOLES AND CORRADO-SU: A STUDY ON IMPLIED VOLATILITY APPLIED TO THE BRAZILIAN CALL OPTION MARKET." PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 2011. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=19082@1.
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COORDENAÇÃO DE APERFEIÇOAMENTO DO PESSOAL DE ENSINO SUPERIORPROGRAMA DE SUPORTE À PÓS-GRADUAÇÃO DE INSTS. DE ENSINO
Algumas literaturas sugerem que a volatilidade implícita das opções de compra de ações não deve ser utilizada como estimador para a volatilidade futura. Contudo, estudos recentes e aplicados ao mercado brasileiro de ações comprovaram que em determinados casos existe relação entre a volatilidade implícita e a volatilidade real (ou realizada). Isso significa dizer que a primeira traz informações sobre a última. Nesse contexto, o objetivo deste estudo é comparar a volatilidade implícita de dois modelos de apreçamento de opções com a volatilidade realizada. Entre os modelos de Black-Scholes (1973) e Corrado-Su (1996), utilizando dados de opções de Petrobras e Vale do Rio Doce, foram calculados, através do erro quadrático, aqueles resultados que mais se aproximaram da volatilidade realizada. Estes resultados trazem indícios de que o modelo de Black-Scholes, em média, foi superior ao Corrado-Su no período que vai de janeiro de 2005 a julho de 2009. Porém, o último, por levar em consideração a assimetria e a curtose da distribuição de retornos, chegou mais perto da volatilidade realizada apenas em alguns momentos específicos das economias brasileira e mundial.
Several authors have proposed that implied volatility from purchase options should not be used as an estimate for future volatility. However, recent studies applied to the Brazilian stock market proved that in certain cases there is relation between implied volatility and realized volatility. This means that the first one provides information on the last. In this context, the objective of this study is to compare implied volatilities from two different option pricing models against the realized volatility. The models are Black-Scholes (1973) and Corrado-Su (1996). Working with purchase options on Petrobras and Vale do Rio Doce, it was calculated the difference, by quadratic error, between the implied volatility of these models and the realized volatility. After this, it was checked those results that came closer to the realized volatility. The results provide evidence that the Black-Scholes model, on average, has higher performance than Corrado-Su from January 2005 to July 2009. However, Corrado-Su by taking into account the asymmetry and kurtosis of the distribution of returns came closer to the realized volatility only in specific moments of the Brazilian and global economies.
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Ayana, Haimanot, and Sarah Al-Swej. "A review of two financial market models: the Black--Scholes--Merton and the Continuous-time Markov chain models." Thesis, Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, 2021. http://urn.kb.se/resolve?urn=urn:nbn:se:mdh:diva-55417.
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The objective of this thesis is to review the two popular mathematical models of the financialderivatives market. The models are the classical Black–Scholes–Merton and the Continuoustime Markov chain (CTMC) model. We study the CTMC model which is illustrated by themathematician Ragnar Norberg. The thesis demonstrates how the fundamental results ofFinancial Engineering work in both models.The construction of the main financial market components and the approach used for pricingthe contingent claims were considered in order to review the two models. In addition, the stepsused in solving the first–order partial differential equations in both models are explained.The main similarity between the models are that the financial market components are thesame. Their contingent claim is similar and the driving processes for both models utilizeMarkov property.One of the differences observed is that the driving process in the BSM model is the Brownianmotion and Markov chain in the CTMC model.We believe that the thesis can motivate other students and researchers to do a deeper andadvanced comparative study between the two models.
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Chen, Hung-Hsiang. "An examination of kurtosis of lognormality in the Black-Scholes option pricing formula in the South African warrants market." Master's thesis, University of Cape Town, 2005. http://hdl.handle.net/11427/5771.
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Includes bibliographical references.The assumption of constant asset price volatility of classical Black-Scholes model hasbeen challenged continuously. The symmetrical distribution emphasises a lognormalized asset. This paper aims to investigate the volatility distribution (i.e. kurtosis) of the South African warrants market at Johannesburg Stock Exchange based on a comparison of option implied distributions of the terminal price of the TOP European Call option with lognormal distribution. The result indicates that the constant volatility of Black-Scholes model does not show in the selected warrant market.
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Zhao, Min. "Risk Measures Extracted from Option Market Data Using Massively Parallel Computing." Digital WPI, 2011. https://digitalcommons.wpi.edu/etd-theses/373.
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The famous Black-Scholes formula provided the first mathematically sound mechanism to price financial options. It is based on the assumption, that daily random stock returns are identically normally distributed and hence stock prices follow a stochastic process with a constant volatility. Observed prices, at which options trade on the markets, don¡¯t fully support this hypothesis. Options corresponding to different strike prices trade as if they were driven by different volatilities. To capture this so-called volatility smile, we need a more sophisticated option-pricing model assuming that the volatility itself is a random process. The price we have to pay for this stochastic volatility model is that such models are computationally extremely intensive to simulate and hence difficult to fit to observed market prices. This difficulty has severely limited the use of stochastic volatility models in the practice. In this project we propose to overcome the obstacle of computational complexity by executing the simulations in a massively parallel fashion on the graphics processing unit (GPU) of the computer, utilizing its hundreds of parallel processors. We succeed in generating the trillions of random numbers needed to fit a monthly options contract in 3 hours on a desktop computer with a Tesla GPU. This enables us to accurately price any derivative security based on the same underlying stock. In addition, our method also allows extracting quantitative measures of the riskiness of the underlying stock that are implied by the views of the forward-looking traders on the option markets.
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Gabih, Abdelali, Matthias Richter, and Ralf Wunderlich. "Dynamic optimal portfolios benchmarking the stock market." Universitätsbibliothek Chemnitz, 2005. http://nbn-resolving.de/urn:nbn:de:swb:ch1-200501244.
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The paper investigates dynamic optimal portfolio strategies of utility maximizing portfolio managers in the presence of risk constraints. Especially we consider
the risk, that the terminal wealth of the portfolio falls short of a certain benchmark level which is proportional to the stock price. This risk is measured by the
Expected Utility Loss. We generalize the findings our previous papers to this case.
Using the Black-Scholes model of a complete financial market and applying martingale methods, analytic expressions for the optimal terminal wealth and the optimal
portfolio strategies are given. Numerical examples illustrate the analytic results.
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Kuys, Wilhelm Cornelis. "Black economic empowerment transactions and employee share options : features of non-traded call options in the South African market." Diss., University of Pretoria, 2011. http://hdl.handle.net/2263/27305.
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Employee share options and Black Economic Empowerment deals are financial instruments found in the South African market. Employee share options (ESOs) are issued as a form of non-cash compensation to the employees of the company in addition to their salaries or bonuses. Its value is linked to the share price and since there is no downside risk for the employee his share option is similar to owning a call option on the stock of his employer. Black economic empowerment (BEE) deals in this report refer to those types of transactions structured by listed South African companies to facilitate the transfer of a portion of their ordinary issued share capital to South African individuals or groups who qualify under the Broad-Based Black Economic Empowerment Act of 2003 (“the Act”). This Act requires a minimum percentage of the company to be black-owned in order to address the disproportionate distribution of wealth amongst racial groups in South Africa due to the legacy of Apartheid. These transactions are usually structured in such a way to allow the BEE partner to participate in the upside of the share price beyond a certain level but not in the downside which replicates a call option on the share price of the issuing company. The cost of both ESOs and BEE deals has to be accounted for on the balance sheet of the issuing company at its fair-value. Neither of these instruments can be traded and their extended option lifetimes are features that distinguish these deals significantly from regular traded options for which liquid markets exist. This makes pricing them a non-trivial exercise. A number of types of mathematical models have been developed to take the unique structure features into account to price them as accurately as possible. Research by Huddart&Lang (1995&1996) has shown that option holders often exercise their vested options long before the maturity of the transactions but are unable to quantify a measure that can be used. The wide variety of factors influencing option holders (recent stock price movements, market-to-strike ratio, proximity of vesting dates, time to maturity, share price volatility and wealth of option holder) as well as little exercise data publicly available prevents the options from being priced in a consistent manner. Various assumptions regarding the exercise behaviour of option holders are used that are not based on empirical observations even though the option prices are sensitive to this input. This dissertation provides an overview of the models, inputs and exercise behaviour assumptions that are recognized in pricing both ESOs and BEE deals under IFRS 2 in South Africa. This puts the reader in a position to evaluate all pricing aspects of these deals. Furthermore, their structuring are also analysed in order to identify the general issues related to them. A number of methods to manage the pricing issue surrounding exercise behaviour on ESOs have been considered for the South African market. The ESO Upper Bound-methodology showed that for each strike there is a threshold at which exercise will occur and the employee can invest the after-tax proceeds in a diversified portfolio with a higher expected return than that of the single equity option. This approach reduces the standard Black-Scholes option value without relying on assumptions about the employee’s exercise behaviour and is a viable alternative for the South African market. The derived option value represents the cost of the option. Seven large listed companies’ BEE transactions are dissected and compared against one another using the fair-value of the transaction as a percentage of the market capitalization of the company. The author shows how this measure is a more equitable way of assigning BEE credits to companies than the current practice which is shareholding-based. The current approach does not reward the effort (read cost) that a company has undertaken to transfer shares to black South Africans but only focuses on the amount that is finally owned by the BEE participants. This leaves the transaction vulnerable to a volatile share price and leads to transactions with extended lock-in periods that do not provide much economic benefit to the BEE participants for many years. Other inefficiencies in the type of BEE transactions that have emerged in reaction to the BEE codes that have been published by the South African government are also considered. Finally the funding model that is often used to facilitate these deals is assessed and the risks involved for the funder (bank) is reflected on.Dissertation (MSc)--University of Pretoria, 2011.
Mathematics and Applied Mathematics
unrestricted
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BAUER, HENRIQUE. "SKEWNESS AND KURTOSIS CONES ON BRAZILIAN STOCK CALL OPTIONS MARKET: AN ANALYSIS OF VOLATILITY CONES BEYOND IMPLIED VOLATILITY CALCULATED BY CORRADO-SU AND BLACK-SCHOLES MODELS." PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 2012. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=19876@1.
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PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIROCONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICO
O presente estudo tem como objetivo mostrar a existência de cones de assimetria e curtose no mercado brasileiro de opções. Além disso, os coeficientes de assimetria e curtose são de suma importância para a aplicação do modelo de Corrado e Su (1996). As volatilidades implícitas calculadas pelo método inverso deste modelo serão sobrepostas aos cones de volatilidade, buscando oportunidades de compra ou de venda de volatilidade. Para efeito de comparação, o modelo de Black e Scholes também será utilizado para a extração de tais medidas de volatilidade implícita. Outra contribuição deste trabalho é mostrar se os efeitos do sorriso de volatilidade e da estrutura a termo da volatilidade são amenizados diante de operações realizadas com os cones de volatilidade, levando-se em consideração a volatilidade implícita calculada pelos diferentes modelos. Para isto, foram realizados testes estatísticos de eficiência, além de uma análise descritiva das variáveis mais importantes para uma correta análise do mercado de opções, em momentos de estabilidade e baixa volatilidade como o verificado no ano de 2010. O estudo mostra a existência de cones de assimetria e curtose no mercado brasileiro de opções e possibilidades de ganhos com as operações feitas através dos cones de volatilidade, porém os resultados obtidos pelos dois modelos não apresentaram diferenças estatisticamente significantes.
The present study aims to show the existence of skewness and kurtosis cones in the Brazilian market. In addition, the coefficients of skewness and kurtosis are of paramount importance for the application of the model of Corrado and Su (1996). The implied volatilities calculated by the inverse of this template will be superimposed to the cones of volatility, seeking opportunities to acquire or dispose of volatility. Comparison of Black and Scholes model will also be used for the extraction of such measures of implied volatility. Another contribution of this paper is to show the effects of the volatility smile and term structure of volatility are amenable before operations performed with the cones of volatility, taking into account the implied volatility calculated by different models. For this, statistical tests were performed, efficiency and a descriptive analysis of the most important variables for a correct analysis of the options market, in times of stability and low volatility as the year of 2010. The study showed the existence of skewness and kurtosis cones in the Brazilian market and gains possibilities with volatility cones operations, but the results obtained with the two models didn´t have significative statistics differences.
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Choi, Yang Ho. "Curvature arbitrage." Diss., University of Iowa, 2007. http://ir.uiowa.edu/etd/166.
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Luccas, Aurélio Ubirajara de. "Modelos de precificação de opções com saltos: análise econométrica do modelo de Kou no mercado acionário brasileiro." Universidade de São Paulo, 2007. http://www.teses.usp.br/teses/disponiveis/12/12139/tde-18102007-095122/.
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Esta dissertação revisa a literatura acadêmica existente sobre a teoria de opções utilizando os modelos de precificação com saltos. Os conceitos foram equalizados, a nomenclatura foi padronizada, sendo gerado um material de referência sobre o assunto. O pressuposto de lognormalidade com volatilidade constante não é aceito pelo mercado financeiro. É freqüente, no meio acadêmico, a busca de modelos que reproduzam os fenômenos observados de leptocurtose ou assimetria dos log-retornos financeiros e que possuam a mesma robustez e facilidade para manipulação analítica do consagrado modelo de Black-Scholes. Os modelos com saltos são uma alternativa para esse problema. Avaliou-se o modelo de Kou no mercado acionário brasileiro composto por um componente de difusão que segue um movimento browniano geométrico e um componente de saltos que segue um processo de Poisson com intensidade do salto descrito por uma distribuição duplamente exponencial. A simulação histórica do modelo aponta, em geral, uma superioridade preditiva do modelo, porém as dificuldades de calibração dos parâmetros e de hedge em mercados incompletos são as principais deficiências para o uso dos modelos com saltos.This master dissertation reviews the academic literature about option pricing and hedging with jumps. The theory was equalized and the notation was standardized, becoming this document a reference document about this subject. The log-normality with constant volatility is not accepted by the market. Academics search consistent models with the same analytical capabilities like Black-Scholes? model which can support the observed leptokurtosis or asymmetry of the financial daily log-returns behavior. The jump models are an alternative to these issues. The Kou?s model was evaluated and this one consists of two parts: the first part being continuous and following a geometric Brownian motion and the second being a jump process with its jump intensity defined by a double exponential distribution. The model backtesting showed a better predictive performance of the Kou´s model against other models. However, there are some handicaps regarding to the parameters calibration and hedging.
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Ganbold, Sanjaasuren, and Andrey Falileev. "Does the existence of option affect cross-listed stock prices? - Empirical investigation of whether there is any effect on stock prices caused by option existence (a study on hardware & technology companies)." Thesis, Umeå universitet, Företagsekonomi, 2014. http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-96177.
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Lazier, Iuri. "Hedge de opção utilizando estratégias dinâmicas multiperiódicas autofinanciáveis em tempo discreto em mercado incompleto." Universidade de São Paulo, 2009. http://www.teses.usp.br/teses/disponiveis/12/12139/tde-11092009-103057/.
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Este trabalho analisa três estratégias de hedge de opção, buscando identificar a importância da escolha da estratégia para a obtenção de um bom desempenho do hedge. O conceito de hedge é analisado de forma retrospectiva e uma teoria geral de hedge é apresentada. Em seguida são descritos alguns estudos comparativos de desempenho de estratégias de hedge de opção e suas metodologias de implementação. Para esta análise comparativa são selecionadas três estratégias de hedge de opção de compra do tipo européia: a primeira utiliza o modelo Black-Scholes-Merton de precificação de opções, a segunda utiliza uma solução de programação dinâmica para hedge dinâmico multiperiódico e a terceira utiliza um modelo GARCH para precificação de opções. As estratégias são comentadas e comparadas do ponto de vista de suas premissas teóricas e por meio de testes comparativos de desempenho. O desempenho das estratégias é comparado sob uma perspectiva dinâmicamente ajustada, multiperiódica e autofinanciável. Os dados para comparação de desempenho são gerados por simulação e o desempenho é avaliado pelos erros absolutos médios e erros quadráticos médios, resultantes na carteira de hedge. São feitas ainda considerações a respeito de alternativas de estimação e suas implicações no desempenho das estratégias.This work analyzes three option hedging strategies, to identify the importance of choosing a strategy in order to achieve a good hedging performance. A retrospective analysis of the concept of hedging is conducted and a general hedging theory is presented. Following, some comparative papers of hedging performance and their implementation methodologies are described. For the present comparative analysis, three hedging strategies for European options have been selected: the first one based on the Black-Scholes-Merton model for option pricing, the second one based on a dynamic programming solution for dynamic multiperiod hedging and the third one based on a GARCH model for option pricing. The strategies are compared under their theoric premisses and through comparative performance testes. The performances of the strategies are compared under a dynamically adjusted multiperiodic and self-financing perspective. Data for performance comparison are generated by simulation and performance is evaluated by mean absolute errors and mean squared errors resulting on the hedging portfolio. An analysis is also done regarding estimation approaches and their implications over the performance of the strategies.
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Summonte, Chiara. "FX modelling under collateralization." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2016. http://amslaurea.unibo.it/11454/.
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We present the market practice for interest rate yield curves construction and pricing interest rate derivatives. Then we give a brief description of the Vasicek and the Hull-White models, with an example of calibration to market data.
We generalize the classical Black-Scholes-Merton pricing formulas, considering more general cases such as perfect or partial collateral, derivatives on a dividend paying asset subject to repo funding, and multiple currencies.
Finally we derive generic pricing formulae for different combinations of cash flow and collateral currencies, and we apply the results to the pricing of FX swaps and CCS, and we discuss curve bootstrapping.
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Campi, Luciano. "Marchés financiers avec une infinité d'actifs, couverture quadratique et délits d'initiés." Phd thesis, Université Pierre et Marie Curie - Paris VI, 2003. http://tel.archives-ouvertes.fr/tel-00004331.
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Cette thèse consiste en une série d'applications du calcul stochastique aux mathématiques financières. Elle est composée de quatre chapitres. Dans le premier on étudie le rapport entre la complétude du marché et l'extrémalité des mesures martingales equivalentes dans le cas d'une infinité d'actifs. Dans le deuxième on trouve des conditions équivalentes à l'existence et unicité d'une mesure martingale equivalente sous la quelle le processus des prix suit des lois n-dimensionnelles données à n fixe. Dans le troisième on étend à un marché admettant une infinité dénombrable d'actifs une charactérisation de la stratégie de couverture optimale (pour le critère moyenne-variance) basé sur une technique de changement de numéraire et extension artificielle. Enfin, dans le quatrième on s'occupe du problème de couverture d'un actif contingent dans un marché avec information asymetrique.
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Hung, Chen-Hui, and 洪丞輝. "A Multidimensional Fitted Finite Volume Method for the Black-Scholes Equation Governing Option Pricing." Thesis, 2004. http://ndltd.ncl.edu.tw/handle/34468120105026895506.
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碩士國立中山大學
應用數學系研究所
92
In this paper we present a finite volume method for a two-dimensional Black-Scholes equation with stochastic volatility governing European option pricing. In this work, we first formulate the Black-Scholes equation with a tensor (or matrix) diffusion coefficient into a conversative form. We then present a finite volume method for the resulting equation, based on a fitting technique proposed for a one-dimensional Black-Scholes equation. We show that the method is monotone by proving that the system matrix of the discretized equation is an M-matrix. Numerical experiments, performed to demonstrate the usefulness of the method, will be presented.
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Marques, Pedro. "Impact of Black-Scholes assumptions on Delta Hedging." Master's thesis, 2016. http://hdl.handle.net/10362/16850.
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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.
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Chen, Le-Hsuan, and 陳樂軒. "The Inference of Price Limits on Black-Scholes Model in Taiwan Stock Market." Thesis, 2005. http://ndltd.ncl.edu.tw/handle/94298856879059930023.
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碩士國立成功大學
統計學系碩博士班
93
In order to avoid heavy volatility on the trades in the Taiwan Stock Market, the daily price limit (up and down 7%) for each stock has been imposed by the R.O.C. official Ministry of Finance since October 1989. After imposing the restriction, the standard Black-Scholes model to the option price is still used as the model for estimation. Unfortunately, the impact of price limit was not clear by using the standard B-S model. In this study, the following objectives will be accomplished: 1. After imposing the daily price limit on Taiwan Stock Market, we modify the distribution assumption on the rate of return to doubly truncated normal. 2. Establishing the “new B-S model” by the doubly truncated normal distribution while all other assumptions remain unchanged as the standard Black-Scholes model required. 3. Using historical stock price data to estimate the volatility of the distribution on the rate of return that is one of the important factors for evaluating option price. 4. Verifying the basic properties of “new B-S model” to see if they agree to those of the “standard Black-Scholes model”. 5. Comparing the difference among the option prices evaluated by the “new B-S model”, the “standard B-S model”, and the settlement option prices provided by Taiwan Future Exchange. The data support the use of the “new B-S model” and the “standard B-S model” to the market with restriction.
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Cheng, Chung-Hsing, and 成中興. "The efficiency research of option market – Black-Scholes pricing model apply to the TXO." Thesis, 2003. http://ndltd.ncl.edu.tw/handle/82196954401316870245.
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碩士輔仁大學
應用統計學研究所
91
This paper discussed the efficiency of Taiwan Stock Index option（TXO） using in the initial stage of listing company. The case study was conducted from January to December in 2002.The opening & closing prices of Taiwan Stock Market Index correspond with option prices. In spot transaction, we used weighted index number to simulate the coming issue of Exchange Traded Funds.（ETF） First, this research is using the Black- Scholes model to find the theoretical price then compare this price with the market price from non-parametric test to examine the variance. Secondly, we deduce arbitrage model and establish the regression model to anticipate both the index closing prices and corresponding option prices, then we run the model to get the arbitrage recompense. Finally, we examine whether its error has any differential, then we judge the market efficiency. Based on the findings, some conclusions are made as follows: 1.There are variances between theoretical price and market price of purchase right during the research period. 2.The regression anticipation model of this research has fairly high abilities of explanation and anticipation. 3.Examine the rate error result shows that Taiwan Stock Market Index option has arbitrage space whether you add the dealing cost or not. In other words, it’s inefficient in the beginning of option market.
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Chang, Wen-Teng, and 張文騰. "An Empirical Study on Taiwan Warrant Market: Comparisons among AMM, CRR, and Black-Scholes Models." Thesis, 2001. http://ndltd.ncl.edu.tw/handle/62229597580754094966.
Full textAbstract:
碩士輔仁大學
管理學研究所
89
The reset warrants issued in 1999 brought the warrant market new wave in Taiwan. At the same time, Figlewski and Gao advanced the Adaptive Mesh Model (AMM) that appeared in theory elastically and efficiently in pricing barrier options. Except evaluating the ability of the AMM to price the call warrants in Taiwan, the study also used the well-known Black-Scholes model and the CRR model to compare the pricing results. The samples included 29 plain vanilla warrants and 8 reset warrants. The observation period was from 1997 to 2001.The purposes of the study are as follows: 1.Observing the regressive results, composing the market prices of the warrants and the theoretical prices of the warrants that the AMM valued by regression analysis. 2.With the percent error analysis to check the degree of mis-pricing. 3.Comparing the theoretical prices and the market prices of the AMM, the CRR model, and the Black-Scholes model to determine the suitability of the AMM in the warrant market in Taiwan. The results were found that the pricing effect of the AMM was not as good as that of the CRR model and the Black-Scholes model, especially in the condition of deep-out-the-money. If it was no longer to match the kurtosis and it gave up the symmetrical assumption, the pricing efficiency would be improved. In addition, the efficiency of the AMM was much better than that of the CRR model in the reset periods for the reset warrants.
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Jen-Chun-Li and 黎仁鈞. "The Method of the Optimal Volatility Estimator In Taiwan Index Options Market under Black and Scholes Model." Thesis, 2004. http://ndltd.ncl.edu.tw/handle/04601085117948163229.
Full textAbstract:
碩士淡江大學
管理科學研究所碩士班
94
Taiwan Futures Exchange has distributed the Taiwan Index Option since 2001, suggested that took the option appraisal tool by Black and Scholes Model. In the model contains five variables, respectively be the Underlying Asset price, Exercise Price, Risklss rate of interest, the Period of Maturity and Volatility. It is not easy thing to predict the volatility precisely. The purpose of this research is to find a suitable estimation method to evaluate the price of Taiwan Index Options and find out which estimator is the best. By using intra data of Taiwan Index Options that are collected from morning 9:00 to 1:30 pm between 07/01/2004 to 12/31/2004 as our sample. In this research, we design four types of volatilities including twenty methods. Four types are History Volatility, Garch Volatility, Implied Volatility and GAIV. The estimated values generated from the models were then bring into the Black and Scholes Model and to evaluate the difference between market price and theory market price with a target to find the optimal volatility measure method. The result we find out whether the options are Calls or Puts VGIV is the best estimator which makes least price errors. The effect of the estimator of Time Series Model is general not good, especially History Volatility. And GAIV can improves the effect of GARCH Volatility which makes the theory market price aloof from the market price.
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Lupi, Diego Juan Nasareno. "Métodos computacionales para el cálculo de la volatilidad implícita del modelo de Black Scholes." Bachelor's thesis, 2020. http://hdl.handle.net/11086/16058.
Full textAbstract:
Tesis (Lic. en Cs. de la Computación)--Universidad Nacional de Córdoba, Facultad de Matemática, Astronomía, Física y Computación, 2020.Las finanzas cuantitativas constituyen, desde hace varias décadas, un área particular de estudio dentro de la matemática. Esta nueva disciplina surge de la necesidad de encontrar modelos cuantitativos que permitan describir el comportamiento aleatorio de activos financieros y, en particular, valorar los productos llamados derivados financieros. Si la hipótesis sobre la dinámica de los activos es que estos siguen un proceso estocástico lognormal, con tendencia y volatilidad constante, entonces la valoración de una opción call sobre el activo está dada por la fórmula de Black-Scholes. Ahora bien, dado que la volatilidad no es observable en el mercado, se define la volatilidad implícita del activo como aquella que iguala la prima del mercado con el valor dado por la fórmula. La obtención de este parámetro de volatilidad implícita permite luego valorar otros derivados financieros como así también comprender movimientos propios del mercado.
In this work, different methods were proposed for calculating the implicit volatility on European calls. The determination of the implied volatility requires the implementation of numerical methods to solve a nonlinear equation without a closed solution. In recent years, many approaches have emerged to use machine learning to model the function that provides implied volatility empirically. This work includes a bibliographic exploration of the implicit volatility concept and its implications, and a survey of computational methods to implement its calculation. It also includes the effective computer implementation of some solutions and a comparative analysis of the computational efficiency of the different methods studied.
Fil: Lupi, Diego Juan Nasareno. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía, Física y Computación; Argentina.
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Chen, Chang-Chih, and 陳昌志. "Pricing and Hedging Strategies of Vulnerable Black-Scholes Option on Defaultable Securities subject to the Intersection of Market and Credit Risk." Thesis, 2005. http://ndltd.ncl.edu.tw/handle/09542402961734392443.
Full textAbstract:
碩士國立高雄第一科技大學
財務管理所
93
ABSTRACT This paper is the first article using reduced-form model to provide the close-form solution for vulnerable options written on the risky securities while counterparty risk depends on reference risk. Our framework extends Jarrow and Turnbull (2000) and Jarrow and Yu (2001) to develop a general model for appraising options subject to the intersection of market and credit risk in various conditions. The availability of this integrated model allows for the pricing of vulnerable options written either on defaultable securities or default-free securities and of default-free options written on defaultable securities. Numerical analysis verifies that counterparty and reference risk can have the reversed impact on the behavior of the option value, and also discover that the sensitivity of the option value to the reference risk is obviously greater than to the counterparty risk. Under twofold default risk, vulnerable option may be more costly than non-vulnerable option.
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Barbosa, Joana Margarida de Sousa. "Are structured products fairly priced?: Barrier reverse convertibles and turbo warrants in the Swiss market." Master's thesis, 2020. http://hdl.handle.net/10071/21625.
Full textAbstract:
The investments in structured products have been increasing in the past few years and,
jointly, also the complexity of such products has substantially intensified.
In accordance, this thesis was developed with the objective to present the current status of
the structured products market, namely in Switzerland, as it is the one of the most developed
markets in Europe. Hence, it was analysed a sample of Barrier Reverse Convertibles and
Turbo Warrants issued by the biggest Swiss financial institutions, which will permit a clear
overview of the price fairness of these financial derivatives and, consequently, support more
accurate and informed investment decisions.
In fact, this thesis was based on previous studies which revealed that the vast majority of this
type of products is substantially overpriced. Thus, besides than presenting a practical
overview of this reality, other main objective was to understand the reasons and motivations
of investors that could justify the increasing demand for such products.
Based on the theoretical price obtained using the Black & Scholes (1973) and Merton (1973)
model, and comparing that value with the market price, it was possible to conclude that, in
general, all products presented an overprice considered economically relevant, being Barrier
Reverse Convertibles typically more overpriced than Turbo Warrants. Regarding the main
issuers of each type of product, Bank Vontobel was the financial institution with most fairly
priced products related to Turbo Warrants, while Bank Julius Baer should be the safest choice
for investments in Barrier Reverse Convertibles.Os investimentos em produtos estruturados têm vindo a aumentar nos últimos anos e, a par dessa evolução, também a complexidade desses produtos se tem intensificado substancialmente. Neste sentido, esta dissertação foi desenvolvida com o objetivo de retratar o estado atual do mercado de produtos estruturados, nomeadamente na Suíça, por ser um dos mercados mais desenvolvidos da Europa. Deste modo, foi analisada uma amostra de Barrier Reverse Convertibles e Turbo Warrants emitidos pelas maiores instituições financeiras suíças, o que permitirá uma visão clara dos preços destes derivados financeiros e, consequentemente, suportar decisões de investimento mais precisas e informadas. A presente tese foi baseada em estudos anteriores, os quais revelaram que o preço da grande maioria deste tipo de produtos está substancialmente inflacionado. Assim, além de apresentar resultados práticos e representativos dessa realidade, outro objetivo principal passou também por entender as razões e motivações dos investidores que justificar o aumento da procura de tais produtos. Com base no preço teórico obtido pelo modelo Black & Scholes (1973) e Merton (1973), e comparando esse valor com o preço de mercado, foi possível concluir que, em geral, todos os produtos apresentaram uma inflação de preço considerada economicamente relevante, sendo este resultado mais evidente em Barrier Reverse Covertibles comparativamente a Turbo Warrants. Em relação aos principais emissores de cada tipo de produto, o Banco Vontobel foi a instituição financeira com preços mais justos, relativamente a Turbo Warrants, enquanto o Banco Julius Baer deverá ser a escolha mais segura para investimentos em Barrier Reverse Convertibles.
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Costa, João de Andrade Dias da. "Carbon markets and emission derivatives: The pricing of derivatives in the EU ETS." Master's thesis, 2012. http://hdl.handle.net/10071/6241.
Full textAbstract:
The European Union’s Emissions Trading Scheme (EU ETS) is the world’s largest carbon market operating and an important piece for European environmental policy. Launched in 2005, this market-scheme trades allowances and derivatives’ contracts that represent the right to emit a certain amount of pollutant gases.
This work intends to understand the role of carbon markets in general, and the pricing of derivatives’ contracts traded in the EU ETS. It was taken as basis the Black-Scholes (1973) model and its further extensions by Merton (1973) and Merton (1976), applying then a model suggested by Daskalakis, Psychoyios and Markellos (2009) to value a call option written on emission allowances. The numerical results suggest that time to maturity and the moneyness degree had influence in the options’ price, while the jump intensity did not have an influence in the obtained results
Based on the application of the model, it was then derived, using the put-call parity, the value of a put option under the same basic features.
It was also conducted a sensitivity analysis to the call option, in which it was concluded that, under the model specifications, volatility shows a strong influence within the studied call options’ value.O Sistema Europeu de Comércio de Emissões (EU ETS) é o maior mercado de emissões em funcionamento a nível mundial e uma peça chave em termos de política ambiental na Europa. Lançado em 2005, este sistema de mercado é utilizado para a comercialização de direitos e produtos derivados sobre a emissão de uma certa quantidade de gases poluentes. Este trabalho procura compreender a função dos mercados de carbono em geral e a valorização de produtos derivados em comercialização no EU ETS. Para tal tomou-se por base o modelo de Black-Scholes (1973) e suas extensões por Merton (1973) e Merton (1976), aplicando-se depois o modelo sugerido por Daskalakis, Psychoyios e Markellos (2009) de modo a valorizar uma opção call sobre direitos de emissões. Os resultados alcançados sugerem que o tempo até à maturidade e o nível do preço de exercício contribuíram para a alteração no valor da opção, ao passo que a intensidade do “salto” não teve influência nos resultados alcançados. Com base na aplicação deste modelo, foi igualmente obtido o valor de uma opção put com as mesmas características, através da paridade put-call. Foi ainda feita uma análise de sensibilidade à opção call, na qual se concluiu que, de acordo com as especificações do modelo, a volatilidade tem uma forte influência no valor das opções call estudadas.
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Laubscher, Eugene Rudolph. "Capital market theories and pricing models : evaluation and consolidation of the available body of knowledge." Diss., 2001. http://hdl.handle.net/10500/17174.
Full textAbstract:
The study investigates whether the main capital market theories and pricing models provide
a reasonably accurate description of the working and efficiency of capital markets,
of the pricing of shares and options and the effect the risk/return relationship has on investor
behaviour. The capital market theories and pricing models included in the study
are Portfolio Theory, the Efficient Market Hypothesis (EMH), the Capital Asset Pricing
Model (CAPM), the Arbitrage Pricing Theory (APT), Options Theory and the BlackScholes
(8-S) Option Pricing Model.
The main conclusion of the study is that the main capital market theories and pricing
models, as reviewed in the study, do provide a reasonably accurate description of
reality, but a number of anomalies and controversial issues still need to be resolved.
The main recommendation of the study is that research into these theories and models
should continue unabated, while the specific recommendations in a South African context
are the following: ( 1) the benefits of global diversification for South African investors
should continue to be investigated; (2) the level and degree of efficiency of the JSE Securities
Exchange SA (JSE) should continue to be monitored, and it should be established
whether alternative theories to the EMH provide complementary or better descriptions
of the efficiency of the South African market; (3) both the CAPM and the APT
should continue to be tested, both individually and jointly, in order to better understand
the pricing mechanism of, and risk/return relationship on the JSE; (4) much South
African research still needs to be conducted on the efficiency of the relatively new
options market and the application of the B-S Option Pricing Model under South African
conditions.Financial Accounting
M. Com. (Accounting)