Dissertations / Theses on the topic 'Options'
To see the other types of publications on this topic, follow the link: Options.
Create a spot-on reference in APA, MLA, Chicago, Harvard, and other styles
Consult the top 50 dissertations / theses for your research on the topic 'Options.'
Next to every source in the list of references, there is an 'Add to bibliography' button. Press on it, and we will generate automatically the bibliographic reference to the chosen work in the citation style you need: APA, MLA, Harvard, Chicago, Vancouver, etc.
You can also download the full text of the academic publication as pdf and read online its abstract whenever available in the metadata.
Browse dissertations / theses on a wide variety of disciplines and organise your bibliography correctly.
1
Matsumoto, Manabu. "Options on portfolios of options and multivariate option pricing and hedging." Thesis, Imperial College London, 2000. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.324627.
Full text
2
OLIVEIRA, ANDRE GIUDICE DE. "ANALYZING BMFEFBOVESPA REFERENCE OPTION PREMIUM: DOLLAR OPTIONS AND IBOVESPA FUTURES OPTIONS." PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 2012. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=20448@1.
Full textAbstract:
PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIROCOORDENAÇÃO DE APERFEIÇOAMENTO DO PESSOAL DE ENSINO SUPERIOR
PROGRAMA DE SUPORTE À PÓS-GRADUAÇÃO DE INSTS. DE ENSINO
O objetivo deste trabalho é realizar uma comparação entre os prêmios de referência da BMEFBovespa e os modelos de Garman Kohlhagen, Corrado-Su Modificado, Difusão com Saltos de Merton, Black e o modelo de Black adaptado para assimetria e curtose para o apreçamento de opções de dólar e sobre futuro de Ibovespa. Para isso, foram definidos cenários de análise e comparados os resultados com os prêmios de referência calculados pela BMEFBovespa no período janeiro de 2006 a setembro de 2011. Os resultados obtidos mostram que, em grande parte dos casos, os prêmios de referência calculados pela Bolsa são superestimados, além de revelar que os valores calculados pelos três modelos para as opções de compra e de venda de dólar e de futuro de Ibovespa encontram-se muito próximos.
This paper proposes a comparison between option reference premiums supplied by BMEF Bovespa and those obtained by the following models: Garman Kohlhagen, modified Corrado-Su, Merton s jump diffusion model, Black and an alternative version of the model, adapted for asymmetry and kurtosis. The underlying assets are futures contracts for Reais/Dolars exchange rate and Ibovespa futures contracts. Base scenarios were created and the results were compared between the models for the January 2006 – September 2011 period. The results show that the majority of the premiums calculated by BMEF Bovespa are overestimated when compared to the proposed models. Furthermore, the results obtained by this models are very similar to one another.
3
Neset, Yngvild. "Spectral Discretizations of Option Pricing Models for European Put Options." Thesis, Norges teknisk-naturvitenskapelige universitet, Institutt for matematiske fag, 2014. http://urn.kb.se/resolve?urn=urn:nbn:no:ntnu:diva-26546.
Full textAbstract:
The aim of this thesis is to solve option pricing models efficiently by using spectral methods. The option pricing models that will be solved are the Black-Scholes model and Heston's stochastic volatility model. We will restrict us to pricing European put options. We derive the partial differential equations governing the two models and their corresponding weak formulations. The models are then solved using both the spectral Galerkin method and a polynomial collocation method. The numerical solutions are compared to the exact solution. The exact solution is also used to study the numerical convergence. We compare the results from the two numerical methods, and look at the time consumptions of the different methods. Analysis of the methods are also given. This includes coercivity, continuity, stability and convergence estimates.For Black-Scholes equation, we study both the original equation and the log transformed equation, and we also compare the results to a solution obtained by using a finite element method solver.
4
Chen, Kwok-wang. "Evaluation of market efficiency of stock options in Hong Kong /." Hong Kong : University of Hong Kong, 1997. http://sunzi.lib.hku.hk/hkuto/record.jsp?B18837372.
Full text
5
Gauthier, Laurent. "Options réelles et options exotiques, une approche probabiliste." Phd thesis, Paris 1, 2002. http://www.theses.fr/2002PA010057.
Full textAbstract:
Cet ouvrage se concentre sur la valorisation et la couverture d'options financières non traitées sur les marchés, les options réelles, qui servent à évaluer des décisions optimales d'investissement. L'objectif de cette thèse est de montrer comment la théorie des options réelles bénéficie des apports des méthodes probabilistes employées pour les options exotiques. L'approche classique des options réelles privilégie l'utilisation de techniques d'équations différentielles, et nous proposons d'évaluer des projets d'investissement en appliquant des méthodes très probabilistes. Cette distinction de méthode permet de généraliser l'approche classique du problème, et d'obtenir des résultats analytiques dans des situations où une technique d'équation différentielle ne le permettrait pas. Nous abordons la valorisation de projets d'investissement sous certaines contraintes particulières : lorsqu’il existe un délai incompressible entre la prise de décision et sa mise en oeuvre, lorsqu'il existe une compétition entre acteurs de caractéristiques différentes, et lorsque l'information sur le marché est imparfaite. Egalement, nous étudions des problèmes de couverture: comment couvrir des options réelles complexes de la manière la plus efficace lorsqu'il existe des coûts de transaction, et comment une nouvelle classe de produits dérivés qui s'apparentent aux options barrières permet de couvrir le risque lié à l’exercice des options réelles. Finalement, nous nous penchons sur la décision optimale d'investissement lorsque l'on peut manipuler le marché; un agent économique qui possède une information privilégiée peut intervenir sur le marché, et influencer la valeur des titres. Les outils mathématiques utilisés sont surtout probabilistes, essentiellement la théorie des excursions, les temps locaux et le contrôle stochastique. Plusieurs nouveaux résultants sont démontrés, concernant en particulier les temps de passage du Brownien et la théorie des excursions.
6
Gauthier, Laurent. "Options Réelles et Options Exotiques, une Approche Probabiliste." Phd thesis, Université Panthéon-Sorbonne - Paris I, 2002. http://tel.archives-ouvertes.fr/tel-00002076.
Full textAbstract:
Cet ouvrage se concentre sur la valorisation et la couverture d'options financières non traitées sur les marchés, les options réelles, qui servent à évaluer des décisions optimales d'investissement en capital pour des entreprises. L'existence pour une entreprise d'un projet d'investissement s'apparente en effet à la possession d'une option financière: l'entreprise possède l'option d'attendre le moment le plus favorable pour lancer son projet. Pour valoriser l'intérêt économique d'un projet, il convient alors de calculer la valeur de l'option d'investir. L'objectif de cette thèse est de montrer comment la théorie des options réelles peut bénéficier des apports des méthodes habituellement employées pour les options exotiques. A la différence de l'approche classique dans le domaine des options réelles, qui privilégie l'utilisation de techniques d'équations différentielles, nous proposons dans cette thèse d'évaluer des projets d'investissement en appliquant des méthodes très probabilistes. Cette distinction de méthode permet non seulement de généraliser l'approche classique du problème, mais encore d'obtenir des résultats analytiques dans des situations ou une technique d'équation différentielle ne permettrait pas de résoudre le problème. Dans cette thèse, nous abordons spécifiquement des problèmes de valorisation de projets d'investissement sous certaines contraintes particulières : lorsqu'il existe un délai incompressible entre la prise de décision et sa mise en oeuvre, lorsqu'il existe une compétition entre deux acteurs économiques de caractéristiques différentes, et lorsque l'information sur le marché de l'entreprise est imparfaite. Egalement, nous étudions des problèmes de couverture de ces projets d'investissement : comment couvrir des options réelles qui sont un peu complexes de la manière la plus efficace lorsqu'il existe des coûts de transaction sur les actifs financiers, et comment une nouvelle classe de produits dérivés qui s'apparentent aux options barrières permet de couvrir le risque lié à l'exercice des options réelles. Finalement, nous nous penchons sur la décision optimale d'investissement lorsque l'on peut manipuler le marché : un agent économique qui possède une information privilégiée sur la valeur d'une entreprise peut intervenir sur le marché afin de l'utiliser, et par la même occasion influencer la valeur des titres émis par l'entreprise. Quelle est sa stratégie optimale ? Les outils mathématiques utilisés sont surtout probabilistes, essentiellement la théorie des excursions, les temps locaux et le contrôle stochastique. Plusieurs nouveaux résultants sont démontrés, concernant en particulier les temps de passage du Brownien et la théorie des excursions.
7
Gunnarsson, Niklas. "Barrier options." Thesis, Uppsala University, Department of Mathematics, 2002. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-122338.
Full text
8
Nilsson, Martin, and Gustaf Kristiansson. "Options Based on CO2 Emissions : A Comparison with Traditional Options." Thesis, Högskolan i Halmstad, Sektionen för ekonomi och teknik (SET), 2009. http://urn.kb.se/resolve?urn=urn:nbn:se:hh:diva-3615.
Full textAbstract:
Abstract Title: Options Based on CO2 Emissions: A Comparison with Traditional Options Seminar date: 2009-06-17 Course: Bachelor thesis in business administration, 15 ECTS Authors: Gustaf Kristiansson, Martin Nilsson Instructor: Bengt Kjellgren Key words: Black & Scholes, Certified Emission Reductions, emission markets, European Union Allowances, options, pricing Purpose: This study intends to compare traditional options with the CO2 based instruments EUAs and CERs options in the fields of pricing, cap and trade, political influence, economical effects and market function. Methodology: A combined research methodology is used in this study, which includes both a quantitative and a qualitative approach. A deductive research approach is brought out over the whole study. Theoretical perspectives: The theoretical framework is based upon previous empirical research concerning the fields in this study. The Black & Scholes formula for option pricing has a central position. Empirical foundation: Market data has been used to analyse the field of pricing. Interviews have been conducted with actors on the European emission trading market for a further understanding of cap and trade, political influence, economical effects and market function. Conclusions: We have in this research identified that the CO2 based market differs from the financial market when it comes to political decisions and price fluctuation. We have also identified that the CO2 based market is not mature enough for a complete internationalisation.En formell presentation utfördes ej pga utlandsstudier.
9
El, Aoud Sofiene. "Dynamique jointe stock/option et application aux stratégies de trading sur options." Thesis, Châtenay-Malabry, Ecole centrale de Paris, 2015. http://www.theses.fr/2015ECAP0020/document.
Full textAbstract:
Cette thèse explore théoriquement et empiriquement les implications de la dynamique jointe action/option sur divers problématiques liées au trading d’options. Dans un premier temps, nous commençons par l’étude de la dynamique jointe entre une option sur un stock et une option sur l’indice de marché. Le modèle CAPM fournit un cadre mathématique adéquat pour cette étude car il permet de modéliser la dynamique jointe d’un stock et son indice de marché. En passant aux prix d’options, nous montrons que le beta et la volatilité idiosyncratique, paramètres du modèle, permettent de caractériser la relation entre les surfaces de volatilité implicite du stock et de l’indice. Nous nous penchons alors sur l’estimation du paramètre beta sous la probabilité risque-neutre en utilisant les prix d’options. Cette mesure, appelée beta implicite, représente l’information contenue dans les prix d’options sur la réalisation du paramètre beta dans le futur.Pour cette raison, nous essayons de voir, si le beta implicite a un pouvoir prédictif du beta futur.En menant une étude empirique, nous concluons que le beta implicite n’améliore pas la capacité de prédiction en comparaison avec le beta historique qui est calculé à travers la régression linéaire des rendements du stock sur ceux de l’indice. Mieux encore, nous remarquons que l’oscillation du beta implicite autour du beta futur peut entraîner des opportunités d’arbitrage, et nous proposons une stratégie d’arbitrage qui permet de monétiser cet écart. D’un autre côté, nous montrons que l’estimateur du beta implicite pourrait être utilisé pour la couverture d’options sur le stock en utilisant des instruments sur l’indice, cette couverture concerne notamment le risque de volatilité et aussi le risque de delta. Dans la deuxième partie de notre travail, nous nous intéressons au problème de market making sur options. Dans cette étude, nous supposons que le modèle de dynamique du sous-jacent sous la probabilité risque-neutre pourrait être mal spécifié ce qui traduit un décalage entre la distribution implicite du sous-jacent et sa distribution historique.Dans un premier temps, nous considérons le cas d’un market maker risque neutre qui vise à maximiser l’espérance de sa richesse future. A travers l’utilisation d’une approche de contrôle optimal stochastique, nous déterminons les prix optimaux d’achat et de vente sur l’option et nous interprétons l’effet de présence d’inefficience de prix sur la stratégie optimale. Dans un deuxième temps, nous considérons que le market maker est averse au risque et essaie donc de réduire l’incertitude liée à son inventaire. En résolvant un problème d’optimisation basé sur un critère moyenne-variance, nous obtenons des approximations analytiques des prix optimaux d’achat et de vente. Nous montrons aussi les effets de l’inventaire et de l’inefficience du prix sur la stratégie optimale. Nous nous intéressons par la suite au market making d’options dans une dimension plus élevée. Ainsi, en suivant le même raisonnement, nous présentons un cadre pour le market making de deux options ayant des sous-jacents différents avec comme contrainte la réduction de variance liée au risque d’inventaire détenu par le market-maker. Nous déterminons dans ce cas la stratégie optimale et nous appuyons les résultats théoriques par des simulations numériques.Dans la dernière partie de notre travail, nous étudions la dynamique jointe entre la volatilité implicite à la monnaie et le sous jacent, et nous essayons d’établir le lien entre cette dynamique jointe et le skew implicite. Nous nous intéressons à un indicateur appelé "Skew Stickiness Ratio"qui a été introduit dans la littérature récente. Cet indicateur mesure la sensibilité de la volatilité implicite à la monnaie face aux mouvements du sous-jacent. Nous proposons une méthode qui permet d’estimer la valeur de cet indicateur sous la probabilité risque-neutre sans avoir besoin d’admettre des hypothèses sur la dynamique du sous-jacent. [...]This thesis explores theoretically and empirically the implications of the stock/option joint dynamics on applications related to option trading. In the first part of the thesis, we look into the relations between stock options and index options under the risk-neutral measure. The Capital Asset Pricing Model offers an adequate mathematical framework for this study as it provides a modeling approach for the joint dynamics between the stock and the index. As we compute option prices according to this model, we find out that the beta and the idiosyncratic volatility of the stock, which are parameters of the model, characterize the relation between the implied volatility surface of the stock and the one of the index. For this reason, we focus on the estimation of the parameter beta under the risk-neutral measure through the use of option prices.This measure, that we call implied beta, is the information contained in option prices concerning the realization of the parameter beta in the future. Trying to use this additional information, we carry out an empirical study in order to investigate whether the implied beta has a predictive power of the forward realized beta. We conclude that the implied beta doesn’t perform better than the historical beta which is estimated using the linear regression of the stock’s returns onthe index returns. We conclude also that the oscillation of the implied beta around the forward realized beta can engender arbitrage opportunities, and we propose an arbitrage strategy which enables to monetize this difference. In addition, we show that the implied beta is useful to hedge stock options using instruments on the index. In the second part of our work, we consider the problem of option market making. We suppose that the model used to describe the dynamics of the underlying under the risk-neutral probability measure can be misspecified which means thatthe implied distribution of the underlying may be different from its historical one. We consider first the case of a risk neutral market maker who aims to maximize the expectation of her final wealth. Using a stochastic control approach, we determine the optimal bid and ask prices on the option and we interpret the effect of price inefficiency on the optimal strategy. Next to that, we suppose that the market maker is risk averse as she tries to minimize the variance of her finalwealth. We solve a mean-variance optimization problem and we provide analytic approximations for the optimal bid and ask prices. We show the effects of option inventory and price inefficiency on the optimal strategy. We try then to extrapolate the study to a higher dimension in order to see the effect of joint dynamics of the different underlyings on the optimal strategy. Thus, we study market making strategies on a pair of options having different underlyings with the aim to reduce the risk due to accumulated inventories in these two options. Through the resolution of the HJB equation associated to the new optimization problem, we determine the optimal strategy and we support our theoretical finding with numerical simulations. In the final part of the thesis, we study the joint dynamics of the at-the-money implied volatility and the spot process. We try to establish a relation between this joint dynamics and the implied skew through the use of a quantity called the Skew Stickiness Ratio which was introduced in the recent literature. The Skew Stickiness Ratio quantifies the effect of the log-return of the spot on the increment of theat-the-money volatility. We suggest a model-free approach for the estimation of the SSR (Skew Stickiness Ratio) under the risk-neutral measure, this approach doesn’t depend on hypothesis on the dynamics of the underlying. [...]
10
Hales, Stanley J. "Valuation of foreign currency options with the Paretian stable option pricing model /." The Ohio State University, 1997. http://rave.ohiolink.edu/etdc/view?acc_num=osu1269364712.
Full text
11
Huang, Liang Hai. "Pricing exchange options." Thesis, University of Macau, 2005. http://umaclib3.umac.mo/record=b1447320.
Full text
12
Samee, Farman. "Options with Prediction." Thesis, University of Manchester, 2009. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.516360.
Full text
13
Černý, Zdeněk. "LIFE INSURANCE OPTIONS." Master's thesis, Vysoká škola ekonomická v Praze, 2008. http://www.nusl.cz/ntk/nusl-4551.
Full textAbstract:
The goal of the thesis is to present and apply mathematical tools that are necessary for proper understanding of valuation of options in life insurance. This includes basic principles of actuarial calculations based on first order assumptions and the basics of stochastic calculus used for derivatives pricing. Afterthat we discuss the difference between first and second order assumptions and apply the mathematical tools to valuation of life insurance options. Finally the appearance of life insurance options within the liability adequacy test and european law is mentioned.
14
Larsson, Karl. "Pricing American Options using Simulation." Thesis, Umeå universitet, Institutionen för matematik och matematisk statistik, 2007. http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-51341.
Full textAbstract:
American options are financial contracts that allow exercise at any time until ex- piration. While the pricing of standard American option contracts has been well researched, with a few exceptions no analytical solutions exist. Valuation of more in- volved American option contracts, which include multiple underlying assets or path- dependent payoff, is still to a high degree an uncharted area. Most numerical methods work badly for such options as their time complexity scales exponentially with the number of dimensions. In this Master’s thesis we study valuation methods based on Monte Carlo sim- ulations. Monte Carlo methods don’t suffer from exponential time complexity, but have been known to be difficult to use for American option pricing due to the forward nature of simulations and the backward nature of American option valuation. The studied methods are: Parametrization of exercise rule, Random Tree, Stochastic Mesh and Regression based method with a dual approach. These methods are evaluated and compared for the standard American put option and for the American maximum call option. Where applicable the values are compared with those from deterministic reference methods. The strengths and weaknesses of each method is discussed. The Regression based method essentially reduces the problem to one of selecting suitable basis functions. This choice is empirically evaluated for the following Amer- ican option contracts; standard put, maximum call, basket call, Asian call and Asian call on a basket. The set of basis functions considered include polynomials in the underlying assets, the payoff, the price of the corresponding European contract as well as certain analytic approximation of the latter. Results from the empirical studies show that the regression based method is the best choice when pricing exotic American options. Furthermore, using available analytical approximations for the corresponding European option values as a basis function seems to improve the performance of the method in most cases.
15
Ncube, Mthuli. "Option pricing and volatility : theory and application to FT-SE 100 Index options." Thesis, University of Cambridge, 1991. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.385718.
Full text
16
Joo, Tan How. "Tests of options market efficiency : a study of the European Options Exchange." Thesis, University of Glasgow, 1990. http://theses.gla.ac.uk/1872/.
Full textAbstract:
The objective of this study is to provide evidence on the efficiency of the stock options market of the European Options Exchange. `Riskless' spreading and hedging strategies using the Black-Scholes call option pricing model with the Merton dividend adjustment, are used to test market efficiency. The results show that, although for the zero transactions costs case above-normal returns are possible, these returns become negative when the bid-ask spread cost is taken into account. These results persist over the two sample periods studied. Two variations of the trading rule that compute model prices by using the same model but with two different estimators of the standard deviation of the underlying stock's return as inputs to the model, also produce similar results. The study concludes that, with respect to the trading rules used and the sample periods studied, there were no inefficiencies on the stock options market of the European Options Exchange.
17
Lee, Seung-Hyun. "Real options theory : implications on entrepreneurship development and options value under uncertainty." The Ohio State University, 2002. http://rave.ohiolink.edu/etdc/view?acc_num=osu1272995868.
Full text
18
Lund, Simon Corvinius. "Real optioner og investering under usikkerhed = Real Options and Investment under Uncertainty /." Aarhus : Institut for Økonomi, Aarhus Universitet, 2008. http://mit.econ.au.dk/Library/Specialer/2008/20020768.pdf.
Full text
19
Mezentsev, Anton, and Anton Pomelnikov. "Valuation of Installment Options." Thesis, Halmstad University, School of Information Science, Computer and Electrical Engineering (IDE), 2009. http://urn.kb.se/resolve?urn=urn:nbn:se:hh:diva-3271.
Full text
20
Karlström, Viktor. "Mathematical analysis of options." Thesis, KTH, Farkost och flyg, 2011. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-43834.
Full text
21
Lowther, George Edward. "Derivative pricing with options." Thesis, University of Cambridge, 1999. https://www.repository.cam.ac.uk/handle/1810/265436.
Full textAbstract:
We consider the problem of pricing and hedging general path dependent derivatives on a single asset, supposing that we already know the prices of the vanilla options. If we are to avoid introducing arbitrage possibilities, then this is the same as finding a model under which the discounted asset price is a martingale and for which every vanilla option has its price equal to the expected value of its discounted payout. It has been shown by Dupire ([1], [2]) that if we restrict ourselves to diffusions, then the local volatility surface can be determined by a simple equation which involves differentiating the option prices with respect to their maturity and strike price. We considerably extend this result of Dupire. First, we show that if we generalise the possible models for the asset price to include what we shall term comparable processes, then there exists a unique such model fitting the observed option prices. The option prices need not be differentiable - just that they are continuous with respect to the maturity. One problem with the method proposed by Dupire is that no matter how many options we may observe in practise, it is impossible to calculate the local volatility surface to within any degree of accuracy. However, we show that the model for the asset price does depend on the observed options in a continuous way, so the proposed method of pricing derivatives is stable. We show that if we use implicit finite differences to fit the observed option prices ever more closely, then the associated model for the asset price will always converge to the unique comparable martingale consistent with these option prices. This theorem requires no preconditions, and works for all possible comparable processes, not just diffusions. The same is true for implicit finite differences, as long the associated trinomial processes do not contain any negative probabilities. Fina~Jy, we extend the well known link between arbitrage and the existence of equivalent martingale measures. We show that if the market consists of non-negative continuous assets, then there exists an equivalent martingale measure if and only if it does not admit arbitrage in a carefully defined approximating sense. This extends a similar result by Delbaen [1], which only concerned bounded processes.
22
Gómez, Moffat Mariana. "Stock options en Chile." Tesis, Universidad de Chile, 2004. http://www.repositorio.uchile.cl/handle/2250/114943.
Full textAbstract:
Memoria (licenciado en ciencias jurídicas y sociales)No autorizada por el autor para ser publicada a texto completo
Se hará un análisis que contempla los rasgos esenciales de los planes de Stock Options y su implementación en Chile. Dicho análisis será diferenciado entre los planes traídos o "importados" desde el extranjero y aquellos planes que se realicen ajustándose a las leyes sobre el mercado de valores y sociedades anónimas en Chile. Dentro de este contexto, se revisarán aquellas normas relacionadas con las normativa cambiaria chilena. Adicionalmente, se revisarán las normas laborales y tributarias aplicables a ambos tipos de planes, para concluir, finalmente, que si bien es cierto las normas aplicables para el otorgamiento de los planes de Stock Options extranjeros son distintas de aquellas establecidas para las sociedades anónimas chilenas que otorgan planes de Stock Options, al no haber normas especiales en materia laboral y tributaria, el criterio a aplicar para determinar si el beneficio que otorga un plan de Stock Options constituye mayor remuneración o no y su tratamiento tributario, será el mismo en unas y otras. Por último, se analizará las Stock Options en Estados Unidos y en Europa, donde han tenido más auge y los casos de Enron y WorldCom que han marcado un antes y un después en materia de Stock Options.
23
Davenport, John D. "Analysis of American options." Connect to online resource, 2007. http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&res_dat=xri:pqdiss&rft_dat=xri:pqdiss:3284479.
Full text
24
Brosch, Rainer. "Portfolios of real options." Berlin Heidelberg Springer, 2008. http://d-nb.info/988972077/34.
Full text
25
Achsnick, Jan. "Options-Modelle im Insolvenzplanverfahren /." Berlin : Duncker & Humblot, 2002. http://www.gbv.de/dms/sbb-berlin/345472632.pdf.
Full text
26
Lenga, Matthias [Verfasser]. "Representable Options / Matthias Lenga." Kiel : Universitätsbibliothek Kiel, 2017. http://d-nb.info/1135607788/34.
Full text
27
Andrews, Joyann A. "Regional options for Caricom." Thesis, Staffordshire University, 2000. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.365313.
Full text
28
Zhai, Jia. "Anomalies in options markets." Thesis, University of Essex, 2010. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.542355.
Full text
29
Hansen, Peder. "Pricing exotic power options." Thesis, Uppsala universitet, Analys och sannolikhetsteori, 2014. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-248571.
Full text
30
Parapoulis, Panagiotis. "Hedging foreign currency options." Thesis, University of Reading, 1992. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.317577.
Full text
31
Firth, Neil Powell. "High dimensional American options." Thesis, University of Oxford, 2005. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.427867.
Full textAbstract:
Pricing single asset American options is a hard problem in mathematical finance. There are no closed form solutions available (apart from in the case of the perpetual option), so many approximations and numerical techniques have been developed. Pricing multi–asset (high dimensional) American options is still more difficult. We extend the method proposed theoretically by Glasserman and Yu (2004) by employing regression basis functions that are martingales under geometric Brownian motion. This results in more accurate Monte Carlo simulations, and computationally cheap lower and upper bounds to the American option price. We have implemented these models in QuantLib, the open–source derivatives pricing library. The code for many of the models discussed in this thesis can be downloaded from quantlib.org as part of a practical pricing and risk management library. We propose a new type of multi–asset option, the “Radial Barrier Option” for which we find analytic solutions. This is a barrier style option that pays out when a barrier, which is a function of the assets and their correlations, is hit. This is a useful benchmark test case for Monte Carlo simulations and may be of use in approximating multi–asset American options. We use Laplace transforms in this analysis which can be applied to give analytic results for the hitting times of Bessel processes. We investigate the asymptotic solution of the single asset Black–Scholes–Merton equation in the case of low volatility. This analysis explains the success of some American option approximations, and has the potential to be extended to basket options.
32
Filis, George N. "Options in emerging markets." Thesis, Bournemouth University, 2004. http://eprints.bournemouth.ac.uk/340/.
Full textAbstract:
Index options are traded in many derivatives markets around the world. These derivatives markets can either operate in efficient or inefficient markets. Most derivatives markets use the best known option pricing model, i. e. the Black and Scholes Option Pricing Model, in order to produce theoretical option prices. However, the model itself assumes that the markets are efficient so that theoretical prices do not differ significantly from market prices. But what is happening in emerging markets? Emerging markets are characterized by many anomalies, which may create problems either to the model or in general to the fair option pricing. This study is concerned with the Athens Stock Exchange and the Athens Derivatives Exchange. Specifically, this research tests the at-the-money index call options on the FTSE/ASE 20 index with two months to expiration. The Greek market is an `emerging' market and this research tries to show that the Black and Scholes model is not an appropriate model for the Athens Stock Exchange or, more generally, for emerging markets, due to its assumptions. Additionally, the research tries to identify market anomalies and to test whether these anomalies have a significant effect on the market option prices. The thesis includes a review of empirical studies on stock and option markets and on the Black and Scholes model. The conclusions of these studies suggest that there are several market anomalies in stock markets that affect option prices. Furthermore, there are many criticisms that can be leveled against the Black and Scholes model and its assumptions. In order to identify the market anomalies and option mis-pricing, we employ a battery of statistical tests. The test results tend to support the previous empirical studies and suggest that the Athens Stock Exchange suffers from several anomalies. The results also indicate the inefficient status of the market. In addition, the Black and Scholes model creates pricing problems in the Greek market. These pricing problems are due to the stock market anomalies and the mis-estimation of the true (historic) volatility from the implied volatility. The final part of the thesis shows the significant effect that the stock market anomalies have on option prices. Market anomalies, such as mis-estimation of the historic volatility, asymmetric information, insider trading and low market depth, have a significant effect on option prices. Adding these anomalies to the Black and Scholes model, we are able to construct a model that can predict market option prices more reliably.
33
Richards, Darren Glyn. "Pricing American exotic options." Thesis, University of Cambridge, 1999. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.624594.
Full text
34
Mullen, Gary James. "Options for decision theory." Thesis, University of Leeds, 2018. http://etheses.whiterose.ac.uk/21735/.
Full text
35
Rodrigues, António Pedro Cortes. "Portfolio optimization with options." Master's thesis, NSBE - UNL, 2009. http://hdl.handle.net/10362/9466.
Full textAbstract:
A Work Project, presented as part of the requirements for the Award of a Masters Degree in Finance from the NOVA – School of Business and EconomicsIn order to address the options returns non normality problem in the investment portfolio theory, this work project aims to discuss and present alternatives to the classic Markowitz risk/return paradigm. The following pages will exploit the Portfolio Selection Theory developed over the last decade, maximizing a standard CRRA utility function, and simulating (MonteCarlo) or deriving from the past data (Bootstrap) the path taken by the S&P 500 stock Index. To conclude, a 5 year back test is developed to evidence the practical implications of the several models exposed.
36
Høegh, Morten W. (Morten Westyne) 1973. "Options on shipbuilding contracts." Thesis, Massachusetts Institute of Technology, 1998. http://hdl.handle.net/1721.1/50479.
Full textAbstract:
Thesis (S.B. and S.M.)--Massachusetts Institute of Technology, Dept. of Ocean Engineering, 1998.Includes bibliographical references (p. 123-124).
Analysis of investment projects and strategic decisions using option theory has gained wide acceptance among corporate finance scholars and professionals. In the shipping and shipbuilding industries, option analysis is still in its infancy, and few professionals are familiar with option valuation tools. At the same time, practically all shipbuilding contracts contain option elements, the value of which most industry players do not know how to calculate. Newbuilding options give shipowners closing newbuilding contracts a right, but not an obligation, to enter into additional newbuilding contracts, with predetermined terms, at a later date. This thesis presents a general introduction to option theory as it applies to traded financial securities. This framework is extended to newbuilding options. Characteristics of the newbuilding markets are given, and fundamental stochastic processes that can describe newbuilding prices are introduced. Based on these stochastic processes, closed-form formulas for calculating the value of newbuilding options are presented. Actual observations of shipbuilding prices are analyzed in the context of the stochastic models. The results of this analysis are discussed as they apply to the option formulas and to the practical aspects of the newbuilding option framework. Recommendations are given on how to analyze real cases in which newbuilding options appear.
by Morten W. Høegh.
S.B.and S.M.
37
Khandelwal, Vasudha. "Volatility of European Options." The Ohio State University, 2019. http://rave.ohiolink.edu/etdc/view?acc_num=osu1554809434581109.
Full text
38
Roubaud, David. "Options réelles et ambiguïté." Thesis, Aix-Marseille 3, 2011. http://www.theses.fr/2011AIX32040.
Full textAbstract:
Cette thèse se positionne au croisement de la théorie de la décision en univers incertain et de la théorie des choix d’investissements irréversibles (options réelles). Elle poursuit trois objectifs principaux :1. Tout d’abord, elle s’inscrit dans un courant de recherche dynamique, notamment en économie et en finance, qui vise à modéliser l’impact de l’ambigüité à laquelle des décideurs sont parfois confrontés lorsqu’ils contemplent des choix aux conséquences irréversibles. 2. Ensuite, elle met l’accent sur la persistance de fortes controverses théoriques portant sur les fondements axiomatiques des modèles de décision face à l’ambigüité. Aussi, nous proposons d’utiliser certaines propriétés des modèles non linéaires pour aborder sous un angle original la représentation de l’ambigüité et des préférences des individus face à celle-ci. En particulier, nous suggérons de ne pas restreindre a priori la nature des préférences individuelles face à l’ambigüité. Pour cela, nous adoptons les fondements de l’approche de Choquet, à savoir tout particulièrement l’emploi de capacités (probabilités non additives) pour pondérer les différentes alternatives ambigües. Tout en proposant ce processus stochastique ambigu, dit Choquet-Brownien, nous soulignons les conditions de l’inévitable arbitrage entre réalisme des hypothèses et souplesse d’utilisation du modèle. D’un point de vue axiomatique, une attention particulière est portée au respect de la cohérence dynamique.3. Enfin, cette thèse vise à encourager une prise en considération plus ambitieuse des sources d’incertitude dans le cadre des options réelles. Alors qu’ils sont présentés comme des outils privilégiés pour affronter le risque, les modèles d’options réelles ont certainement beaucoup à gagner à s’enrichir par la prise en compte également de l’ambigüité. En effet, alors que le risque est largement discuté dans la littérature des options réelles, l’impact de l’ambigüité est très largement ignoréThe need to elaborate innovative methods to analyze risk and uncertainty has become increasingly obvious over the last decades, especially due the growing perception of the multiplicity of social and economical issues characterized by the weight of uncertainty (natural disasters, ecological risk, financial crises…).This thesis is at the crossroad between decision theory under uncertainty and the irreversible investment theory (real options). Consequently, the main goal of this thesis is three-fold: 1. First, it contributes to the dynamic stream of literature in economics and finance that models the impact of ambiguity that individuals may often face and/or perceive when contemplating irreversible choices.2. Next, this thesis emphasizes that even with the plethora of decision models already dealing with uncertainty, elaborating sound axiomatic foundations largely remains an open question. This leads us to recommending the use of non linear models (such as multiple-priors, Choquet expected utility, robust control, smooth ambiguity), which in turn raises many challenging theoretical and practical obstacles. We explore original ways of addressing some of these issues and suggest the construction of ambiguous stochastic processes in a Choquet expected utility framework (that are called Choquet-Brownian motions): ambiguity preferences are thereby directly embedded into the trajectory of some random variables that may drive a decision, such as the expected cash flows of an investment project or its exit value.3. Finally, this thesis also aims specifically at encouraging the enrichment of real option models. It is striking that only the impact of risk has been widely discussed by the real option theory so far, while the specific impact of ambiguity has been largely ignored. Considering that the real option theory is directly concerned with sources of flexibility, irreversibility and uncertainty in general, ambiguity represents a promising expansion
39
Lin, Nicole Yueh-Neng. "Option pricing under stochastic volatility for S & P 500 FTSE 100 index options." Thesis, University of Manchester, 1999. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.632541.
Full textAbstract:
This thesis examines option pricing under stochastic volatility for S&P 500 and FTSE 100 index options. The main contributions of the thesis are: (i) it provides empirical evidence of stochastic volatility in S&P 500 and FTSE 100 index returns; (ii) it explains empirically the impact of stochastic volatility on option pricing for index options; (iii) it tests whether option prices are consistent with the time series properties of the underlying asset price; and (iv) it investigates the magnitude and sign of volatility risk premlums. The empirical evidence shows that changes in S&P 500 and FTSE 100 index prices have distributions with fatter tails than the normal distribution and non-zero skewness. This leads to a consideration of non-normal distributions and possible explanations for deviations from normality. Of the possible explanations for the documented leptokurtosis in stock returns, stochastic volatility is generally regarded as the most likely candidate. The GARCH( 1,1 LTX model is shown to capture the volatile nature of our data well. A diffusion limit of the GARCH(1, 1 L TX process is the mean-reverting square root volatility process used in Heston's (1993) option pricing formula. This research considers Heston's (1993) stochastic volatility (SV) option pricing model as the empirical challenger to the Black-Scholes (BS) model, which assumes that the distribution of stock price changes is normally distributed with constant volatility. Insample pricing, out-of-sample forecasting, diagnosis of implied volatility curves, and internal consistency with the time series of implied volatilities and with the GARCH( 1,1 L TX process are examined to investigate the performance of the BS and SV models. We also conduct careful and detailed data screening for our empirical work. Our results reveal significant evidence of stochastic volatility implicit in option prices, and suggest that this phenomenon is essential to improving the performance of the BS model for index options. Nevertheless, internal consistency test results report inconsistency of both the BS and SV models with time-series data, indicating residual SV model misspecification for SPX and FTSE-I00 options. This has the important implication that stochastic volatility is a significant factor in option pricing but not the only factor affecting stock index option prices. Option pricing under stochastic volatility involves a preference issue since volatility is a nontraded asset. This research assumes that the volatility risk premium is proportional to the spot volatility level, which is internalised in the risk-neutral parameters. The actual volatility parameters can be recovered either from the time series of implied volatilities using option prices or from the GARCH( 1,1 L TX process using index returns. By comparing actual parameters with their risk-neutral counterparts, an estimate of the unit volatility risk premium can be thus obtained. Negative premiums for volatility risk are consistently observed in the SPX option market while there are mixed results for the S&P 500 index, FTSE 100 index and options markets. Nevertheless, the magnitudes of these estimates indicate that compensation for volatility risk is a significant component of the risk premiums in the S&P 500 and FTSE 100 index and option markets. However, the possibility of misspecification in the SV and GARCH(I,ILTX models should be kept in mind when explaining the magnitude and sign of risk premiums.
40
Lai, Wei-Chiang, and 賴瑋鎗. "Option Pricing Theory : Implementation of Heston Model for Index Options and FX Options." Thesis, 2016. http://ndltd.ncl.edu.tw/handle/exgp5f.
Full textAbstract:
碩士國立中央大學
財務金融學系
104
After Black &; Scholes Theory born, people from business and academic fields were devoting to fix the flawless and implement BS Model in a more practical way. With well-developed mathematics theories and high-efficient computers, the ways we pricing are more accurate than it was, especially Heston Model. In Heston Model, we have to do parameters calibration before Monte-Carol simulation. In this paper, we focused on parameters calibration section and try to find a loss function that is the most accurate in calibration. Also, we examined the consistency of parameters so that we can know if parameter will be changed by information flow in the market. On the other hand, we did Monde-Carol simulation by different time space to find out the most efficient simulation step. Last but not the least, we made a comparison between BS Model &; Heston Model to search if there is any difference between those two popular option pricing theories. The big discovery is that the winning probability of BS and the winning probability of Heston are not the same because of the basic assumption.
41
Cheng, Hsiu-wen, and 鄭綉紋. "A Pricing Model of Fuzzy Path Dependent Option: Options on Extrema, Limit Risk Options and Partial Lookback Options as Examples." Thesis, 2013. http://ndltd.ncl.edu.tw/handle/68639642235357188244.
Full textAbstract:
碩士國立雲林科技大學
資訊管理系碩士班
101
Black and Scholes proposed the European option pricing model as a closed form solution which can calculate the option price directly in 1973. The B-S model can also be used in lookback option with assuming the parameters as constant value. However, riskless interest rate and volability of the stock, the main parameters in B-S model, are stochastic and nonconstant. This study apply fuzzy theory to option pricing model that the uncertainty existing in environment is considered and solve the irrational assumptions from B-S model. The results comparing fuzzy lookback option pricing model and ordenary oprion pricing model is that the expected value of the call price of in the money and at the money are over-estimated, but the expected value of the call price of out of money is under-estimated without considering fuzziness. This affects the decision of investors which results the loss. There is no closed form solution for an American lookback option. It can only be estimated in a rational price intervel. In this study, an American lookback option can be solved through binomial method tree under uncertain environment. It is assumed that the future fluctuation of the stock price can be up-movement u and down-movement d in binomial method tree. The fuzziness is applied by fuzzy number to make the call price more suitable for the real price.
42
Cheng, Tsun-Hung, and 鄭圳宏. "Deep Learning for Option Pricing Using TAIEX Options." Thesis, 2019. http://ndltd.ncl.edu.tw/handle/ff87uk.
Full textAbstract:
碩士國立臺北商業大學
財務金融系研究所
107
This paper explores the pricing of TAIEX put options with deep learning. We first choose the contracts which volume over 1000 lots to avoid the problem of liquidity, then convert call premiums with high strike price to those of put by using the put-call parity. Moreover, we use TAIEX future, historical volatility, and 30-days money market rate as underlying, volatility, and risk-free rate respectively. The inputs of deep learning include the underlying, strike price, volatility, time to maturity, and risk-free rate, as those in the Black-Scholes-Merton Framework. The results show that the pricing error of deep learning is small than that of Black-Scholes-Merton model for the at-the-money and out-of-the money contracts, based on the criteria of mean square error and mean absolute error. However, the result is opposite for the in-the-money contract. The summary is that the performance of deep learning is slightly better than that of Black-Scholes-Merton model for all contracts.
43
Lin, Jian-Jyun, and 林堅鈞. "Pricing Taiwanese Employee Stock Options by Barrier Option Model." Thesis, 2009. http://ndltd.ncl.edu.tw/handle/xgbc7f.
Full textAbstract:
碩士銘傳大學
財務金融學系碩士班
97
After Financial Accounting Standards No. 39 “Share-based Payment” formally carried out, it is necessary to assess the fair value of the employee stock options, which will result in direct or indirect impacts on financial statements. In the way of the fair value method on pricing employee stock options, we will recognize higher expense through conventional Black-Scholes or binomial option pricing model. This would lead to the decrease in net income on Income Statement, and hence diluting the earnings per share (EPS). Furthermore, the conventional pricing model would easily overvalue the additional pay-in-capital on Balance Sheet, therefore, causing to undervalue return on equity (ROE) and return on assets (ROA).Therefore, the main purpose of this study is to price employee stock options by using barrier option model in hope to obtain more reasonable and fair values. The empirical results indicate that pricing the employee stock options by using barrier option model would generate less fair value than by using Black-Scholes or binomial option pricing model. This would help to improve the situation for undervaluing net income on Income Statement and overvaluing the stockholder equity; and further to avoid underestimating EPS, ROE, and ROA. Finally, based on sensitivity analysis, in addition to cancellation rate, the average maturity, stock price under exercise to exercise price ratio, and the correlation between the former two could play an important role of pricing Taiwanese employee stock options.
44
Chen, Yu_Lin, and 陳玉玲. "The NGARCH Option Pricing Model: Application to TAIEX Options." Thesis, 2002. http://ndltd.ncl.edu.tw/handle/87334832343648722641.
Full textAbstract:
碩士國立交通大學
應用數學系
90
Following the work of Black and Scholes, we consider a discrete time option model of the NGARCH asset return process. At the same time, a new numerical method named by Empirical Martingale Simulation (EMS) takes the place of crude Monte Carlo Simulation (MCS) to calculate the generated option price. Combining these techniques, we investigate the Taiwan Stock Exchange Capitalization Weighted Stock Index (TAIEX) options which were introduced on December 24, 2001. The result shows that the valuation model is better than the Black-Scholes model.
45
Chen, Chun-Hao, and 陳俊豪. "Model Risk of Option Pricing Models for TAIEX Options." Thesis, 2005. http://ndltd.ncl.edu.tw/handle/75726979602795598669.
Full textAbstract:
碩士長庚大學
企業管理研究所
94
Since B-S model been developed in 1973, its assumptions that volatility and risk-free rate are constant are inconsistentent with reality. These assumptions result in estimation error while using B-S model to price options. The risk that results from pricing model is called model risk. Figlewski and Green (1999) pointed out that model risk result from incomplete or incorrect pricing model, including erroneous estimation of parameters and incorrect volatility estimator. Main sources of model risk separate two parts. First, there is the risk that a given pricing model may be mis-specified. A second important source of model risk in estimation error of volatility model ( history volatility、GARCH model ). The research uses B-S (1973) model and Hull & White (1987) stochastic volatility model to observe whether Hull & White (1987) model can significant decrease model risk .In the other way, we try to discuss whether different volatility models have significant difference in using history volatility and GARCH model. In according to empirical results, different models indeed exist model risk. Both Pricing models and volatility models can produce certain degree model risk. Empirical results proved no significant difference of model risk between Hull & White (1987) stochastic volatility model and B-S (1973) model. In the other way, GARCH model is better volatility model than history volatility in estimating volatility.
46
吳智偉. "Comparison of option pricing estimating：Empirical evidence from TAIEX options." Thesis, 2010. http://ndltd.ncl.edu.tw/handle/78911688374048571656.
Full textAbstract:
碩士明新科技大學
企業管理研究所
98
In the early 1970s, Fischer Black, Myron Scholes, and Robert Merton achieved a major breakthrough in the pricing of stock options. This involved the development of what has become known as the Black-Scholes（1973）model. The model has had a huge influence on the way that trader’s price and hedge options. As a result of many unduly simplified assumptions of the Black-Scholes（1973）model, many scholars started to modify the Black-Scholes（1973）model, such as the stochastic volatility option model,stochastic interest rate option model and stochastic volatility and Poisson jump diffusion option model. Therefore, the purpose of this study is estimate for Black-Scholes（1973） option prices model and Heston (1993) option pricing model to find out which option pricing model is the most suitable for evaluating the TXO. In this paper three loss function are used to estimate the Heston (1993) estimated values are incorporated into the Heston (1993) option pricing model to calculate the theoretical prices. Furthermore,estimating of Black-Scholes（1973）and Heston (1993) the difference between the theoretical price and the market price is calculated using the statistical error measures to find the optimum option pricing model. The results show that the theoretical price with Heston (1993) option pricing model is closest to the market price, and therefore the Heston (1993) option pricing model is the option price model for evaluating the TXO.
47
WANG, GING-YI, and 王清義. "Research for options and accounting for options." Thesis, 1989. http://ndltd.ncl.edu.tw/handle/79100170257224950785.
Full text
48
Zi-Xin, Tong, and 童子星. "Option Pricing Model with Liquidity-Evidence from Taiwan Stock Options." Thesis, 2007. http://ndltd.ncl.edu.tw/handle/39762383711385619726.
Full textAbstract:
碩士輔仁大學
經濟學研究所
95
This study evaluates the Taiwan stock option price based on the model developed by 沈文玲(2004). The option pricing model extends Black-Scholes Model by considering the liquidity of both underlying and option markets. Top five trading volume Taiwan stock options include AUO, CMO, CHB, CPT and TSMO are analyzed in this thesis. The theoretical prices of the stock options are calculated by the finite difference method. The empirical daily data cover the period of 2005/3-2006/12. In order to test the accuracy of option pricing model with liquidity B-S model price are compared with the extended model by measures of MAE, MAPE, RMSPE , RMSE and population mean. The result shows that the extended model’s performance is better than the basic B-S model in terms of MAE, MAPE, RMSE, RMSPE and mean.
49
Liu, Ming-Tsang, and 劉明滄. "Static Hedge of Barrier Options and Lookback Options." Thesis, 1998. http://ndltd.ncl.edu.tw/handle/85484420983684271873.
Full text
50
董春福. "Path-dependent Exotic Options Pricing Approach----Lookback Options." Thesis, 1999. http://ndltd.ncl.edu.tw/handle/09780995631839638536.
Full textAbstract:
碩士中原大學
企業管理學系
87
This research is going to use the Lookback Options of Path-dependent Exotic Options as example. And, here, we are going to choose United Microelectronics Corporation and Cathay Life as the underlying assets. The Analytic Model (closed-form solution), Monte Carlo Simulation Model, and the Numerical Model (Binomial Trees) will be three different assessment models. The purposes are going to tell the advantages or disadvantages of these three assessments and to adjust the parameter during the actual imitative experiment process. Besides, people can see the possible results/influences/impacts. Moreover, these results could be provided as good information for all investors to analyze or compare. According to the imitative experiment, we can get the following conclusions： 1.The call options prices of these three pricing models is very similar. It shows that the assessment results of these three pricing models should have the value of references. However, the assessment result of the numerical model could be cheaper than the others. Therefore, it should be better to the investors. 2.According to the research, the Analytic Model (closed-form solution) just could be used to value the European Options. Actually it is also a good choice for the assessment of European Options, not American Options, because the efficiency is better. However, the Monte Carlo Simulation Model has to be used by the way of discrete time intervals and to repeat the imitative tests again and again, the efficiency is worse. Therefore, it is not appropriate for the American Options. The Numerical Model (Binomial Trees), when the prices can reach the result of the convergence, it should be subdivided five thousand time steps more, but this model appropriate for the American Options adjust and compute. Therefore, it is also a good choice for the assessment of American Options. 3.In our finding, the influence on call options price by parameter in the relationship of volatility and call options price is positive(same direction), so is Time to Maturity; but striking price has opposite relation with call options price. Since striking price has significant effect on call options price, the decision on striking price must be made with great concern. In a word, all these three assessment models have their advantages and disadvantages. It is impossible to tell which one is better or worse just depending one model. The best way is to choose an appropriate one and then apply it according to the situation.