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Sun, Xihao. "Pricing Options with Monte Carlo and Binomial Tree Methods." Digital WPI, 2011. https://digitalcommons.wpi.edu/etd-theses/687.
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This report describes our work in pricing options using computational methods. First, I collected the historical asset prices for assets in four economic sectors to estimate model parameters, such as asset returns and covariances. Then I used these parameters to model asset prices using multiple geometric Brownian motion and simulate new asset prices. Using the generated prices, I used Monte Carlo methods and control variates to price call options. Next I used the binomial tree model to price put options, which I was introduced to in the course Math 571: Financial Mathematics I. Using the estimated put and call option prices together with some stocks, I formed a portfolio in an Interactive Brokers paper account . This project was done a part of the masters capstone course Math 573: Computational Methods of Financial Mathematics.
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Van, Wyk Ettienne. "Binomial and trinomial tree methods in derivatives pricing / Ettienne van Wyk." Thesis, North-West University, 2006. http://hdl.handle.net/10394/1269.
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Tree methods for the valuation of financial derivative securities represent a recognized
and well-established pricing paradigm. It has formed part of the financial engineer's
"toolbox" for close on 30 years. The tree approach is multi-dimensional though: there
are for example, various ways in which trees can be parameterized. Incorporating eccentricities
of the financial markets like the paying of discrete dividends and volatility
skews add some further complexity to the approach. A full perspective on the place
of tree methods requires knowledge of the relation between the said and other pricing
paradigms like numerical integration techniques and finite difference methods. Convergence
properties are of definite interest to a practitioner as well. This dissertation
aims to provide a general introduction to tree methods, and well by treating on the
enumerated issues.Thesis (M.Sc. (Risk Analysis))--North-West University, Potchefstroom Campus, 2007.
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Stewart, Thomas Gordon. "Generalized Random Walks, Their Trees, and the Transformation Method of Option Pricing." Diss., CLICK HERE for online access, 2008. http://contentdm.lib.byu.edu/ETD/image/etd2608.pdf.
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Yang, Yuankai. "Pricing American and European options under the binomial tree model and its Black-Scholes limit model." Thesis, Linnéuniversitetet, Institutionen för matematik (MA), 2017. http://urn.kb.se/resolve?urn=urn:nbn:se:lnu:diva-68264.
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We consider the N step binomial tree model of stocks. Call options and put options of European and American type are computed explicitly. With appropriate scaling in time and jumps, convergence of the stock prices and the option prices are obtained as N-> infinite. The obtained convergence is the Black-Scholes model and, for the particular case of European call option, the Black-Scholes formula is obtained. Furthermore, the Black-Scholes partial differential equation is obtained as a limit from the N step binomial tree model. Pricing of American put option under the Black-Scholes model is obtained as a limit from the N step binomial tree model. With this thesis, option pricing under the Black-Scholes model is achieved not by advanced stochastic analysis but by elementary, easily understandable probability computation. Results which in elementary books on finance are mentioned briefly are here derived in more details. Some important Java codes for N step binomial tree option prices are constructed by the author of the thesis.
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Lewenhaupt, Hugo. "Optimizing the Number of Time-steps Used in Option Pricing." Thesis, Linköpings universitet, Institutionen för datavetenskap, 2019. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-159648.
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Calculating the price of an option commonly uses numerical methods and can becomputationally heavy. In general, longer computations result in a more precisresult. As such, improving existing models or creating new models have been thefocus in the research field. More recently the focus has instead shifted towardcreating neural networks that can predict the price of a given option directly.This thesis instead studied how the number of time-steps parameter can beoptimized, with regard to precision of the resulting price, and then predict theoptimal number of time-steps for other options. The number of time-stepsparameter determines the computation time of one of the most common models inoption pricing, the Cox-Ross-Rubinstein model (CRR). Two different methodsfor determining the optimal number of time-steps were created and tested. Bothmodels use neural networks to learn the relationship between the input variablesand the output. The first method tried to predict the optimal number oftime-steps directly. The other method instead tried to predict the parameters ofan envelope around the oscillations of the option pricing method. It wasdiscovered that the second method improved the performance of the neuralnetworks tasked with predicting the optimal number of time-steps. It was furtherdiscovered that even though the best neural network that was found significantlyoutperformed the benchmark method, there was no significant difference incalculation times, most likely because the range of log moneyness and pricesthat were used. It was also noted that the neural network tended tounderestimate the parameter and that might not be a desirable property of asystem in charge of estimating a price in the financial sector.
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Twarog, Marek B. "Pricing security derivatives under the forward measure." Link to electronic thesis, 2007. http://www.wpi.edu/Pubs/ETD/Available/etd-053007-142223/.
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Ribeiro, Lucas Vioto dos Santos. "Modelos de precificação de Opções Americanas a partir de plataformas paralelas." Universidade de São Paulo, 2017. http://www.teses.usp.br/teses/disponiveis/55/55137/tde-05022018-103941/.
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O objetivo desta dissertação é fornecer primeiramente o arcabouço necessário para o entendimento do derivativo opções, muito utilizado nos mercados financeiros mundiais, e posteriormente executar precificações de opções americanas a partir dos modelos dos mínimos quadrados de Monte Carlo (LSM), o modelo de árvore binomial com extrapolação de Richardson e a aproximação analítica de Bjerksund e Stensland (B&S), aplicando duas plataformas de processamento paralelo computacional, a TPL (Task Parallel Library) nativa no .NET framework 4.5 e a plataforma CUDA (Compute Unified Device Architecture), demonstrando o comparativo dos resultados obtidos a cada modelo diante de cada plataforma.The objective of this dissertation is to provide first the necessary framework for the understanding of the derivative options, widely used in the world financial markets, and later to execute the American option pricing from Monte Carlo least squares models (LSM), the binomial tree model with Richardson extrapolation and the Bjerksund and Stensland analytic approach (BJS) by applying two parallel computational processing platforms, the native TPL (Task Parallel Library) in the .NET framework 4.5 and the CUDA platform (Compute Unified Device Architecture), demonstrating the comparison of the obtained results to each model before each platform.
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Lendacký, Peter. "Modely úrokovej miery a ocenenie úrokových opcií." Master's thesis, Vysoká škola ekonomická v Praze, 2010. http://www.nusl.cz/ntk/nusl-18693.
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The interest rate dynamics is an important fundamental for valuation more complex structures of interest rate derivatives. The goal of this diploma thesis is to describe the use of models of interest rate for interest rate option pricing. The paper could be logically divided into two parts, the theoretical one and practical one. In the first part the essentials for pricing theory are introduced as risk neutrality, martingales, stochastic differential calculus, and theory of arbitrage. On their basis four basic yield curve models are derived, Vasicek model, model Cox-Ingersoll-Ross , Black-Derman-Toy and two factor Heath-Jarrow-Morton model. Second part provides the analysis of yields of U.S. Treasury bonds with different maturity. At the end CIR model and BDT binomial tree are used for valuation of option on 10 years yield.
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Coelho, Afonso Valente Ricardo de Seabra. "American options and the Black-Scholes Model." Master's thesis, Instituto Superior de Economia e Gestão, 2020. http://hdl.handle.net/10400.5/20735.
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Mestrado em Mathematical FinanceOs problemas de apreçamento de opções têm sido um dos principais assuntos de em Matemática Financeira, desde a criação desse conceito nos anos 70. Mais especificamente, as opções americanas são de grande interesse nesta área do conhecimento porque são matematicamente muito mais complexas do que as opções europeias padrão e o modelo de Black-Scholes não fornece, na maioria dos casos, uma fórmula explícita para a determinação do preço deste tipo de opções. Nesta dissertação, mostramos como o estudo de opções americanas conduz à análise de problemas de fronteira livre devido à possibilidade de exercício antecipado, onde nosso principal objetivo é encontrar o preço de exercício ótimo. Também apresentamos a reformulação do problema em termos de um problema de complementaridade linear e de desigualdade variacional parabólica. Além disso, também abordamos a caracterização probabilística das opções americanas com base no conceito de tempos de paragem ótima. Essas formulações, aqui tratadas em termos analíticos ou probabilísticos, podem ser muito úteis na aplicação de métodos numéricos ao problema de precificação de opções do estilo americano, uma vez que, na maioria dos casos, é quase impossível encontrar soluções explícitas. Além disso, utilizamos o Método da Árvore Binomial, que é um método numérico muito simples do ponto de vista matemático, para ilustrar alguns aspectos da teoria estudada ao longo desta tese e para comparar as opções americanas com as opções europeias e bermudas, por meio de alguns exemplos numéricos.
Option pricing problems have been one of the main focuses in the field of Mathematical Finance since the creation of this concept in the 1970s. More specifically, American options are of great interest in this area of knowledge because they are much more complex mathematically than the standard European options and the Black-Scholes model cannot give an explicit formula to value this style options in most cases. In this dissertation, we show how pricing American options leads to free boundary problems because of the possibility of early exercise, where our main goal is to find the optimal exercise price. We also present how to reformulate the problem into a linear complementarity problem and a parabolic variational inequality. Moreover, we also address the probabilistic characterization of American options based on the concept of stopping times. These formulations, here viewed from the analytical and probabilistic point of view, can be very useful for applying numerical methods to the problem of pricing American style options since, in most cases, it is almost impossible to find explicit solutions. Furthermore, we use the Binomial Tree Method, which is a very simple numerical method from the mathematical point of view, to illustrate some aspects of the theory studied throughout this thesis and to compare American options with European and Bermudan Options, by means of a few numerical examples.
info:eu-repo/semantics/publishedVersion
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Bock, Alona Verfasser], and Ralf [Akademischer Betreuer] [Korn. "Edgeworth Expansions for Binomial Trees / Alona Bock. Betreuer: Ralf Korn." Kaiserslautern : Technische Universität Kaiserslautern, 2014. http://d-nb.info/1058104284/34.
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Bock, Alona [Verfasser], and Ralf [Akademischer Betreuer] Korn. "Edgeworth Expansions for Binomial Trees / Alona Bock. Betreuer: Ralf Korn." Kaiserslautern : Technische Universität Kaiserslautern, 2014. http://nbn-resolving.de/urn:nbn:de:hbz:386-kluedo-38616.
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Karungi, Doreen, and Wenqing Huang. "Applications of ROA to Value a Dotcom Start-up and a Professional Basketball player." Thesis, Mälardalens högskola, Akademin för hållbar samhälls- och teknikutveckling, 2012. http://urn.kb.se/resolve?urn=urn:nbn:se:mdh:diva-14793.
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This paper attempts to evaluate a dotcom start-up company and a professional young basketball player using Real Option Analysis in the investors’ points of view. That is, we are standing in the financers’ shoes and valuing both cases if they are worth investing in. We believe that real option analysis is the most appropriate valuation method from our current knowledge compared to other traditional valuation methods notably like the Net Present Value (NPV), therefore we try to prove that using both qualitative and quantitative descriptions. The authors concentrate more on applying quantitative methods than giving detailed definitions of real options. Binomial Pricing Model and Monte Carlo simulation with the help of MS Excel and MATLAB were used in the evaluation. The paper consists of two case studies, each tackled differently but both summarized up all together. The paper concludes with a table exhibiting when real options are valuable and a belief that game theory is essential in ROA.Matlab Codes and Simulation&Binary Tree Model(Excel)
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CASTILLO, OSCAR ENRIQUE MIRANDA. "A REAL OPTION MODEL FOR VALUING PROJECTS USING IMPLIED BINOMIAL TREES ADJUSTED BY PROJECT SKEWNESS AND KURTOSIS." PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 2017. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=36994@1.
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PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIROCOORDENAÇÃO DE APERFEIÇOAMENTO DO PESSOAL DE ENSINO SUPERIOR
PROGRAMA DE SUPORTE À PÓS-GRADUAÇÃO DE INSTS. DE ENSINO
A avaliação dos projetos de investimentos é uma tarefa difícil para muitas empresas, especialmente para aqueles cujo fluxo de caixa depende dos preços das commodities, já que o nível de incerteza nos preços tem um alto impacto na determinação do momento adequado para o investimento. Os métodos de avaliação tradicionais, que não levam em consideração a flexibilidade gerencial nem a modelagem da incerteza do projeto, podem levar a decisões não ótimas. Esta pesquisa desenvolve um modelo que considera estas variáveis, usando árvores binomiais implícitas ajustados por outros indicadores de risco, como assimetria e curtose da rentabilidade do projeto. O nível de incerteza pode não só ser medido pela volatilidade do retorno do projeto, mas também pela probabilidade de se obter um resultado baixo ou negativo no projeto. A magnitude dessa probabilidade poderia ser a avaliada conhecendo-se o valor da assimetria e curtose do retorno do projeto. Para modelar o comportamento de um projeto, esta dissertação apresenta dois tipos de árvores binomiais implícitas, recombinantes e não recombinante. Cada árvore tem sua própria abordagem específica para determinar o valor do projeto, incluindo opções. Um caso aplicado é apresentado considerando uma empresa de mineração. Os resultados sugerem que o nível de assimetria contribui para uma melhor avaliação do risco do projeto, que combinado com a metodologia de opções reais captura melhor o valor das flexibilidades do projeto; o que é uma importante contribuição do modelo proposto nesta dissertação.
Valuation of capital investment projects is a difficult task for many companies, especially for those whose cash flows depend on commodity prices. The level of uncertainty in commodity prices has a significant impact in determining the proper timing for an investment. Traditional valuation methods, which do not take into account managerial flexibility or project uncertainty modeling can lead to non-optimal decisions. This research develops a dynamic model that considers these variables, and uses implied binomial trees adjusted by other indicators of risk, such as project return s skewness and kurtosis. The level of uncertainty can not only be measured by the project return s volatility, but also by how probable is the occurrence of a low or negative result in the project. The magnitude of this probability could be assessed by knowing the project return s skewness and kurtosis. To model the project s behavior, this dissertation presents two kinds of implied binomial trees, recombining and non-recombining trees. Each tree has its own specific approach to determining the value of the project, including options or managerial flexibility. An applied case is presented considering a mining project. The results suggest that the level of skewness helps to have a better measure of project risk, which combined with the real option approach, allows capturing the value of project managerial flexibilities; which is an important contribution of the proposed model in this dissertation.
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Arotiba, Gbenga Joseph. "Pricing American Style Employee Stock Options having GARCH Effects." Thesis, University of the Western Cape, 2010. http://etd.uwc.ac.za/index.php?module=etd&action=viewtitle&id=gen8Srv25Nme4_3057_1298615964.
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We investigate some simulation-based approaches for the valuing of the employee stock options. The mathematical models that deal with valuation of such options include the work of Jennergren and Naeslund [L.P Jennergren and B. Naeslund, A comment on valuation of executive stock options and the FASB proposal, Accounting Review 68 (1993) 179-183]. They used the Black and Scholes [F. Black and M. Scholes, The pricing of options and corporate liabilities, Journal of Political Economy 81(1973) 637-659] and extended partial differential equation for an option that includes the early exercise. Some other major relevant works to this mini thesis are Hemmer et al. [T Hemmer, S. Matsunaga and T Shevlin, The influence of risk diversification on the early exercise of employee stock options by executive officers, Journal of Accounting and Economics 21(1) (1996) 45-68] and Baril et al. [C. Baril, L. Betancourt, J. Briggs, Valuing employee stock options under SFAS 123 R using the Black-Scholes-Merton and lattice model approaches, Journal of Accounting Education 25 (1-2) (2007) 88-101]. The underlying assets are studied under the GARCH (generalized autoregressive conditional heteroskedasticity) effects. Particular emphasis is made on the American style employee stock options.
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Baptiste, Julien. "Problèmes numériques en mathématiques financières et en stratégies de trading." Thesis, Paris Sciences et Lettres (ComUE), 2018. http://www.theses.fr/2018PSLED009.
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Le but de cette thèse CIFRE est de construire un portefeuille de stratégies de trading algorithmique intraday. Au lieu de considérer les prix comme une fonction du temps et d'un aléa généralement modélisé par un mouvement brownien, notre approche consiste à identifier les principaux signaux auxquels sont sensibles les donneurs d'ordres dans leurs prises de décision puis alors de proposer un modèle de prix afin de construire des stratégies dynamiques d'allocation de portefeuille. Dans une seconde partie plus académique, nous présentons des travaux de pricing d'options européennes et asiatiquesThe aim of this CIFRE thesis is to build a portfolio of intraday algorithmic trading strategies. Instead of considering stock prices as a function of time and a brownian motion, our approach is to identify the main signals affecting market participants when they operate on the market so we can set up a prices model and then build dynamical strategies for portfolio allocation. In a second part, we introduce several works dealing with asian and european option pricing
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Aldossary, Fahad. "Valuation of callable convertible bonds using binomial trees model with default risk, convertible hedging and arbitrage, duration and convexity." Thesis, University of Sussex, 2018. http://sro.sussex.ac.uk/id/eprint/76492/.
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In this thesis, I develop a valuation model to price convertible bonds with call provision. Convertible bonds are hybrid instruments that possess both equity and debt characteristics. The purpose of this study is to build a pricing model for convertible and callable bonds and to compare the mathematical results of the model with real world market performance. I construct a two-factor valuation model, in which both the interest rate and the stock price are stochastic. I derive the partial differential equation of two stochastic variables and state the final and boundary conditions of the convertible bond using the mean reversion model on interest rate. Because it is difficult to obtain a closed solution for the American convertible bond due to its structural complexity, I use the binomial tree model to value the convertible bond by constructing the interest rate tree and stock price tree. As a convertible bond is a hybrid security of debt and equity, I combine the interest rate tree and stock price tree into one single tree. Default risk is added to the valuation tree to represent the event of a default. The model is then tested and compared with the performance of the Canadian convertible bond market. Moreover, I study the duration, convexity and Greeks of convertible bonds. These are important risk metrics in the portfolio management of the convertible bond to measure risks linked to interest rate, equity, volatility and other market factors. I investigate the partial derivative of the value of the convertible bond with respect to various parameters, such as the interest rate, stock price, volatility of the interest rate, volatility of the stock price, mean reversion of the interest rate and dividend yield of the underlying stock. A convertible bond arbitrage portfolio is constructed to capture the abnormal returns from the Delta hedging strategy and I describe the risks associated with these returns. The portfolio is created by matching long positions in convertible bonds, with short positions in the underlying stock to create a Delta hedged convertible bond position, which captures income and volatility.
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Peterson, Sandra Jane. "The application of binomial trees to calculate complex option prices, two-factor stochastic interest rate option prices and value-at-risk." Thesis, Lancaster University, 1999. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.302414.
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Couto, José Carlos Maltez do. "Utilização do método de opções reais para análise de investimentos em infraestrutura: o caso do trem de alta velocidade (TAV Brasil)." reponame:Repositório Institucional do FGV, 2013. http://hdl.handle.net/10438/11074.
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The project of high-speed train that will transport passengers between the two largest cities of the country is a major investment Acceleration Plan (PAC). After the failure shown in the first bidding process, due to the absence of a proposal from private investors, the Federal Government decided to amend its participation in the investment plan, in addition, this second attempt, scheduled for September 2013, the Government reported that reduce the minimum amount of grant to be paid by the concessionaire winner at 3.2%, which will increase the state's investment of approximately R$ 900 million. The public sector search through the measures outlined, increasing the attractiveness of the project and reported that may increase its stake in the project, 45% of the shares of the SPE control the TAV to about 80%. This study discusses the granting of a guarantee of minimum demand of passengers, the results obtained through the methodology of real options indicate that they can generate an increase in NPV of 22.2% and a cost to the public purse of only 2.86 % of total investment in the project.
O projeto do trem de alta velocidade que fará o transporte de passageiros entre as duas maiores metrópoles do país é um dos principais investimentos do Plano de Aceleração do Crescimento (PAC). Depois do insucesso apresentado no primeiro processo de licitação, devido à falta de proposta de investidores privados, o Governo Federal decidiu alterar a sua participação no plano de investimentos, adicionalmente, nesta segunda tentativa, prevista para ocorrer em setembro de 2013, o Governo informou que reduzirá o valor mínimo da outorga a ser pago pelo concessionário vencedor em 3,2%, o que aumentará o investimento do Estado em cerca de R$ 900 milhões. O setor público busca através das medidas destacadas, aumentar a atratividade do projeto e divulgou que poderá aumentar a sua participação acionária no projeto, de 45% das cotas da SPE que controlará o TAV para cerca de 80%. O presente estudo discute a concessão de uma garantia de demanda mínima de passageiros, os resultados obtidos através da metodologia de opções reais indicam que elas podem gerar um aumento do VPL de 22,2% e um custo para os cofres públicos de apenas 2,86% do total investido no projeto.
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Damberg, Petter, and Alexander Gullnäs. "Interest rate derivatives: Pricing of Euro-Bund options : An empirical study of the Black Derman & Toy model (1990)." Thesis, Örebro universitet, Handelshögskolan vid Örebro Universitet, 2012. http://urn.kb.se/resolve?urn=urn:nbn:se:oru:diva-24472.
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The market for interest rate derivatives has in recent decades grown considerably and the need for proper valuation models has increased. Interest rate derivatives are instruments that in some way are contingent on interest rates such as bonds and swaps and most financial transactions are in some way exposed to interest rate risk. Interest rate derivatives are commonly used to hedge this risk. This study focuses on the Black Derman & Toy model and its capability of pricing interest rate derivatives. The purpose was to simulate the model numerically using daily Euro-Bunds and options data to identify if the model can generate accurate prices. A second purpose was to simplify the theory of building a short rate binomial tree, since existing theory explains this step in a complex way. The study concludes that the BDT model have difficulties valuing the extrinsic value of options with longer maturities, especially out-of-the money options.
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Saha, Dibakar. "Improved Criteria for Estimating Calibration Factors for Highway Safety Manual (HSM) Applications." FIU Digital Commons, 2014. http://digitalcommons.fiu.edu/etd/1701.
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The Highway Safety Manual (HSM) estimates roadway safety performance based on predictive models that were calibrated using national data. Calibration factors are then used to adjust these predictive models to local conditions for local applications. The HSM recommends that local calibration factors be estimated using 30 to 50 randomly selected sites that experienced at least a total of 100 crashes per year. It also recommends that the factors be updated every two to three years, preferably on an annual basis. However, these recommendations are primarily based on expert opinions rather than data-driven research findings. Furthermore, most agencies do not have data for many of the input variables recommended in the HSM. This dissertation is aimed at determining the best way to meet three major data needs affecting the estimation of calibration factors: (1) the required minimum sample sizes for different roadway facilities, (2) the required frequency for calibration factor updates, and (3) the influential variables affecting calibration factors.
In this dissertation, statewide segment and intersection data were first collected for most of the HSM recommended calibration variables using a Google Maps application. In addition, eight years (2005-2012) of traffic and crash data were retrieved from existing databases from the Florida Department of Transportation. With these data, the effect of sample size criterion on calibration factor estimates was first studied using a sensitivity analysis. The results showed that the minimum sample sizes not only vary across different roadway facilities, but they are also significantly higher than those recommended in the HSM. In addition, results from paired sample t-tests showed that calibration factors in Florida need to be updated annually.
To identify influential variables affecting the calibration factors for roadway segments, the variables were prioritized by combining the results from three different methods: negative binomial regression, random forests, and boosted regression trees. Only a few variables were found to explain most of the variation in the crash data. Traffic volume was consistently found to be the most influential. In addition, roadside object density, major and minor commercial driveway densities, and minor residential driveway density were also identified as influential variables.
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Mismer, Romain. "Convergence et spike and Slab Bayesian posterior distributions in some high dimensional models." Thesis, Sorbonne Paris Cité, 2019. http://www.theses.fr/2019USPCC064.
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On s'intéresse d'abord au modèle de suite gaussienne parcimonieuse. Une approche bayésienne empirique sur l'a priori Spike and Slab permet d'obtenir la convergence à vitesse minimax du moment d'ordre 2 a posteriori pour des Slabs Cauchy et on prouve un résultat de sous-optimalité pour un Slab Laplace. Un meilleur choix de Slab permet d'obtenir la constante exacte. Dans le modèle d'estimation de densité, un a priori arbre de Polya tel que les variables de l'arbre ont une distribution de type Spike and Slab donne la convergence à vitesse minimax et adaptative pour la norme sup de la loi a posteriori et un théorème Bernstein-von Mises non paramétriqueThe first main focus is the sparse Gaussian sequence model. An Empirical Bayes approach is used on the Spike and Slab prior to derive minimax convergence of the posterior second moment for Cauchy Slabs and a suboptimality result for the Laplace Slab is proved. Next, with a special choice of Slab convergence with the sharp minimax constant is derived. The second main focus is the density estimation model using a special Polya tree prior where the variables in the tree construction follow a Spike and Slab type distribution. Adaptive minimax convergence in the supremum norm of the posterior distribution as well as a nonparametric Bernstein-von Mises theorem are obtained
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BROCCARDO, ELEONORA. "Le strutture innovative per la cartolarizzazione del prestiti: valore economico del tranching e modelli di misurazione del rischio di credito." Doctoral thesis, Università Cattolica del Sacro Cuore, 2007. http://hdl.handle.net/10280/130.
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L'elemento che distingue un'operazione di cartolarizzazione consiste, secondo la definizione espressa nell'accordo di Basilea2, nell'identificazione di almeno due differenti posizioni di rischio (tranche), stratificate e subordinate, emesse a fronte di uno specifico portafoglio di attività. Nonostante il ricorso al tranching sia ampiamente diffuso e standardizzato le determinanti che giustificano il ricorso all'emissione multi-tranche sono ad oggi poco approfondite. Inoltre, i titoli emessi a fronte di operazioni di cartolarizzazione (CDO) possiedono profili di esposizione al rischio di credito differenziati, in termini di incidenza delle perdite attese ed inattese, ed in termini di correlazione con altri fattori di rischio: la valutazione del profilo di rischio è condizione necessaria per l'attribuzione di un giudizio di rating e per la definizione di un appropriato premio al rischio (pricing). Si rivela necessaria tanto la stima della distribuzione delle perdite del portafoglio (credit risk modelling) quanto l'analisi strutturale dei flussi di cassa generati e l'allocazione degli stessi alle tranche (cash flow modelling). Sulla base della letteratura di security design la tesi intende valutare l'efficienza del processo di intermediazione basato sulla cartolarizzazione multi-tranche rispetto all'intermediazione bancaria tradizionale e a forme di asset-backed security con unica tranche e focalizza l'analisi attraverso una verifica empirica delle teorie economiche a supporto del tranching, con particolare riferimento alla cartolarizzazione dei prestiti concessi ad imprese di piccola e media dimensione, oggetto di analisi specifica condotta nell'ambito di un'esperienza di stage presso il Fondo europeo degli investimenti. Quindi, grazie alla realizzazione di un modello computazionale sviluppato con un software di pianificazione finanziaria multidimensionale (Quantrix), la tesi presenta un approfondimento delle technicalities, mediante una modellizzazione dei flussi e della loro allocazione (Waterfall Payment Order), allo scopo di apprezzare il valore aggiunto di queste strutture di intermediazione. Aspetto, questo, non sviluppato nella letteratura accademica. L'analisi si rivolge alle operazioni realizzate nell'ambito dei due principali programmi di cartolarizzazione dei prestiti alle PMI attuati in Europa (Ftpyme e Promise).Securitisation is a structured finance instrument which involves pooling of financial assets (such as loans and bonds) and creating multiple tranched liabilities, collateralized debt obligation (CDO), of a single issuer with different risk-return characteristics, which are sold as separate securities. According to the New Basel Capital Accord, tranching is the key feature that distinguishes securitisation transactions; although commonly applied, the factors that determine the extent and the nature of tranching remain largely unknown. Moreover, because tranching allows the risk characteristics of the collateral pool to be transformed, it contributes to transaction complexity in assessing the risk properties of such structured instruments: the risk profile that can be generated through tranched exposure, in terms both of expected/unexpected incidence losses and correlated default of pool assets, can lead to substantial differences among tranches, depending on the level of subordination below a certain tranche. Key to the reliability of structured finance pricing and ratings is the accuracy in assessing the credit risk in the underlying portfolio (credit risk modelling), as well as the accurate modelling of the distribution of cash flows to different classes of CDO (cash flow modelling). By analyzing the finance literature relating to security design and securitization this thesis provides an analysis of the efficiency of financial intermediation model based on securitisation and an empirical test of theories supporting the economic added value of tranching, with regard to SMEs loan securitisation, which topic was specifically investigated during a stage at the European Investment Fund. By realization of a computational model, performed using a multidimensional modelling software (Quantrix), the thesis closely examines securitisation transaction's technicalities, by modelling both portfolio cash flows and funds allocation (Waterfall Payment Order), in order to asses the ability of the structure to withstand various stressed scenarios. This analysis offers an analytical and micro-approach to securitisation transactions, which has not deeply investigated in academic literature yet. The model applies to SMEs loan securitisation transactions, concluded within specific securitisation European Programme (Ftpyme in Spain and Promise in Germany).
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Huang, Syuan-Ren. "Smooth Convergence in Binomial Tree." 2008. http://www.cetd.com.tw/ec/thesisdetail.aspx?etdun=U0001-2506200811153000.
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Huang, Syuan-Ren, and 黃炫仁. "Smooth Convergence in Binomial Tree." Thesis, 2008. http://ndltd.ncl.edu.tw/handle/71220069253027709620.
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碩士國立臺灣大學
數學研究所
96
The products of derivative develop rapidly in recent years. There are many methods to price derivatives including using binomial tree, partial differential equations, martingale methods, and Monte Carlo simulation, etc. In these methods, binomial tree model is the simplest method that is used widely. The binomial model of Cox, Ross, and Rubinstein, CRR model, is well known. But CRR model converge to correct option price oscillatory and non-monotonic. Some models use a "tilt" parameter that alters the shape and span of the binomial tree to improve the behavior of convergence. In these models, Tian''s flexible model, Widdicks, Andricopoulos, Newton, and Duck''s WAND model, Joshi''s model, and Chang and Palmer''s center binomial model are significant. In this article, we use the main theorem of Chang-Palmer to prove the convergence rate that is not unspecitied in their paper of WAND model, and we use some relation to estimate the implied n of WAND model to save the computation of using Newton-Raphson iteration. Finally, we compared with the numerical results of these models.
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Chang, Chen-Wei, and 張振威. "Dividend-Stock Option Pricing–Binomial Value Tree." Thesis, 2014. http://ndltd.ncl.edu.tw/handle/a59v57.
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碩士義守大學
財務金融學系
102
The research focuses on pricing stock option with dividend. In order to incorporate dividend, Black (1976) directly adjusted stock yield and normal quantiles in BS option pricing model. The enumeration approach by CRR binomial model is somewhat complicated, while Hull (2009) dealt cases of ex-dividend. Unfortunately, these methods seem too arbitrary. This research introduces binomial value tree model that incorporate dividend to separate between stock price and stock value. Therefore, the value model arrange to setup relative return rate including bonds rate and dividend rate, divide duration into n times, appoint down-pricing number of in-the-money equal to (n-1)/2 and only for odds, and use normal quantiles in BS model to estimate down-pricing probability and adjusted probability in binomial distribution. Moreover, the research (1) makes the exercise of stock follow strike price, (2) the down-pricing probability of stock-exercise decided by the normal distribution probability in BS model, and (3) the up-pricing and down-pricing probability decided by the down-pricing probability and adjusted probability to avoid the low-efficiency of CRR convergence. Because the right-tail form cumulative probability in CRR model is apparently as different as in BS model, the paper sets up exercise of price based on number of down-pricing. Therefore, Binomial Value Tree model not only improves the drawbacks in CRR model but develops American options trees of VBA function in Excel to use. We chose the most top 10 volumes of stock options (AU Optronics Corp., United Microelectronics Corp., and WALSIN LIHWA Corp.) in Taiwan during the whole year of 2013. The research discovers that the convergence of Binomial Value Tree model is more efficient than CRR model. It proves that there is an efficient convergence that has monotone increasing in Binomial Value Tree model. Finally, Binomial Value Tree in this research not only considers dividends but also improves the convergence and right-tail form problems in CRR. Binomial Value Tree model can provide investors with an accurate tool when evaluating stocks or options with dividends.
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CHANG, JING-FEN, and 張菁芬. "A comparison of binomial-tree and trinomial-tree interest-rate models." Thesis, 1997. http://ndltd.ncl.edu.tw/handle/74856014911407586010.
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碩士國立臺灣大學
國際企業學系
85
Dynamic interest rate models play an important role in pricing interest rate sensitive securities. The raise of interest rate risk caused by financial liberalization has enhanced the demand for hedging instruments. To reflect market need, dynamic interest rate models have made significant progress during the past 20 years. These models are usually used in transactions, portfolio management, risk control and other application. This research compares a binomial tree model-Black, Derman and Toy (1990) model, and a trinomial tree model-Hull and White (1993) model. Both of them are no-arbitrage models. They can be used not only in pricing interest rate sensitive securities, but also in forecasting spot rates in the future. We design a computer program for expanding the trees. Using Taiwan fixed-income security market data and suitable parameters, we compare the performances of the two models. The conclusion is that Hull and White model have a better result under the circumstances of Taiwan. In the light of the empirical result, this research also discusses the assumptions and restrictions of the two models in order to better address their applicability in Taiwan.
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Hsun-Cheng, Chan. "Implied Binomial Tree Method for Pricing TAITEX Options." 2006. http://www.cetd.com.tw/ec/thesisdetail.aspx?etdun=U0001-2806200621160500.
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Chiu, Yi-Lung, and 邱奕隆. "pricing discrete barrier options with trino-binomial tree." Thesis, 2007. http://ndltd.ncl.edu.tw/handle/90435836182016534886.
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碩士中原大學
應用數學研究所
95
With the rapid growth of financial market today, each firm must consider all of the risks they may encounter, such as price risk and credit risk. Since risks may lead to financial loss, how to hedge becomes more and more important. There are many ways of hedging, and derivative is one of hedge tools on which each business puts emphasis. Among derivative, options is the most important product, and how to evaluate exact option value becomes an interesting question. Practically, we usually apply numerical model to evaluate exact option value. When we simulate for more and more times, we can get the more precise theoretical value. Generally speaking, there are some possible sources of error when we apply numerical model, such as distribution error and the nonlinearity error. If we want to evaluate options, we must apply different methods according to the option since different options have different features. Although errors cannot be fully avoided, we still have to revise the method while applying it in order to get the more precise option value. This article mainly applies TBT model (Trino-Binomial Tree) to Discrete Barrier Options, revising the original model to reduce possible errors and gets the more accurate outcome.
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Chih, Ting-Chun, and 遲廷峻. "Using Binomial Tree to Price American Asian Option." Thesis, 2007. http://ndltd.ncl.edu.tw/handle/15704157358104421819.
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碩士國立交通大學
財務金融研究所
95
This paper compares the results of the three different models which are Hull-White(1993), Chalasani et al.(1998) and Costabile-Massabó-Russo(2006). We compare the CPU time needed for each model and try to explain the relationship of their valuation. To make our result more reasonable, we add another three models for our study when comparing the price. They are Dai-Huang-Lyuu(2005), Dai-Wang-Wei(2007) and Longstaff-Schwartz (2001). Finally, in this paper, we conclude that Hull-White model performs the best in CPU time, but the other models provide relatively stable price when the number of the steps of a tree is larger.
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Chan, Hsun-Cheng, and 詹勳政. "Implied Binomial Tree Method for Pricing TAITEX Options." Thesis, 2006. http://ndltd.ncl.edu.tw/handle/24241902326492299239.
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碩士國立臺灣大學
資訊工程學研究所
94
ABSTRACT Building a recombining tree consistent with the volatility smile from observed options in the market is important for pricing. We adopts Barle and Cakici’s (1998) implied tree that modifies some features in Derman and Kani’s (1994) and use it to price TAIEX (Taiwan Stock Exchange Capitalization Weighted Stock Index) options, which are European options. Then one can price other exotic or path-dependant options by using implied binomial trees which satisfy implied volatilities under different maturities and strike prices. With this feature, the prices of derivatives will be more consistent with market quotes. Therefore, the result is a very practical and market-oriented tree model that helps us price new derivatives.
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楊智能. "Option pricing under smile effect and Impled binomial tree." Thesis, 2000. http://ndltd.ncl.edu.tw/handle/20184488627950949726.
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碩士國立臺灣大學
國際企業學研究所
88
This thesis discusses pricing under smile effect. “Smile effect” means that options at the same maturity date and underlying but different exercise prices have different implied volatilities. Under smile effect, general pricing models can’t calculate the same prices with the market and lose the value of reference. So we need a new suitable model for pricing. In Taiwan, there are warrants with the same underlying and different exercise prices but without the same maturity date. Unfortunately, there is no research discussing about this directly. The main point of this thesis is to modify the Rubinstein’s “Implied binomial tree model”, which probes about the smile effect at the same maturity date. We will restructure it to fit options that exercise at different dates in market of Taiwan. Rubinstein’s model requires strong assumption and path independence. This paper tries to adapt the strong assumption and path independence in Rubinstein''s model , and rebuild up another model which is path dependent and without the same maturity dates. The “Implied binomial tree model” would be applicable to general situation. In other word, it means the Rubinstein’s model would be the special case in the new model. Finally, this research checks new model with the warranrs in Taiwan(南亞、華新、台積電權證), then draw their smile curve. The result show us : the new models would reflex the market phenomenon exactly.
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Chan, Yi-Chi, and 詹益齊. "Asian Basket Option Pricing by a Simple Binomial Tree." Thesis, 2014. http://ndltd.ncl.edu.tw/handle/67745251312481612529.
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碩士國立臺灣大學
資訊工程學研究所
102
Asian basket option is hard to price. This thesis presents a new approach to price European-style and American-style Asian basket options. First, we use approximation and moment-matching techniques to find the random variable following the shifted lognormal distribution to approximate the basket value. Second, we use the random variable to build a binomial tree and combine it with the Hull-White methodology for pricing path-dependent options to price Asian basket options. Finally, we compare our numerical results with Monte Carlo simulation for European-style Asian basket options and with the least-squares Monte Carlo for American-style ones. They show that the European-style Asian basket option prices obtained by our approach are accurate and the American-style ones are overpriced by our approach.
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Ju, Jann-Jyh, and 朱展志. "Convertible Bond Pricing : a 2-Factor Binomial Tree Approach." Thesis, 1999. http://ndltd.ncl.edu.tw/handle/97796463265099551500.
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碩士國立臺灣大學
商學研究所
87
Abstract This thesis is to develop a pricing model for convertible bonds via the 2-factor binomial tree model, which simultaneously takes both changes of stock price and interest rate into account and includes all provisions in the contract . With assumptions that stock price follows Geometric Brownian Motion and risk-free interest rate follows Cox , Ingersoll & Ross ( 1985 ) process, this thesis builds a quadro tree for stock price and interest rate. The convertible bond is priced by dividing the contract into two parts : the straight bond and the warrant of stock. To price the reset provision on the convertible bond, the approach similar to look-back ladders option is applied to calculate this reset option value, so that the theoretical price of convertible bond with a reset option can be accurately and efficiently calculated. This thesis takes Acer 04 convertible bond as an example to demonstrate the approach introduced here. Some conclusions are reached as follows : (1).Parameters of interest rate model have less significant impact on the theoretical price of convertible bond than those of stock price model . (2).The value of the reset provision is higher if the number of reset is higher, the timing of reset is earlier, and the reset barrier is lower . (3).The value of the reset provision is reduced when simultaneously taking dilution effect and call provision into account.
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Hung-Tai, Cheng, and 鄭宏泰. "Static Hedges for Barrier Options: An Implied Binomial Tree Approach." Thesis, 2001. http://ndltd.ncl.edu.tw/handle/75878613196986052414.
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碩士國立中央大學
財務管理研究所
89
Abstract This paper investigates static hedge portfolios for barrier options with volatility “smile.” We try to value the option with an implied binomial tree approach. We replace the traditional dynamic hedging strategy with a static replication under this volatility structure. Moreover, in valuing options with barriers, we use the enhanced numerical method to make the value approach the analytic result much more rapidly. We define the smile in terms of implied volatility by giving a formula relating strike price to implied volatility, assuming the smile to be time independent. In constructing the implied binomial tree, “bad probability” is a big problem. We replace the bad nodes that generate a violation of the probabilities with the good nodes, which keep the implied local volatility function smooth. In addition, barrier options valued on an implied tree have no analytic solution. The enhanced method saves computing time and provides greater accuracy than an unenhanced binomial solution. When we hedge the options with a static replicating portfolio, the number of options should be chosen to balance an inaccurate replication against the options’ cost. The more options there are in our replication portfolio, the better the replication is, and the greater the transaction costs are as well. In the example, our findings show that the replication mismatch is much smaller when using ten options to replicate the target option instead of a five-option replication portfolio. We also compare the effect of the static replication between the implied volatility approach and the constant volatility framework.
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Tan, Patrick, and 湯麒國. "An Empirical Study for Bivariate Binomial Tree Pricing Models of Covered Warrant." Thesis, 2000. http://ndltd.ncl.edu.tw/handle/58764851611205861834.
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碩士銘傳大學
金融研究所
88
Abstract This research acquires a warranty binominal theoretic pricing by taking historic volatility into B-S Model and taking GARACH-family Model into Boyle(1989) Bivariate Binominal Tree Pricing Model and through comparing with realistic market pricing for expecting to find out an effective evaluating formula of stock pricing fluctuation and a pricing model which is applicable to Taiwan warranty binominal market. 1. General speaking, during the period of the warranty binominal going on sale, among all Electronic underlying warranty binominals issued by stock brokers, the remunerative ratio distribution of electronic stocks being located at significant level of 95%, almost can accept and take remunerative ratio as hypothesis under normal distribution ,However while stock brokers issuing non-electronic stocks underlying warranty binominal all of them reject to take remunerative ratio as normal distribution hypothesis under 95% of significant level. 2. During sampling, considering of whole situation, to use GARCH-family model to evaluate the future volatility of underlying stocks: (1) the effect of non-electronic stock is better (2) the GARCH effect of GARCH(1,1), EGARCH(1,1), and GARCH-M (1,1) model is remarkable (3) the leverage effect on EGARCH(1,1) model is not obviously (4) the premium on GARCH-M(1,1) model is not obviously 3. Between non-electronic stock warranty binominal and electronic stock warranty binominal , the ordering price difference of Boyle model is obviously smaller than B-S model, no matter out of money or at money. Only the electronic stock warranty binominal is in the money, B-S model carries a smaller ordering price difference. 4. While evaluating the choosing right on out of money and at money, the theoretic pricing of B-S and Boyle(1988) Model incline under market pricing. But during studying in the money choosing right, some of theoretic pricing of B-S and Boyle(1988) models are higher than market pricing, but some are lower. 5. For 3 kinds of Heteroscdeasticity Models GARCH(1,1), EGARCH(1,1) and GARCH-M(1,1), they don''t make an obvious difference on future fluctuation predicated ability. Keyword : Black & Scholes Model, Bivariate Binominal Tree Option Model ,Warrant, Heteroscdeasticity, Volatility
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Chen, Jing-yi, and 陳靜怡. "The Credit Risk Model for SMEG： Based on Time Varying and Binomial Tree Approach." Thesis, 2010. http://ndltd.ncl.edu.tw/handle/67373315981614015501.
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Wang, Tianyang. "Multivariate real options valuation." Thesis, 2011. http://hdl.handle.net/2152/ETD-UT-2011-05-2797.
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This dissertation research focuses on modeling and evaluating multivariate uncertainties and the dependency between the uncertainties.
Managing risk and making strategic decisions under uncertainty is critically important for both individual and corporate success. In this dissertation research, we present two new methodologies, the implied binomial tree approach and the dependent decision tree approach, to modeling multivariate decision making problems with practical applications in real options valuation.
First, we present the implied binomial tree approach to consolidate the representation of multiple sources of uncertainty into univariate uncertainty, while capturing the impact of these uncertainties on the project’s cash flows. This approach provides a nonparametric extension of the approaches in the literature by allowing the project value to follow a generalized diffusion process in which the volatility may vary with time and with the asset prices, therefore offering more modeling flexibility. This approach was motivated by the Implied Binomial Tree (IBT) approach that is widely used to value complex financial options. By constructing the implied recombining binomial tree in a way so as to be consistent with the simulated market information, we extended the finance-based IBT method for real options valuation — when the options are contingent on the value of one or more market related uncertainties that are not traded assets.
Further, we present a general framework based on copulas for modeling dependent multivariate uncertainties through the use of a decision tree. The proposed dependent decision tree model allows multiple dependent uncertainties with arbitrary marginal distributions to be represented in a decision tree with a sequence of conditional probability distributions. This general framework could be naturally applied in decision analysis and real options valuations, as well as in more general applications of dependent probability trees. While this approach to modeling dependencies can be based on several popular copula families as we illustrate, we focus on the use of the normal copula and present an efficient computational method for multivariate decision and risk analysis that can be standardized for convenient application.text
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Ho, Chun-Ju, and 何俊儒. "Using the LIBOR Market Model to Price the Interest Rate Derivatives: A Recombining Binomial Tree Methodology." Thesis, 2008. http://ndltd.ncl.edu.tw/handle/27317458743176539969.
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碩士國立交通大學
財務金融研究所
96
In this thesis, we adapt the recombining node methodology proposed by Ho, Stapleton, and Subrahmanyam to implement the LIBOR market model (LMM). The lattice method we proposed is more efficient in comparison with Monte Carlo simulation as pricing the interest rate derivatives. The results of the bond option value and the caplet value are approximate to the theoretical value respectively.
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Hong-yiu, Lin. "Fast Fourier Transform with Applications to Pricing Discrete European Barrier Options under Binomial and Trinomial Tree Models." 2006. http://www.cetd.com.tw/ec/thesisdetail.aspx?etdun=U0001-2806200614570000.
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Lin, Hong-yiu, and 林虹佑. "Fast Fourier Transform with Applications to Pricing Discrete European Barrier Options under Binomial and Trinomial Tree Models." Thesis, 2006. http://ndltd.ncl.edu.tw/handle/19639656494687507249.
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碩士國立臺灣大學
資訊工程學研究所
94
A derivative is a financial instrument which is constructed from other more basic underlying assets, such as bonds or stocks. With the dramatic growth of the derivatives markets, more and more derivatives have been designed and issued by financial institutions. This thesis presents a method that can be used to speed up the pricing of discrete European barrier options under binomial and trinomial tree models. Binomial tree and trinomial tree are two common and efficient models for pricing options. However, in practice, almost all barrier options are discretely monitored and the refection principle no longer works. It seems that the only way to price discrete barrier options is to traverse the whole tree, which takes quadratic time. This thesis gives the first subquadratic-time algorithm for the problem.
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KO, SHIH-CHIANG, and 柯仕強. "The Pricing Model of RMB Currency Option Under Expecting the Changes of RMB Exchange Rate ：A n Application of Implied Binomial Tree Model and GRACH Model." Thesis, 2004. http://ndltd.ncl.edu.tw/handle/08866884189484178143.
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碩士國立臺北大學
合作經濟學系
92
China authority facing the pressures coming from the U.S. and EU to give up the control of RMB prepares to loosen restrictions of the exchange rate of RMB. Under this situation, the investors must exposure the exchangeable risk of exchange rate of RMB, hence this study tries to perform three scenarios of the appreciation of RMB in the future. Furthermore, using three kinds of measures (historic volatility, Newton-Raphson and GARCH model) to measure the volatilities and then substitute them to the option pricing model (Implied Binomial Tree model and Binomial Tree model). By means of finding the most suitable RMB currency option price, it moreover could compare the sensitivity to each other. According to the simulated results of scenarios, the major conclusions of this empirical research are as follows: Firstly, under lacking ample information about RMB currency option, using Newton-Raphson method, it can make the volatility of option price larger, hence, it also make the price of RMB currency option higher. Secondly, under above situation, using GARCH model to calculate the volatility, it can get the more authentic option price. Besides, the RMB currency option has speculative and hedged functions via using GARCH model. Thirdly, under the situations of exchange rate of RMB unchange and that appreciates at one time, the volatility using GARCH model to gain is too small to issue currency option. Finally, if the China authority will make the appreciation of RMB step by step, the volatility is more authentic. It means that investors are hardly to predict the exchange rate of RMB on this situation. Therefore, issued RMB currency option on this situation is valuable and the product, RMB currency option, is worthy of speculation, arbitration, investment and hedge.
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Müller, Stefanie [Verfasser]. "The binomial approach to option valuation : getting binomial trees into shape / Stefanie Müller." 2010. http://d-nb.info/999701673/34.
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Wang, Yu-Chun, and 王禹鈞. "Using Recombining Binomial Trees To Implement LIBOR Market Models." Thesis, 2007. http://ndltd.ncl.edu.tw/handle/19590344475865782047.
Full textAbstract:
碩士國立臺灣大學
資訊工程學研究所
95
The thesis is concerned with the implementation of the LIBOR market model, using the Ho, Stapleton and Subrahmanyam(1995) model, a recombining tree model. The recombining tree model provides a fast and accurate approach for the valuation of path{ dependent interest rate derivatives.
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Wang, Yu-Chun. "Using Recombining Binomial Trees To Implement LIBOR Market Models." 2007. http://www.cetd.com.tw/ec/thesisdetail.aspx?etdun=U0001-1607200706405400.
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Cruz, Aricson César Jesus da. "Three essays on option pricing." Doctoral thesis, 2018. http://hdl.handle.net/10071/18898.
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This thesis addresses option pricing problem in three separate and self-contained papers:
A. The Binomial CEV Model and the Greeks
This article compares alternative binomial approximation schemes for computing the option hedge ratios studied by Pelsser and Vorst (1994), Chung and Shackleton (2002), and Chung et al. (2011) under the lognormal assumption, but now considering the constant elasticity of variance (CEV) process proposed by Cox (1975) and using the continuous-time analytical Greeks recently offered by Larguinho et al. (2013) as the benchmarks. Among all the binomial models considered in this study, we conclude that an extended tree binomial CEV model with the smooth and monotonic convergence property is the most efficient method for computing Greeks under the CEV diffusion process because one can apply the two-point extrapolation formula suggested by Chung et al. (2011).
B. Valuing American-Style Options under the CEV Model: An Integral Representation Based Method
This article derives a new integral representation of the early exercise boundary for valuing American-style options under the constant elasticity of variance (CEV) model. An important feature of this novel early exercise boundary characterization is that it does not involve the usual (time) recursive procedure that is commonly employed in the so-called integral representation approach well known in the literature. Our non-time recursive pricing method is shown to be analytically tractable under the local volatility CEV process and the numerical experiments demonstrate its robustness and accuracy.
C. A Note on Options and Bubbles under the CEV Model: Implications for Pricing and Hedging
The discounted price process under the constant elasticity of variance (CEV) model is not a martingale for options markets with upward sloping implied volatility smiles.
The loss of the martingale property implies the existence of (at least) two option prices for the call option, that is the price for which the put-call parity holds and the price representing the lowest cost of replicating the payoff of the call. This article derives closed-form solutions for the Greeks of the risk-neutral call option pricing solution that are valid for any CEV process exhibiting forward skew volatility smile patterns. Using an extensive numerical analysis, we conclude that the differences between the call prices and Greeks of both solutions are substantial, which might yield significant errors of analysis for pricing and hedging purposes.Esta tese aborda a avaliação de opções em três artigos distintos: A. The Binomial CEV Model and the Greeks Este artigo compara diferentes aproximações binomiais para o cálculo dos Greeks das opções estudadas por Pelsser and Vorst (1994), Chung and Shackleton (2002), e Chung et al. (2011), no âmbito da distribuição lognormal, mas agora considerando o processo constant elasticity of variance (CEV) proposto por Cox (1975), utilizando os Greeks analíticos em tempo contínuo, recentemente propostos por Larguinho et al. (2013) como referência. Entre os modelos binomiais considerados neste estudo, concluímos que um modelo extended tree binomial CEV com uma aproximação convergente e monótona é o método mais eficiente para o cálculo dos Greeks no âmbito do processo de difusão CEV porque podemos aplicar a fórmula de extrapolação de dois pontos, sugerido por Chung et al. (2011). B. Valuing American-Style Options under the CEV Model: An Integral Representation Based Method Este artigo deriva uma nova representação integral da barreira de exercício antecipado para a avaliação das opções Americanas no âmbito do modelo constant elasticity of variance (CEV), um importante aspecto desta nova caracterização da barreira de exercício antecipado é que este não envolve o usual processo recursivo que é habitualmente aplicado e conhecido na literatura como a abordagem de representação integral. O nosso método de avaliação não recursivo é de fácil tratamento analítico sob o processo de difusão CEV e os resultados numéricos demonstram a sua robustez e precisão. C. A Note on Options and Bubbles under the CEV Model: Implications for Pricing and Hedging O processo de desconto de preço no âmbito do modelo constant elasticity of variance (CEV) não é um martingale para os mercados de opções com uma volatility smile de inclinação ascendente. A perda da propriedade martingale implica a existência de (pelo menos) dois preços de opção para a opção de compra, que é o preço para qual se verifica a paridade put-call e este preço representa o menor custo de replicação do payoff da call. Este artigo deriva as soluções em fórmula fechada para os Greeks da opção call no risco neutral que são válidas para qualquer processo CEV que possui padrões de enviesamento ascendentes. Tendo por base uma analise numérica extensiva, concluímos que a diferença entre os preços da call e os Greeks de ambas as soluções são substanciais, o que pode gerar erros significativos de análises no cálculo do preço da call e dos Greeks.
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Peng, Tao. "Portfolio credit risk modelling and CDO pricing - analytics and implied trees from CDO tranches." 2010. http://hdl.handle.net/2100/1104.
Full textAbstract:
One of the most successful and most controversial innovative financial products in recent years has been collateralised debt obligations (CDOs). The dimensionality of dependency embedded in a typical CDO structure poses great challenges for researchers - in both generating realistic default dynamics and correlation, and in the mean time achieving fast and accurate model calibration. The research presented in this thesis contributes to the class of bottom-up models, which, as opposed to top-down models, start by modelling the individual obligor default process and then moving them up through the dependency structures to build up the loss distributions at the portfolio level. The Gaussian model (Li 2000) is a static copula model. It has only on correlation parameter, which can be calibrated to one CDO tranche at a time. Its simplicity achieves wide spread industry application even though it suffers from the problem of ’correlation smile’. In other words, it cannot fit the market in an arbitrage-free manner in the capital-structure dimension. The first contribution of this thesis is the sensitivities analysis with regard to model parameters of expected losses of CDO tranches in the Gaussian and NIG copula models. The study provided substantial insight into the essence of the dependency structure. In addition, we apply the intensity approach to credit modelling in order to imply market distributions non-parametrically in the form of a binomial lattice. Under the same framework, we developed a series of three models. The static binomial model can be calibrated to the CDS index tranches exactly, with one set of parameters. The model can be seen as a non-parametric copula model that is arbitrage free in the capital-structure dimension. Static models are not suitable to price portfolio credit derivatives that are dynamic in nature. The static model can be naturally developed into a dynamic binomial model and satisfies no-arbitrage conditions in the time dimension. This setup, however, reduces model flexibility and calibration speed. The computational complexity comes from the non-Markovian character of the default process in the dynamic model. Inspired by Mortensen (2006), in which the author defines the intensity integral as a conditioning variable, we modify the dynamic model into a Markovian model by modelling the intensity integral directly, which greatly reduces the computational time and increases model fit in calibration. We also show that, when stochastic recovery rates are involved, there is a third no-arbitrage condition for the expected loss process that needs to be built into the Markovian model. For all binomial models, we adopt a unique optimisation algorithm for model calibration - the Cross Entropy method. It is particularly advantageous in solving large-scale non-linear optimsation problems with multiple local extrema, as encountered in our model.
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Lin, Dun-Shun, and 林敦舜. "The Study of Pricing for Taiwan Call Warrants－the Pricing Differences between Binomial Trees Model and Trinomial Trees Model." Thesis, 2002. http://ndltd.ncl.edu.tw/handle/76352106163389167847.
Full textAbstract:
碩士國立交通大學
經營管理研究所
90
This study adopts three option pricing models ( Black-Scholes model, binomial trees model and trinomial trees model ) with the historical volatility and the implied volatility to price the Taiwan call warrants. We hope to find out the pricing model that is fitting in with Taiwan warrants market. In addition, we study the number of time steps of trees models to understand the pricing outcomes of different number of time steps. The findings are as follows : All pricing models with the historical volatility underestimate warrants obviously, but they obtain a better pricing performance with the implied volatility. Black-Scholes model with the implied volatility is the best pricing model and having the best pricing performance. Using the historical volatility, trees models of different number of time steps have not a regular pricing performance; But using the implied volatility, trees models have a better pricing performance when the number of time steps is bigger, and trinomial trees model is better than binomial trees model.