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1
Harr, Martin. "Option Pricing in the Presence of Liquidity Risk." Thesis, Umeå University, Department of Physics, 2010. http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-35100.
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The main objective of this paper is to prove that liquidity costs do exist in option pricingtheory. To achieve this goal, a martingale approach to option pricing theory is usedand, from a model by Jarrow and Protter [JP], a sound theoretical model is derived toshow that liquidity risk exists. This model, derived and tested in this extended theory,allows for liquidity costs to arise. The expression liquidity cost is used in this paper tomeasure liquidity risk relative to the option price.
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Lei, Ngai Heng. "Martingale method in option pricing theory." Thesis, University of Macau, 2003. http://umaclib3.umac.mo/record=b1447303.
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Dranev, Yury. "Equivalent Martingale measures and option pricing in jump-diffusion markets." Thesis, University of Ottawa (Canada), 2004. http://hdl.handle.net/10393/10794.
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One of the key questions in financial mathematics is the choice of an appropriate model for the financial market. There are a number of models available, such as Geometrical Brownian motion and different types of Levy processes, that are not general enough to reflect all the characteristics of fluctuations in stock price but for which the parameters can be estimated with relative ease. There are more general semimartingale models for which parameter estimation and numerical calculation become very difficult questions. The goal of this thesis is to present a tractable model for which we can carry out computations, and it seems that by varying the parameters this model can be related to real market data. We will use the equivalent measure approach to obtain estimates of the price of European call options for our model. Since our market is incomplete, a consequence of the inclusion of jump processes in the model, we will choose the "best" equivalent martingale measure by applying various techniques and compare the results for different choices. We will also illustrate how this theory works on particular examples. We consider applications not only to the cases of continuous and Levy process markets but also to cases that reflect the main advantages of our jump diffusion model. Finally we numerically illustrate option pricing in our setting.
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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.
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Hao, Wenyan. "Quantum mechanics approach to option pricing." Thesis, University of Leicester, 2018. http://hdl.handle.net/2381/43020.
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Options are financial derivatives on an underlying security. The Schrodinger and Heisenberg approach to the quantum mechanics together with the Dirac matrix approaches are applied to derive the Black-Scholes formula and the quantum Cox- Rubinstein formula. The quantum mechanics approach to option pricing is based on the interpretation of the option price as the Schrodinger wave function of a certain quantum mechanics model determined by Hamiltonian H. We apply this approach to continuous time market models generated by Levy processes. In the discrete time formulization, we construct both self-adjoint and non selfadjoint quantum market. Moreover, we apply the discrete time formulization and analyse the quantum version of the Cox-Ross-Rubinstein Binomial Model. We find the limit of the N-period bond market, which convergences to planar Brownian motion and then we made an application to option pricing in planar Brownian motion compared with Levy models by Fourier techniques and Monte Carlo method. Furthermore, we analyse the quantum conditional option price and compare for the conditional option pricing in the quantum formulization. Additionally, we establish the limit of the spectral measures proving the convergence to the geometric Brownian motion model. Finally, we found Binomial Model formula and Path integral formulization gave are close to the Black-Scholes formula.
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Chen, Si S. M. Massachusetts Institute of Technology. "Robust option pricing : An [epsilon]-arbitrage approach." Thesis, Massachusetts Institute of Technology, 2009. http://hdl.handle.net/1721.1/55108.
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Thesis (S.M.)--Massachusetts Institute of Technology, Computation for Design and Optimization Program, 2009.In title on title-page, "[epsilon]" appears as the lower case Greek letter. Cataloged from PDF version of thesis.
Includes bibliographical references (p. 59-60).
This research aims to provide tractable approaches to price options using robust optimization. The pricing problem is reduced to a problem of identifying the replicating portfolio which minimizes the worst case arbitrage possible for a given uncertainty set on underlying asset returns. We construct corresponding uncertainty sets based on different levels of risk aversion of investors and make no assumption on specific probabilistic distributions of asset returns. The most significant benefits of our approach are (a) computational tractability illustrated by our ability to price multi-dimensional options and (b) modeling flexibility illustrated by our ability to model the "volatility smile". Specifically, we report extensive computational results that provide empirical evidence that the "implied volatility smile" that is observed in practice arises from different levels of risk aversion for different strikes. We are able to capture the phenomenon by appropriately finding the right risk-aversion as a function of the strike price. Besides European style options which have fixed exercising date, our method can also be adopted to price American style options which we can exercise early. We also show the applicability of this pricing method in the case of exotic and multi-dimensional options, in particular, we provide formulations to price Asian options, Lookback options and also Index options. These prices are compared with market prices, and we observe close matches when we use our formulations with appropriate uncertainty sets constructed based on market-implied risk aversion.
by Si Chen.
S.M.
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Chuang, Chienmin. "Multi-asset option pricing problems : a variational approach." Thesis, University of Birmingham, 2012. http://etheses.bham.ac.uk//id/eprint/3917/.
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Options are important and frequently traded products in the modern financial market. How to price them fairly and reasonably is always an interesting issue for academia and industry. This research is performed under the classical multi-asset Black-Scholes-Merton (BSM) model and can be extended to other exotic models. We show how to reformulate the multi-asset Black-Scholes-Merton partial differential equation/inequality (BSM PDE/PDI) and provide theorems to justify the unique solution of reformulations. In terms of discretization, we adopt the finite element method (FEM) in space and finite difference method (FDM) in time. Moreover, we develop the closed-form formulas for the elemental matrices used in the finite element assembly process in a general high-dimensional framework. The discrete systems of option pricing problems are presented in the form of linear system of equations (LSE) and linear complementary problems (LCP) for European and American/perpetual options respectively. Up to six different algorithms for the LCP are introduced and compared on the basis of computational efficiency and errors. The option values of European, American and perpetual types are calibrated when given various payoffs and up to three assets. Particularly, their numerical free boundaries are identified and presented in the form of (d - 1)-dimensional manifold in a d-assetframework. In the last chapter, we conclude our research with our contributions and potential extension.
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Liu, Lu. "Pricing energy path-dependent option using tree based approach." Thesis, Imperial College London, 2009. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.512006.
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Grandits, Peter, and Werner Schachinger. "Leland's approach to option pricing. The evolution of a discontinuity." SFB Adaptive Information Systems and Modelling in Economics and Management Science, WU Vienna University of Economics and Business, 1999. http://epub.wu.ac.at/1448/1/document.pdf.
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A claim of Leland (1985) states that in the presence of transaction costs a call option on a stock S, described by geometric Brownian motion, can be perfectly hedged using Black-Scholes delta hedging with a modified volatility. Recently Kabanov and Safarian (1997) disproved this claim, giving an explicit (up to an integral) expression of the limiting hedging error, which appears to be strictly negative and depends on the path of the stock price only via the stock price at expiry ST . We prove in this paper that the limiting hedging error, considered as a function of ST, exhibits a removable discontinuity at the exercise price. Furthermore, we provide a quantitative result describing the evolution of the discontinuity, which shows that its precursors can very well be observed also in cases of reasonable length of revision intervals. (author's abstract)Series: Report Series SFB "Adaptive Information Systems and Modelling in Economics and Management Science"
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Bart, Adde Tiffany, and Kadek Maya Sri Puspita. "American Option pricing under Mutiscale Model using Monte Carlo and Least-Square approach." Thesis, Mälardalens högskola, Utbildningsvetenskap och Matematik, 2017. http://urn.kb.se/resolve?urn=urn:nbn:se:mdh:diva-35848.
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In the finance world, option pricing techniques have become an appealing topic among researchers, especially for pricing American options. Valuing this option involves more factors than pricing the European style one, which makes it more computationally challenging. This is mainly because the holder of American options has the right to exercise at any time up to maturity. There are several approaches that have been proved to be efficient and applicable for maximizing the price of this type of options. A common approach is the Least squares method proposed by Longstaff and Schwartz. The purpose of this thesis is to discuss and analyze the implementation of this approach under the Multiscale Stochastic Volatility model. Since most financial markets show randomly variety of volatility, pricing the option under this model is considered necessary. A numerical study is performed to present that the Least-squares approach is indeed effective and accurate for pricing American options.
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Chang, Shou-Wei. "Valuing the firm and its equity : a cash flow contingent claims approach." Thesis, University of Southampton, 1998. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.266522.
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Cuningham, Blake. "Comparing GARCH models for gold price data, using a statistical loss function approach and an option pricing approach." Master's thesis, University of Cape Town, 2011. http://hdl.handle.net/11427/10289.
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Derivative instruments that rely on the price of gold are traded in large volumes. A significant number of these instruments are influenced by the volatility of gold price movements. Hence, it is important to understand the volatility of this commodity when developing successful trading and hedging strategies. In this thesis, use is made of various GARCH models that are evaluated using both in-sample and out-of-sample criteria.
13
Willder, Mark. "An option pricing approach to charging for maturity guarantees given under unitised with-profits policies." Thesis, Heriot-Watt University, 2004. http://hdl.handle.net/10399/316.
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Dickmann, Fabian Verfasser], Denis [Akademischer Betreuer] Belomestny, John [Akademischer Betreuer] [Schoenmakers, and Mikhail [Akademischer Betreuer] Urusov. "Multilevel approach for Bermudan Option Pricing / Fabian Dickmann. Gutachter: John Schoenmakers ; Mikhail Urusov. Betreuer: Denis Belomestny." Duisburg, 2015. http://d-nb.info/1074825233/34.
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Kaya, Deniz. "Pricing a Multi-Asset American Option in a Parallel Environment by a Finite Element Method Approach." Thesis, Uppsala universitet, Matematiska institutionen, 2011. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-155546.
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There is the need for applying numerical methods to problems that cannot be solved analytically and as the spatial dimension of the problem is increased the need for computational recourses increase exponentially, a phenomenon known as the “curse of dimensionality”. In the Black-Scholes-Merton framework the American option pricing problem has no closed form solution and a numerical procedure has to be employed for solving a PDE. The multi-asset American option introduces challenging computational problems, since for every added asset the dimension of the PDE is increased by one. One way to deal with the curse of dimensionality is threw parallelism. Here the finite element method-of-lines is used for pricing a multi-asset American option dependent on up to four assets in a parallel environment. The problem is also solved with the PSOR method giving a accurate benchmark used for comparison. In finance the put option is one of the most fundamental derivatives since it is basically asset-value insurance and a lot of research is done in the field of quantitative finance on accurate and fast pricing techniques for the multi-dimensional case. “What most experimenters take for granted before they begin their experiments is infinitely more interesting than any results to which their experiments lead.” Norbert Wiener “As soon as an Analytical Engine exists, it will necessarily guide the future course of the science. Whenever any result is sought by its aid, the question will then arise – by what course of calculation can these results be arrived at by the machine in the shortest time?” Charles Babbage
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Jung, Dosub. "The model risk of option pricing models when volatility is stochastic : a Monte Carlo simulation approach /." free to MU campus, to others for purchase, 2000. http://wwwlib.umi.com/cr/mo/fullcit?p9974644.
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Dickmann, Fabian [Verfasser], Denis Akademischer Betreuer] Belomestny, John [Akademischer Betreuer] [Schoenmakers, and Mikhail [Akademischer Betreuer] Urusov. "Multilevel approach for Bermudan Option Pricing / Fabian Dickmann. Gutachter: John Schoenmakers ; Mikhail Urusov. Betreuer: Denis Belomestny." Duisburg, 2015. http://d-nb.info/1074825233/34.
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Mohammad, Omar, and Rafi Khaliqi. "American option prices and optimal exercise boundaries under Heston Model–A Least-Square Monte Carlo approach." Thesis, Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, 2020. http://urn.kb.se/resolve?urn=urn:nbn:se:mdh:diva-48928.
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Pricing American options has always been problematic due to its early exercise characteristic. As no closed-form analytical solution for any of the widely used models exists, many numerical approximation methods have been proposed and studied. In this thesis, we investigate the Least-Square Monte Carlo Simulation (LSMC) method of Longstaff & Schwartz for pricing American options under the two-dimensional Heston model. By conducting extensive numerical experimentation, we put the LSMC to test and investigate four different continuation functions for the LSMC. In addition, we consider investigating seven different combination of Heston model parameters. We analyse the results and select the optimal continuation function according to our criteria. Then we uncover and study the early exercise boundary foran American put option upon changing initial volatility and other parameters of the Heston model.
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Li, Wen. "Numerical methods for the solution of the HJB equations arising in European and American option pricing with proportional transaction costs." University of Western Australia. School of Mathematics and Statistics, 2010. http://theses.library.uwa.edu.au/adt-WU2010.0098.
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This thesis is concerned with the investigation of numerical methods for the solution of the Hamilton-Jacobi-Bellman (HJB) equations arising in European and American option pricing with proportional transaction costs. We first consider the problem of computing reservation purchase and write prices of a European option in the model proposed by Davis, Panas and Zariphopoulou [19]. It has been shown [19] that computing the reservation purchase and write prices of a European option involves solving three different fully nonlinear HJB equations. In this thesis, we propose a penalty approach combined with a finite difference scheme to solve the HJB equations. We first approximate each of the HJB equations by a quasi-linear second order partial differential equation containing two linear penalty terms with penalty parameters. We then develop a numerical scheme based on the finite differencing in both space and time for solving the penalized equation. We prove that there exists a unique viscosity solution to the penalized equation and the viscosity solution to the penalized equation converges to that of the original HJB equation as the penalty parameters tend to infinity. We also prove that the solution of the finite difference scheme converges to the viscosity solution of the penalized equation. Numerical results are given to demonstrate the effectiveness of the proposed method. We extend the penalty approach combined with a finite difference scheme to the HJB equations in the American option pricing model proposed by Davis and Zarphopoulou [20]. Numerical experiments are presented to illustrate the theoretical findings.
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Celep, Saziye Betul. "Stochastic Volatility And Stochastic Interest Rate Model With Jump And Its Application On General Electric Data." Master's thesis, METU, 2011. http://etd.lib.metu.edu.tr/upload/12613192/index.pdf.
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In this thesis, we present two different approaches for the stochastic volatility and stochastic interest rate model with jump and analyze the performance of four alternative models. In the first approach, suggested by Scott, the closed form solution for prices on European call stock options are developed by deriving characteristic functions with the help of martingale methods. Here, we study the asset price process and give in detail the derivation of the European call option price process. The second approach, suggested by Bashki-Cao-Chen, describes the closed form solution of European call option by deriving the partial integro-differential equation. In this one we g ive the derivations of both asset price dynamics and the European call option price process. Finally, in the application part of the thesis, we examine the performance of four alternative models using General Electric Stock Option Data. These models are constructed by using the theoretical results of the second approach.
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Hung, Chien Chia, and 洪千加. "Option Pricing and the Martingale Restriction: Examine on Taiwan Option Market." Thesis, 2009. http://ndltd.ncl.edu.tw/handle/82257894575276932762.
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碩士國立屏東科技大學
財務金融研究所
97
This study investigates Longstaff’s martingale restriction on Taiwan stock index option, where the martingale restriction means that the value of the underlying asset implied by option prices must equal its actual market value. Additionally, the study compares the pricing performance of Black-Scholes model with relaxing martingale restriction’s Black-Scholes model. Moreover, the study examines whether the pricing performance from restricted and unrestricted model can be explained by moneyness and time to maturity. Finally, we attempt to explore if the violation of martingale restriction is due to the lack of liquidity. The empirical results are as follows. First, the implied indexes separately extracted from call and put option prices are significantly larger than the actual index. Second, because of Black-Scholes bias, the pricing performance of the unrestricted model reveals significantly better than the restricted model. Third, moneyness and time to maturity have stronger explanatory power in restricted model than in unrestricted model. Finally, the best fitting regression model provided by this study shows that the percentage pricing differences of call option and put option are related to open interest; the percentage pricing differences of option is related to open interest and option volume. These results implied the lack of liquidity in option market maybe influence the option pricing performance.
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Suh, Sangwon. "Orthogonal polynomials in pricing options by the PDE and Martingale approaches." 2005. http://wwwlib.umi.com/dissertations/fullcit/3168470.
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Chung, Pomin, and 張柏閔. "Nonparametric approach in option pricing." Thesis, 1998. http://ndltd.ncl.edu.tw/handle/48303108327464928008.
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Huang, Hui-Jun, and 黃卉君. "Pricing Crop Revenue Insurance by Option Approach." Thesis, 2013. http://ndltd.ncl.edu.tw/handle/89132764275464177959.
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碩士國立高雄第一科技大學
風險管理與保險研究所
101
Too frequent natural disasters always bring tremendous crop loss and fluctuate crop price. Agriculturists have faced high risk of price and production in Taiwan. This study used the data of pomelo, considering the two different risks: the price risk, which is caused by production cost and the huge fluctuate of trading price; and the production risk, which is mainly caused by the production loss from typhoon. Given these, two different models are set up separately. Meanwhile, this study considered the correlation of transaction price and production cost. On the application of European call option and Bull call spread, this study utilized Monte Carlo method to simulate premiums of crop revenue insurance on different limit levels of claims. In the results, we found that the larger correlation coefficient the smaller premiums by European call option. And by Bull call spread, when we price the section of revenue the larger correlation coefficient the larger premiums; when we price the section of loss the larger correlation coefficient the smaller premiums.
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chen, wen-cheng, and 陳文政. "European Style Multi-Factor Option Pricing Approach-Numerical Analysis Pricing Method." Thesis, 2001. http://ndltd.ncl.edu.tw/handle/52779068495888344858.
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碩士中原大學
企業管理研究所
89
This study uses the binomial model and Monte Carlo simulation model to evaluate the dual-strike options, and options on the minimum or maximum value of two risky assets. This work attempts to compare the values obtained by these three models. Furthermore, this investigation explores the impact of the change in the various parameters on the option value by adjusting each parameter. Since the extent of the stock price change is highly correlated with the options value, the volatility of stock price is a critical factor. Through calculating the historical volatility of stock price, the study chooses four stocks of two industry combinations as the underlying assets whose volatility of stock price are the most highest - IC manufacture industry (UMC、MXIC) and DRAM manufacture industry (PSC、Etron). This study obtained four empirical results as follows: 1.The European call value of both options obtained by the binomial option pricing model and Monte Carlo simulation model are very close. It implies that the results of two pricing method are calculated accurately. 2.Since the Monte Carlo simulation will cause the error of estimation, three-dimensional binomial tree is more stable and accurate than Monte Carlo simulation method when one estimates the true value of call option. 3.Because the stock price and volatility of stock price of the DRAM industry are both higher than that of the IC industry, the call option value is higher when the underlying asset is DRAM industry. 4.Through sensitivity analysis, the value of call option has a positive relationship with the stock price and the volatility of stock price； Furthermore, the value of call option does not certainly have a positive relationship with the time to maturity.
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Chia-Ling, Wu, and 吳佳玲. "Optional Lending and Capitalization－The Option Pricing Approach." Thesis, 1999. http://ndltd.ncl.edu.tw/handle/09722894450843370917.
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碩士淡江大學
國際貿易學系
87
A banker uses the specialist to analysis any business, and puts the funds to profitable category. Bank lending behavior is affected by the business cycle. For example, in the beginning of the 1990s, New England banks had experienced failures. The primary cause of the collapse was the extensive bank exposure to real estate loans. When real estate prices began to decline, collateral became impaired and many loans stooped performing. The consequent increased provision for expected loan loss (loan loss reserve) caused a rapid deterioration in bank capital. The timing was inopportune, occurring just as regulators, in response to the legislation and international agreements, increasingly emphasized the importance of adequate bank capital/assets ratios. Having just lost a significant proportion of their capital, many banks tried to satisfy their capital/asset ratio requirements by shrinking their institutions. The purpose of the thesis is to establish an optimal lending model by the management of bank capital and option pricing approach. Another one is comparative analysis, how the optional lending is influenced by assets risks and capital prices. The conclusion is that optimal lending must be under the situation that capital marginal return equals to marginal cast. In the model, when the assets risks increase, a loan manager may not necessary to reduce its lending business.
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Cheng, Po-Hung, and 鄭博鴻. "TAIEX option pricing : A semiparametric GARCH model approach." Thesis, 2015. http://ndltd.ncl.edu.tw/handle/24777499953810448134.
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碩士國立臺北大學
統計學系
103
This study focuses on TAIEX option pricing by using a semiparametric GARCH approach. This method has been proposed by Alexandru M. Badescu and Reg J. Kulperger (2008) to price S&P500 Index option. Instead of assuming a specific parametric distribution for the driving noise, we estimate the GARCH parameters by Quasi-maximum likelihood technique and then approximate the unknown innovation distribution function using a kernel density estimator based on the standardized residuals. Then we calculate the option prices by Esscher transform measure which is consistent with local risk neutral valuation relationship (LRNVR) for normal GARCH models and use Monte Carlo method. The pricing performances of Black-Scholes model and our semiparametric GARCH approach will be compared.
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Lin, Yung-Chun, and 林永春. "A Gaussian Quadrature Approach for Pricing American GARCH Option." Thesis, 2005. http://ndltd.ncl.edu.tw/handle/25101581955047401448.
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碩士東吳大學
商用數學系
93
A Gaussian-Legendre quadrature method is combined with analytical formulas for moments of the cumulative return under GARCH for pricing American option. To enhance the convergence speed for pricing American GARCH options, a modified Richardson extrapolation technique was employed. We show that the Gaussian-Legendre Quadrature (GLQ) GARCH option model performs superior, in both accuracy and computational time, than the alternative tree methods.
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Luo, Lieh-Ming, and 羅烈明. "Applications of Option Pricing Approach to Insurance and Technology." Thesis, 2006. http://ndltd.ncl.edu.tw/handle/xswp5b.
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博士國立暨南國際大學
國際企業學系
95
This dissertation proposes an alternative asset pricing model, which especially accounts for an important uncertainty resource causing termination of evolution of the asset value. The first effort for this dissertation is devoted to establish the alternative pricing model, and then derive the general solution form. This valuation framework then is applied to two pricing issues. Thus the application study of the proposed pricing model contains two essays. In the first essay, an alternative valuation method for the variable life insurance is developed from a pure no-arbitrage perspective. The conventional pricing approach of such the insurance contract is also reviewed in this no-arbitrage valuation framework. The conventional approach, initiated by Brennan and Schwartz (1976) and Boyle and Schwartz (1977), has been adopted in many relevant researches. Two crucial assumptions, that are the financial risk is independent of mortality and the insurer is risk neutral with respect to mortality, are required in the conventional approach. Under the relaxation of the two assumptions, the price process of a reference fund and the death process of an insured are combined to create a new underlying process, in which the pricing model is referred as to an incomplete market. The no-arbitrage price of this insurance contract is bounded by a range rather than a specific value. It is verified that the price obtained by the conventional approach is a no-arbitrage one with respect to a specified martingale measure. By this way, the properties of the contract as well as the content embedded in the conventional method could be understood from another viewpoint. In addition, the good-deal asset pricing principle, as proposed by Cochrane and Saa-Requejo (2000), is applied in this incomplete market case. The fair price by the good-deal approach is different from the outcome of the conventional approach. It also could be verified that the conventional approach could be derived as a special case of the good-deal approach. According to the numerical results, the fair price by the good-deal approach would yield the reasonable economic implication, which is consistent with the proposed relationship embodied in the consumption-based pricing approach. The study in the second essay is aimed to evaluating new technology development projects under the valuation framework proposed in this research. As suggested by Boer (2000), a successful R&D is a systematic reduction of unique risk. It is implied that firms, when investing in an R&D project, will adopt diversification or hedging actions to reduce the unique risk of the project. So while firms evaluate the research and development project, it should be important to take the hedging behavior into account. The purpose of this study is to value an R&D project using real option approach, in considering the hedging actions of firms. The valuation method we propose can obtain more reasonable assessment for new technology development, and does not receive the influence of R&D firm's subjective views. It also is compared with conventional evaluation methods through numerical examples. Particularly, the results indicate that high degree of hedging effect on an R&D project can not only reduce the unique risk faced of firms, but also can enhance the value of the project. In summary, we have modeled a specific stochastic process to adequately describe risk characteristics for insurance products and technology projects. An alternative evaluation method is provided and several pricing issues for insurance and technology are explored in this dissertation.
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Visagie, Izak Jacobus Henning. "On the calibration of Lévy option pricing models / Izak Jacobus Henning Visagie." Thesis, 2015. http://hdl.handle.net/10394/15765.
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In this thesis we consider the calibration of models based on Lévy processes to option
prices observed in some market. This means that we choose the parameters of the option
pricing models such that the prices calculated using the models correspond as closely as
possible to these option prices. We demonstrate the ability of relatively simple Lévy option
pricing models to nearly perfectly replicate option prices observed in nancial markets.
We speci cally consider calibrating option pricing models to barrier option prices and
we demonstrate that the option prices obtained under one model can be very accurately
replicated using another. Various types of calibration are considered in the thesis.
We calibrate a wide range of Lévy option pricing models to option price data. We con-
sider exponential Lévy models under which the log-return process of the stock is assumed
to follow a Lévy process. We also consider linear Lévy models; under these models the
stock price itself follows a Lévy process. Further, we consider time changed models. Under
these models time does not pass at a constant rate, but follows some non-decreasing Lévy
process. We model the passage of time using the lognormal, Pareto and gamma processes.
In the context of time changed models we consider linear as well as exponential models.
The normal inverse Gaussian (N IG) model plays an important role in the thesis.
The numerical problems associated with the N IG distribution are explored and we
propose ways of circumventing these problems. Parameter estimation for this distribution
is discussed in detail.
Changes of measure play a central role in option pricing. We discuss two well-known
changes of measure; the Esscher transform and the mean correcting martingale measure.
We also propose a generalisation of the latter and we consider the use of the resulting
measure in the calculation of arbitrage free option prices under exponential Lévy models.PhD (Risk Analysis), North-West University, Potchefstroom Campus, 2015
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chen-yu, Tsai, and 蔡鎮宇. "Pricing Moving Average Exchange Option under Numerical and Analytical Approximation Approach." Thesis, 2008. http://ndltd.ncl.edu.tw/handle/37533465502997780155.
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碩士輔仁大學
金融研究所
96
In this thesis, we construct an efficient and accurate model for pricing moving-average exchange option. Moving-average exchange option is an exotic option which combines exchange option with Asian option, its payoff is the distance between two asset’s moving-average price. We use numerical and analytical approximation to build this model. The traditional methods for pricing exotic option, such as Monte Carlo simulation, are simple to use, but time-consuming. We build up two models for pricing moving-average exchange option. First, we Use Turnbull and Wakeman (1991), Levy (1992) model to find out the distribution of average price, and solve option value by numerical integration. Then, we set a approximation model by apply Margrabe (1978) Exchange Option model to price moving-average exchange option more efficiently and accurately. And we also find out the Hedge Parameters, delta and gamma.
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Lin, Tsai I., and 蔡伊玲. "The timing and pricing of Initial Public Offerings ~Real option approach." Thesis, 2002. http://ndltd.ncl.edu.tw/handle/97165678568419762953.
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碩士銘傳大學
金融研究所
90
For timing selection, prior studies showed that optimal timing for IPO should occur after abnormal run-ups in their industry market index. For issuing price, the price is usually calculated by a common formula suggested by SEC in Taiwan. However, the concepts of this formula are mainly based on the historic performance of a firm, and can’t reflect actual value of firm’s future cash flows. Actually, the going-public decision can be considered as a real option. When the firm is private, the entrepreneur has a claim to the dividend stream and possesses the timing option as a call option to go public at any time. By claiming going-public, this call option is exercised, and in the meantime the entrepreneur obtains a right as a put option to delay IPO in a permitted grace period. Therefore, the objectives of this paper are two-fold. The first is applying a real option approach to develop a dynamic model amended from Jason Draho (2000) for the timing selection and accompanied a signal hypothesis for issuing price of IPO under two situations of price run-ups and run-downs, then observing the sensitive analysis of IPO and option. The second objective is to use the dynamic model for the sample firms in Taiwan stock markets during the period of 1997-2001, and to evaluate whether the timings of IPOs are optimal, IPOs has investment value, and the common formula suggested by SEC is reasonable. The results would help the government and firms to refine the going-public decisions. 1.The timings of IPOs are optimal. 2.Investing IPOs in the peak season and holding to the year-end would acquire higher return than in the off-season. 3.Pricing by real option approach is reasonable than that by common formula suggested by SEC.
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Huang, Jun Yuan, and 黃俊源. "The Approach of Real Option Pricing Model under the Urban Renewal Investment." Thesis, 2001. http://ndltd.ncl.edu.tw/handle/74946198427678348136.
Full textAbstract:
碩士朝陽科技大學
財務金融系碩士班
89
The Statue of Urban Renewal has been promulgated and enforced since November 11,1998. By putting the statue into practice, those decaying areas could be restored; the government could levy lands for public works to elevate local living quality. Furthermore, those decaying areas could revive their advantage of location and raise the value of real estates. The Urban Renewal Investments are involved in more uncertain factors than traditional real estate investments are. Net Present Value Method (NPV) is traditionally the major assessing norm for financial projects, while there are some faults within it, such as only accepting investments when their NPV are over 0, neglecting the cash flow outside the calculating term, and ignoring the fact that managers could modify investing scale freely. Real Option means that the managers have optional rights in a real asset investment. It combines concepts of “elasticity” and “risk” to resolve the problems of uncertainty and management flexibility in urban renewal investments, which is the major difference between Real Option and traditional NPV. It is confirmed that lowering developers’ expenditures is the best means to stimulate the urban renewal investment while the value of real estate is declining nowadays.
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劉育名. "Using real option pricing approach to evaluate the flexibility value embedded in an acquisition." Thesis, 2006. http://ndltd.ncl.edu.tw/handle/89567967978538724154.
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Chen, Kun-Hsien, and 陳昆賢. "The Study of the Pricing of Mortgage-Backed Securities- The Application of Option-Adjusted Spread Approach." Thesis, 2002. http://ndltd.ncl.edu.tw/handle/58487210722855742254.
Full textAbstract:
碩士朝陽科技大學
財務金融系碩士班
90
As the banking institutions originate and hold mortgage loans is the asset, they bear the prepayment risk until borrowers pay off at maturity. In ORDER to reduce prepayment risks and manage interest rate risks, the banking industry can pool the mortgages of low liquidity, repackage and sell them to the capital markets through issuing mortgage-backed securities (MBS), whose cash flows come FROM the underlying pool of mortgages. This study firstly introduces the asset securitization concept and the process for developing the secondary mortgage markets. Secondly, several prepayment models are reviewed for merits and limitations. Finally, Monte Carlo simulation analysis is adopted for approaching the MBS prices. As SHOW in this study, the value of ARM will more in proportion to its adjusted time period of contract rates.
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Hutchinson, James M. "A Radial Basis Function Approach to Financial Time Series Analysis." 1993. http://hdl.handle.net/1721.1/6783.
Full textAbstract:
Nonlinear multivariate statistical techniques on fast computers offer the potential to capture more of the dynamics of the high dimensional, noisy systems underlying financial markets than traditional models, while making fewer restrictive assumptions. This thesis presents a collection of practical techniques to address important estimation and confidence issues for Radial Basis Function networks arising from such a data driven approach, including efficient methods for parameter estimation and pruning, a pointwise prediction error estimator, and a methodology for controlling the "data mining'' problem. Novel applications in the finance area are described, including customized, adaptive option pricing and stock price prediction.
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Saeterboe, Marius. "FinTech valuation : is real option valuation a suitable approach to value US listed FinTech companies?" Master's thesis, 2019. http://hdl.handle.net/10400.14/29147.
Full textAbstract:
The aim of this study is to assess whether a real option valuation model used on the internet industry is suitable to value FinTech’s. More specifically, try to answer how close or far the estimated firm value is from observed market value disclosed in the financial statement. We argue that commonly used valuation models are limited when it comes to valuation of FinTech businesses. Additionally, we explain that FinTechs are facing many similarities in comparison with Internet companies in the 2000’s. We adopt and apply a real option model, originally developed to value Internet companies, on a U.S listed FinTech, Square Inc. Revenues are imitated and forecasted as a discrete approximation of a continuous time stochastic mean-reverting process. Further, the revenues are risk-adjusted, to avoid the need of estimation of an uncertain WACC, and therefore discounted at an appropriate risk-free rate. The model estimates FinTechs stock prices closer to the traded market price than a traditional NPV DCF-model, since traditional NPV DCFs neglect the value from the flexibility option. Stock prices of FinTechs might be rational if one put a high enough value on the growth of revenues. Notwithstanding that the model requires estimation of many parameters, it is suggested to look closer into how life-expectancy of FinTechs affect the valuation and find a better predictor or proxy.O objetivo deste estudo é avaliar se o modelo de avaliação para opções reais utilizado na indústria da internet é aplicável para a avaliação de FinTech’s. Mais especificamente, procura mensurar o desvio da avaliação entre o valor intrínseco da empresa e o registado nas demonstrações financeiras das empresas da indústria de FinTech. Adicionalmente, é feita uma comparação com as empresas tecnológicas dos inícios da primeira década do século XXI. É adotado um modelo desenvolvido na avaliação da FinTech, Square Inc. As receitas são estimadas como uma aproximação discreta de um processo de reversão estocástica da média. Seguidamente, as receitas são ajustadas ao risco evitando assim estimar o WACC, descontando, por isso, à taxa sem risco. O modelo estima os preços das ações da FinTech mais próximos do preço de mercado negociado do que o modelo tradicional de VAL-DCF. Os preços das ações das FinTechs poderão ser racionais se colocarmos um valor alto o suficiente no crescimento das receitas. De qualquer forma, o modelo requer a estimativa de muitos parâmetros. Sugere-se examinar mais pormenorizadamente como a expectativa de vida de uma empresa ou projeto da FinTech afeta o valor e estabelecer um proxy mais adequado.