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21	外匯選擇權的定價－馬可夫鏈蒙地卡羅法(MCMC)之績效探討任紀為 Unknown Date (has links) 在真實世界中，我們可以觀察到許多財務或經濟變數(股價、匯率、利率等)有時波動幅度非常微小，呈現相對穩定的狀態(Regime)；有時會由於政治因素或經濟環境的變動，突然一段期間呈現瘋狂震盪的狀態。針對這種現象，已有學者提出狀態轉換波動度模型(Regime Switching Volatility Model，簡稱RSV)來捕捉此一現象。本篇論文選擇每年交易金額非常龐大的外匯選擇權市場，以RSV模型為基礎，採用馬可夫鏈蒙地卡羅法 ( Markov Chain Monte Carlo，簡稱MCMC ) 中的吉普斯抽樣(Gibbs Sampling)法來估計RSV模型的參數，依此預測外匯選擇權在RSV模型下的價格。我們再將此價格與Black and Scholes(BS)法及實際市場交易的價格資料作比較，最後並提出笑狀波幅與隱含波動度平面的結果。結果顯示經由RSV模型與MCMC演算法所計算出來的選擇權價格確實優於傳統的BS方法，且能有效解釋波動率期間結構 (Volatility Term Structure) 與笑狀波幅 (Volatility Smile) 的現象，確實反應且捕捉到了市場上選擇權價格所應具備的特色。馬可夫鍵蒙地卡羅狀態轉換波動吉普斯抽樣笑狀波幅 Markov-chain Monte Carlo Regime-switching volatility Gibbs sampling Volatility smile
22	Distribuições preditiva e implícita para ativos financeiros / Predictive and implied distributions of a stock price Oliveira, Natália Lombardi de 01 June 2017 (has links) Submitted by Alison Vanceto (alison-vanceto@hotmail.com) on 2017-08-28T13:57:07Z No. of bitstreams: 1 DissNLO.pdf: 2139734 bytes, checksum: 9d9000013e5ab1fd3e860be06fc72737 (MD5) / Approved for entry into archive by Ronildo Prado (ronisp@ufscar.br) on 2017-09-06T13:18:03Z (GMT) No. of bitstreams: 1 DissNLO.pdf: 2139734 bytes, checksum: 9d9000013e5ab1fd3e860be06fc72737 (MD5) / Approved for entry into archive by Ronildo Prado (ronisp@ufscar.br) on 2017-09-06T13:18:12Z (GMT) No. of bitstreams: 1 DissNLO.pdf: 2139734 bytes, checksum: 9d9000013e5ab1fd3e860be06fc72737 (MD5) / Made available in DSpace on 2017-09-06T13:28:02Z (GMT). No. of bitstreams: 1 DissNLO.pdf: 2139734 bytes, checksum: 9d9000013e5ab1fd3e860be06fc72737 (MD5) Previous issue date: 2017-06-01 / Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) / We present two different approaches to obtain a probability density function for the stock?s future price: a predictive distribution, based on a Bayesian time series model, and the implied distribution, based on Black & Scholes option pricing formula. Considering the Black & Scholes model, we derive the necessary conditions to obtain the implied distribution of the stock price on the exercise date. Based on predictive densities, we compare the market implied model (Black & Scholes) with a historical based approach (Bayesian time series model). After obtaining the density functions, it is simple to evaluate probabilities of one being bigger than the other and to make a decision of selling/buying a stock. Also, as an example, we present how to use these distributions to build an option pricing formula. / Apresentamos duas abordagens para obter uma densidade de probabilidades para o preço futuro de um ativo: uma densidade preditiva, baseada em um modelo Bayesiano para série de tempo e uma densidade implícita, baseada na fórmula de precificação de opções de Black & Scholes. Considerando o modelo de Black & Scholes, derivamos as condições necessárias para obter a densidade implícita do preço do ativo na data de vencimento. Baseando-se nas densidades de previsão, comparamos o modelo implícito com a abordagem histórica do modelo Bayesiano. A partir destas densidades, calculamos probabilidades de ordem e tomamos decisões de vender/comprar um ativo. Como exemplo, apresentamos como utilizar estas distribuições para construir uma fórmula de precificação. Volatilidade implícita Smile da volatilidade Modelo autorregressivo Bayesiano Implied volatility Volatility smile Implied probability density function Predictive probability density function Autorregressive Bayesian model
23	Distribuição preditiva do preço de um ativo financeiro: abordagens via modelo de série de tempo Bayesiano e densidade implícita de Black & Scholes / Predictive distribution of a stock price: Bayesian time series model and Black & Scholes implied density approaches Natália Lombardi de Oliveira 01 June 2017 (has links) Apresentamos duas abordagens para obter uma densidade de probabilidades para o preço futuro de um ativo: uma densidade preditiva, baseada em um modelo Bayesiano para série de tempo e uma densidade implícita, baseada na fórmula de precificação de opções de Black & Scholes. Considerando o modelo de Black & Scholes, derivamos as condições necessárias para obter a densidade implícita do preço do ativo na data de vencimento. Baseando-se nas densidades de previsão, comparamos o modelo implícito com a abordagem histórica do modelo Bayesiano. A partir destas densidades, calculamos probabilidades de ordem e tomamos decisões de vender/comprar um ativo. Como exemplo, apresentamos como utilizar estas distribuições para construir uma fórmula de precificação. / We present two different approaches to obtain a probability density function for the stocks future price: a predictive distribution, based on a Bayesian time series model, and the implied distribution, based on Black & Scholes option pricing formula. Considering the Black & Scholes model, we derive the necessary conditions to obtain the implied distribution of the stock price on the exercise date. Based on predictive densities, we compare the market implied model (Black & Scholes) with a historical based approach (Bayesian time series model). After obtaining the density functions, it is simple to evaluate probabilities of one being bigger than the other and to make a decision of selling/buying a stock. Also, as an example, we present how to use these distributions to build an option pricing formula. Modelo autorregressivo Bayesiano Smile da volatilidade Volatilidade implícita Auto regressive Bayesian model Implied probability density funcion Implied volatility,Volatility smile Predictive probability density function
24	位移與混合型離散過程對波動度模型之解析與實證 / Displaced and Mixture Diffusions for Analytically-Tractable Smile Models 林豪勵, Lin, Hao Li Unknown Date (has links) Brigo與Mercurio提出了三種新的資產價格過程，分別是位移CEV過程、位移對數常態過程與混合對數常態過程。在這三種過程中，資產價格的波動度不再是一個固定的常數，而是時間與資產價格的明確函數。而由這三種過程所推導出來的歐式選擇權評價公式，將會導致隱含波動度曲線呈現傾斜曲線或是微笑曲線，且提供了參數讓我們能夠配適市場的波動度結構。本文利用台指買權來實證Brigo與Mercurio所提出的三種歐式選擇權評價公式，我們發現校準結果以混合對數常態過程優於位移CEV過程，而位移CEV過程則稍優於位移對數常態過程。因此，在實務校準時，我們建議以混合對數常態過程為台指買權的評價模型，以達到較佳的校準結果。 / Brigo and Mercurio proposed three types of asset-price dynamics which are shifted-CEV process, shifted-lognormal process and mixture-of-lognormals process respectively. In these three processes, the volatility of the asset price is no more a constant but a deterministic function of time and asset price. The European option pricing formulas derived from these three processes lead respectively to skew and smile in the term structure of implied volatilities. Also, the pricing formula provides several parameters for fitting the market volatility term structure. The thesis applies Taiwan’s call option to verifying these three pricing formulas proposed by Brigo and Mercurio. We find that the calibration result of mixture-of-lognormals process is better than the result of shifted-CEV process and the calibration result of shifted-CEV process is a little better than the result of shifted-lognormal process. Therefore, we recommend applying the pricing formula derived from mixture-of-lognormals process to getting a better calibration. 資產價格的動態過程風險中立機率測度選擇權評價公式波動度傾斜波動度微笑非線性規劃參數校準 asset-price dynamics risk-neutral density option pricing formula volatility skew volatility smile nonlinear programming calibration of parameters
25	狀態轉換跳躍相關模型下選擇權定價:股價指數選擇權之實證 / Option pricing under regime-switching jump model with dependent jump sizes: evidence from stock index option 李家慶, Lee, Jia-Ching Unknown Date (has links) Black and Scholes (1973)對於報酬率提出以B-S模型配適，但B-S模型無法有效解釋報酬率不對稱高狹峰、波動度微笑、波動度叢聚、長記憶性的性質。Merton (1976)認為不尋常的訊息來臨會影響股價不連續跳躍，因此發展B-S模型加入不連續跳躍風險項的跳躍擴散模型，該模型可同時描述報酬率不對稱高狹峰和波動度微笑兩性質。Charles, Fuh and Lin (2011)加以考慮市場狀態提出狀態轉換跳躍模型，除了保留跳躍擴散模型可描述報酬率不對稱高狹峰和波動度微笑，更可以敘述報酬率的波動度叢聚和長記憶性。本文進一步拓展狀態轉換跳躍模型，考慮不連續跳躍風險項的帄均數與市場狀態相關，提出狀態轉換跳躍相關模型。並以道瓊工業指數與S&P 500指數1999年至2010年股價指數資料，採用EM和SEM分別估計參數與估計參數共變異數矩陣。使用概似比檢定結果顯示狀態轉換跳躍相關模型比狀態轉換跳躍獨立模型更適合描述股價指數報酬率。並驗證狀態轉換跳躍相關模型也可同時描述報酬率不對稱高狹峰、波動度微笑、波動度叢聚、長記憶性。最後利用Esscher轉換法計算股價指數選擇權定價公式，以敏感度分析模型參數對於定價結果的影響，並且市場驗證顯示狀態轉換跳躍相關模型會有最小的定價誤差。 / Black and Scholes (1973) proposed B-S model to fit asset return, but B-S model can’t effectively explain some asset return properties, such as leptokurtic, volatility smile, volatility clustering and long memory. Merton (1976) develop jump diffusion model (JDM) that consider abnormal information of market will affect the stock price, and this model can explain leptokurtic and volatility smile of asset return at the same time. Charles, Fuh and Lin (2011) extended the JDM and proposed regime-switching jump independent model (RSJIM) that consider jump rate is related to market states. RSJIM not only retains JDM properties but describes volatility clustering and long memory. In this paper, we extend RSJIM to regime-switching jump dependent model (RSJDM) which consider jump size and jump rate are both related to market states. We use EM and SEM algorithm to estimate parameters and covariance matrix, and use LR test to compare RSJIM and RSJDM. By using 1999 to 2010 Dow-Jones industrial average index and S&P 500 index as empirical evidence, RSJDM can explain index return properties said before. Finally, we calculate index option price formulation by Esscher transformation and do sensitivity analysis and market validation which give the smallest error of option prices by RSJDM. 股價指數選擇權狀態轉換跳躍相關模型波動聚集波動度微笑 EM演算法 Esscher轉換法 index option regime-switching jump dependent model volatility clustering volatility smile EM algorithm Esscher transformation
26	狀態轉換下利率與跳躍風險股票報酬之歐式選擇權評價與實證分析 / Option Pricing and Empirical Analysis for Interest Rate and Stock Index Return with Regime-Switching Model and Dependent Jump Risks 巫柏成, Wu, Po Cheng Unknown Date (has links) Chen, Chang, Wen and Lin (2013)提出馬可夫調控跳躍過程模型(MMJDM)描述股價指數報酬率，布朗運動項、跳躍項之頻率與市場狀態有關。然而，利率並非常數，本論文以狀態轉換模型配適零息債劵之動態過程，提出狀態轉換下的利率與具跳躍風險的股票報酬之二維模型(MMJDMSI)，並以1999年至2013年的道瓊工業指數與S&P 500指數和同期間之一年期美國國庫劵價格為實證資料，採用EM演算法取得參數估計值。經由概似比檢定結果顯示無論道瓊工業指數還是S&P 500指數，狀態轉換下利率與跳躍風險之股票報酬二維模型更適合描述報酬率。接著，利用Esscher轉換法推導出各模型下的股價指數之歐式買權定價公式，再對MMJDMSI模型進行敏感度分析以評估模型參數發生變動時對於定價公式的影響。最後，以實證資料對各模型進行模型校準及計算隱含波動度，結果顯示MMJDMSI在價內及價外時定價誤差為最小或次小，且此模型亦能呈現出波動度微笑曲線之現象。 / To model asset return, Chen, Chang, Wen and Lin (2013) proposed Markov-Modulated Jump Diffusion Model (MMJDM) assuming that the Brownian motion term and jump frequency are all related to market states. In fact, the interest rate is not constant, Regime-Switching Model is taken to fit the process of the zero-coupon bond price, and a bivariate model for interest rate and stock index return with regime-switching and dependent jump risks (MMJDMSI) is proposed. The empirical data are Dow Jones Industrial Average and S&P 500 Index from 1999 to 2013, together with US 1-Year Treasury Bond over the same period. Model parameters are estimated by the Expectation-Maximization (EM) algorithm. The likelihood ratio test (LRT) is performed to compare nested models, and MMJDMSI is better than the others. Then, European call option pricing formula under each model is derived via Esscher transformation, and sensitivity analysis is conducted to evaluate changes resulted from different parameter values under the MMJDMSI pricing formula. Finally, model calibrations are performed and implied volatilities are computed under each model empirically. In cases of in-the-money and out-the-money, MMJDMSI has either the smallest or the second smallest pricing error. Also, the implied volatilities from MMJDMSI display a volatility smile curve. EM演算法 Esscher轉換法歐式買權定價公式敏感度分析模型校準波動度微笑曲線 MMJDMSI model EM algorithm Esscher Transformation European call option pricing formula sensitivity analysis; model model calibration volatility smile curve
27	Théorie des options et fonctions d'utilité : stratégies de couverture en présence des fluctuations non gaussiennes / Options theory and utility functions : hedging strategies in the presence of non-gaussian fluctuations Hamdi, Haykel 04 March 2011 (has links) L'approche traditionnelle des produits dérivés consiste, sous certaines hypothèses bien définies, à construire des stratégies de couverture à risque strictement nul. Cependant,dans le cas général ces stratégies de couverture "parfaites" n'existent pas,et la théorie doit plutôt s'appuyer sur une idée de minimisation du risque. Dans ce cas, la couverture optimale dépend de la quantité du risque à minimiser. Dans lecadre des options, on considère dans ce travail une nouvelle mesure du risque vial'approche de l'utilité espérée qui tient compte, à la fois, du moment d'ordre quatre,qui est plus sensible aux grandes fluctuations que la variance, et de l'aversion aurisque de l'émetteur d'une option vis-à-vis au risque. Comparée à la couverture endelta, à l'optimisation de la variance et l'optimisation du moment d'ordre quatre,la stratégie de couverture, via l'approche de l'utilité espérée, permet de diminuer lasensibilité de la couverture par rapport au cours du sous-jacent. Ceci est de natureà réduire les coûts des transactions associées / The traditional approach of derivatives involves, under certain clearly defined hypothesis, to construct hedging strategies for strictly zero risk. However, in the general case these perfect hedging strategies do not exist, and the theory must be rather based on the idea of risk minimization. In this case, the optimal hedging strategy depends on the amount of risk to be minimized. Under the options approach, we consider here a new measure of risk via the expected utility approach that takes into account both, the moment of order four, which is more sensitive to fluctuations than large variance, and risk aversion of the investor of an option towards risk. Compared to delta hedging, optimization of the variance and maximizing the moment of order four, the hedging strategy, via the expected utilitiy approach, reduces the sensitivy of the hedging approach reported in the underlying asset price. This is likely to reduce the associated transaction costs. Aversion au risque Densité neutre au risque Densité subjective Fonctions d'utilité Evaluation des options Options sur l'indice CAC40 Stratégie de couverture optimale Smile de volatilité VaR CVaR EVT Risque extrême Evaluation du risque de marché Fluctuations non gaussiennes Risk aversion Risk neutral density Subjective density Utility functions Options pricing CAC 40 index options Optimal hedging strategy Volatility smile VaR CVar EVT Extreme risk Density functionals Risk assessment Mathematical optimization Hedging (finance) Options (finance)
28	Empirical Performance and Asset Pricing in Markov Jump Diffusion Models / 馬可夫跳躍擴散模型的實證與資產定價林士貴, Lin, Shih-Kuei Unknown Date (has links) 為了改進Black-Scholes模式的實證現象，許多其他的模型被建議有leptokurtic特性以及波動度聚集的現象。然而對於其他的模型分析的處理依然是一個問題。在本論文中，我們建議使用馬可夫跳躍擴散過程，不僅能整合leptokurtic與波動度微笑特性，而且能產生波動度聚集的與長記憶的現象。然後，我們應用Lucas的一般均衡架構計算選擇權價格，提供均衡下當跳躍的大小服從一些特別的分配時則選擇權價格的解析解。特別地，考慮當跳躍的大小服從兩個情況，破產與lognormal分配。當馬可夫跳躍擴散模型的馬可夫鏈有兩個狀態時，稱為轉換跳躍擴散模型，當跳躍的大小服從lognormal分配我們得到選擇權公式。使用轉換跳躍擴散模型選擇權公式，我們給定一些參數下研究公式的數值極限分析以及敏感度分析。 / To improve the empirical performance of the Black-Scholes model, many alternative models have been proposed to address the leptokurtic feature of the asset return distribution, and the effects of volatility clustering phenomenon. However, analytical tractability remains a problem for most of the alternative models. In this dissertation, we propose a Markov jump diffusion model, that can not only incorporate both the leptokurtic feature and volatility smile, but also present the economic features of volatility clustering and long memory. Next, we apply Lucas's general equilibrium framework to evaluate option price, and to provide analytical solutions of the equilibrium price for European call options when the jump size follows some specific distributions. In particular, two cases are considered, the defaultable one and the lognormal distribution. When the underlying Markov chain of the Markov jump diffusion model has two states, the so-called switch jump diffusion model, we write an explicit analytic formula under the jump size has a lognormal distribution. Numerical approximations of the option prices as well as sensitivity analysis are also given. 均衡分析歐式選擇權拉氏倒轉變換長記憶馬可夫跳躍擴散模型馬可夫控制瓦松過程數值倒轉方法換跳躍擴散過程變波動聚集波動度微笑 Equilibrium analysis European call option Laplace inverse transform Leptokurtic Long memory Markov jump diffusion model Markov modulated Poisson process Numerical inversion method Switch jump diffusion model Volatility clustering Volatility smile
29	Highway Development Decision-Making Under Uncertainty: Analysis, Critique and Advancement El-Khatib, Mayar January 2010 (has links) While decision-making under uncertainty is a major universal problem, its implications in the field of transportation systems are especially enormous; where the benefits of right decisions are tremendous, the consequences of wrong ones are potentially disastrous. In the realm of highway systems, decisions related to the highway configuration (number of lanes, right of way, etc.) need to incorporate both the traffic demand and land price uncertainties. In the literature, these uncertainties have generally been modeled using the Geometric Brownian Motion (GBM) process, which has been used extensively in modeling many other real life phenomena. But few scholars, including those who used the GBM in highway configuration decisions, have offered any rigorous justification for the use of this model. This thesis attempts to offer a detailed analysis of various aspects of transportation systems in relation to decision-making. It reveals some general insights as well as a new concept that extends the notion of opportunity cost to situations where wrong decisions could be made. Claiming deficiency of the GBM model, it also introduces a new formulation that utilizes a large and flexible parametric family of jump models (i.e., Lévy processes). To validate this claim, data related to traffic demand and land prices were collected and analyzed to reveal that their distributions, heavy-tailed and asymmetric, do not match well with the GBM model. As a remedy, this research used the Merton, Kou, and negative inverse Gaussian Lévy processes as possible alternatives. Though the results show indifference in relation to final decisions among the models, mathematically, they improve the precision of uncertainty models and the decision-making process. This furthers the quest for optimality in highway projects and beyond. highway development decision making under uncertainty real options jump processes infinitely divisible distributions Lévy processes measure theory characteristic function characteristic exponent Lévy jump measure probability measure cádlág stochastic process Wiener process Poisson process compound Poisson process finite activity models jump diffusion models Merton model Gaussian jump process Kou model double exponential jump process leptokurtic volatility smile infinite activity models pure jumps process generalized hyperbolic model modified Bessel function negative inverse Gaussian model geometric Brownian motion model log-normal distribution model normality assumption heavy-tailed distribution asymmetric distribution quantile-quantile plot Rydberg algorithm parameter calibration moments cummulants sum of squares Monte Carlo simulation least-squares regression backward dynamic programming discrete-time Markov chain land price traffic demand highway service quality index data collection traffic volume Annual Average Daily Traffic Ontario Ministry of Transportation Land Registry Office Freedom of Information Act seasonality value of transportation types of transportation systems importance of highway systems cost of wrong decisions monetary cost private sector cost human cost land expropriation environmental cost irreversibility cost factor time cost factor political cost factor opportunity cost opportunity cost of wrong decisions economic cost of wrong decisions economic cost of mis-estimation economic profit of wrong decisions cost of inaction price of making right decisions scope of decisions rehabilitation decision land acquisition decision expansion decision uncertainty modeling land acquisition cost expropriation cost construction cost material cost Montréal-Mirabel International Airport Pickering Airport 407 Express Toll Route Highway 407 Statistics
30	Highway Development Decision-Making Under Uncertainty: Analysis, Critique and Advancement El-Khatib, Mayar January 2010 (has links) While decision-making under uncertainty is a major universal problem, its implications in the field of transportation systems are especially enormous; where the benefits of right decisions are tremendous, the consequences of wrong ones are potentially disastrous. In the realm of highway systems, decisions related to the highway configuration (number of lanes, right of way, etc.) need to incorporate both the traffic demand and land price uncertainties. In the literature, these uncertainties have generally been modeled using the Geometric Brownian Motion (GBM) process, which has been used extensively in modeling many other real life phenomena. But few scholars, including those who used the GBM in highway configuration decisions, have offered any rigorous justification for the use of this model. This thesis attempts to offer a detailed analysis of various aspects of transportation systems in relation to decision-making. It reveals some general insights as well as a new concept that extends the notion of opportunity cost to situations where wrong decisions could be made. Claiming deficiency of the GBM model, it also introduces a new formulation that utilizes a large and flexible parametric family of jump models (i.e., Lévy processes). To validate this claim, data related to traffic demand and land prices were collected and analyzed to reveal that their distributions, heavy-tailed and asymmetric, do not match well with the GBM model. As a remedy, this research used the Merton, Kou, and negative inverse Gaussian Lévy processes as possible alternatives. Though the results show indifference in relation to final decisions among the models, mathematically, they improve the precision of uncertainty models and the decision-making process. This furthers the quest for optimality in highway projects and beyond. highway development decision making under uncertainty real options jump processes infinitely divisible distributions Lévy processes measure theory characteristic function characteristic exponent Lévy jump measure probability measure cádlág stochastic process Wiener process Poisson process compound Poisson process finite activity models jump diffusion models Merton model Gaussian jump process Kou model double exponential jump process leptokurtic volatility smile infinite activity models pure jumps process generalized hyperbolic model modified Bessel function negative inverse Gaussian model geometric Brownian motion model log-normal distribution model normality assumption heavy-tailed distribution asymmetric distribution quantile-quantile plot Rydberg algorithm parameter calibration moments cummulants sum of squares Monte Carlo simulation least-squares regression backward dynamic programming discrete-time Markov chain land price traffic demand highway service quality index data collection traffic volume Annual Average Daily Traffic Ontario Ministry of Transportation Land Registry Office Freedom of Information Act seasonality value of transportation types of transportation systems importance of highway systems cost of wrong decisions monetary cost private sector cost human cost land expropriation environmental cost irreversibility cost factor time cost factor political cost factor opportunity cost opportunity cost of wrong decisions economic cost of wrong decisions economic cost of mis-estimation economic profit of wrong decisions cost of inaction price of making right decisions scope of decisions rehabilitation decision land acquisition decision expansion decision uncertainty modeling land acquisition cost expropriation cost construction cost material cost Montréal-Mirabel International Airport Pickering Airport 407 Express Toll Route Highway 407 Statistics

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