Spelling suggestions: "subject:"martingale measure"" "subject:"martingales measure""
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由選擇權市場價格建構具一致性之評價模型 / Building a Consistent Pricing Model from Observed Option Prices via Linear Programming劉桂芳, Liu, Kuei-fang Unknown Date (has links)
本論文研究如何由觀測的選擇權市場價格還原風險中立機率測度(等價平賭測度)。首先建構選擇權投資組合的套利模型,其中假設選擇權為單期,到期日時的狀態為離散點且個數有限,並且對應同一標的資產且不同履約價格。若市場不存在套利機會時,可使用拉格朗日乘數法則將選擇權套利模型導出拉格朗日乘子的可行性問題。將可行性問題作為限制式重新建構線性規劃模型以還原風險中立機率測度,並且利用此風險中立機率測度評價選擇權的公正價格。最後,我們以台指選擇權(TXO)為例,驗證此模型的評價能力。 / This thesis investigates how to recover the risk-neutral probability (equivalent martingale measure) from observed market prices of options. It starts with building an arbitrage model of options portfolio in which the options are assumed to be in one-period time, finite discrete-states, and corresponding to the same underlying asset with different strike prices. If there is no arbitrage opportunity in the market, we can use Lagrangian multiplier method to obtain a Lagrangian multiplier feasibility problem from the arbitrage model. We employ the feasibility problem as the constraints to construct a linear programming model to recover the risk-neutral probability, and utilize this risk-neutral probability to evaluate the fair price of options. Finally, we take TXO as an example to verify the pricing ability of this model.
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Spojité modely trhu se stochastickou volatilitou / Continuous market models with stochastic volatilityPetrovič, Martin January 2018 (has links)
Vilela Mendes et al. (2015), based on the discovery of long-range dependence in the volatility of stock returns, proposed a stochastic volatility continuous mar- ket model where the volatility is given as a transform of the fractional Brownian motion (fBm) and studied its No-Arbitrage and completeness properties under va- rious assumptions. We investigate the possibility of generalization of their results from fBm to a wider class of Hermite processes. We have reworked and completed the proofs of the propositions in the cited article. Under the assumption of indepen- dence of the stock price and volatility driving processes the model is arbitrage-free. However, apart from a case of a special relation between the drift and the volatility, the model is proved to be incomplete. Under a different assumption that there is only one source of randomness in the model and the volatility driving process is bounded, the model is arbitrage-free and complete. All the above results apply to any Hermite process driving the volatility. 1
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Some Applications of Markov Additive Processes as Models in Insurance and Financial MathematicsBen Salah, Zied 07 1900 (has links)
Cette thèse est principalement constituée de trois articles traitant des processus markoviens additifs, des processus de Lévy et d'applications en finance et en assurance.
Le premier chapitre est une introduction aux processus markoviens additifs (PMA), et une présentation du problème de ruine et de notions fondamentales des mathématiques financières. Le deuxième chapitre est essentiellement l'article "Lévy Systems and the Time Value of Ruin for Markov Additive Processes" écrit en collaboration avec Manuel Morales et publié dans la revue European Actuarial Journal. Cet article étudie le problème de ruine pour un processus de risque markovien additif. Une identification de systèmes de Lévy est obtenue et utilisée pour donner une expression de l'espérance de la fonction de pénalité actualisée lorsque le PMA est un processus de Lévy avec changement de régimes. Celle-ci est une généralisation des résultats existant dans la littérature pour les processus de risque de Lévy et les processus de risque markoviens additifs avec sauts "phase-type".
Le troisième chapitre contient l'article "On a Generalization of the Expected Discounted Penalty Function to Include Deficits at and Beyond Ruin" qui est soumis pour publication. Cet article présente une extension de l'espérance de la fonction de pénalité actualisée pour un processus subordinateur de risque perturbé par un mouvement brownien. Cette extension contient une série de fonctions escomptée éspérée des minima successives dus aux sauts du processus de risque après la ruine. Celle-ci a des applications importantes en gestion de risque et est utilisée pour déterminer la valeur espérée du capital d'injection actualisé. Finallement, le quatrième chapitre contient l'article "The Minimal entropy martingale measure (MEMM) for a Markov-modulated exponential Lévy model" écrit en collaboration avec Romuald Hervé Momeya et publié dans la revue Asia-Pacific Financial Market. Cet article présente de nouveaux résultats en lien avec le problème de l'incomplétude dans un marché financier où le processus de prix de l'actif risqué est décrit par un modèle exponentiel markovien additif. Ces résultats consistent à charactériser la mesure martingale satisfaisant le critère de l'entropie. Cette mesure est utilisée pour calculer le prix d'une option, ainsi que des portefeuilles de couverture dans un modèle exponentiel de Lévy avec changement de régimes. / This thesis consists mainly of three papers concerned with Markov additive processes, Lévy processes and applications on finance and insurance.
The first chapter is an introduction to Markov additive processes (MAP) and a presentation of the ruin problem and basic topics of Mathematical Finance. The second chapter contains the paper "Lévy Systems and the Time Value of Ruin for Markov Additive Processes" written with Manuel Morales and that is published in the European Actuarial Journal. This paper studies the ruin problem for a Markov additive risk process. An expression of the expected discounted penalty function is obtained via identification of the Lévy systems. The third chapter contains the paper "On a Generalization of the Expected Discounted Penalty Function to Include Deficits at and Beyond Ruin" that is submitted for publication. This paper presents an extension of the expected discounted penalty function in a setting involving aggregate claims modelled by a subordinator, and Brownian perturbation. This extension involves a sequence of expected discounted functions of successive minima reached by a jump of the risk process after ruin. It has important applications in risk management and in particular, it is used to compute the expected discounted value of capital injection. Finally, the fourth chapter contains the paper "The Minimal Entropy Martingale Measure (MEMM) for a Markov-Modulated Exponential" written with Romuald Hérvé Momeya and that is published in the journal Asia Pacific Financial Market. It presents new results related to the incompleteness problem in a financial market, where the risky asset is driven by Markov additive exponential model. These results characterize the martingale measure satisfying the entropy criterion. This measure is used to compute the price of the option and the portfolio of hedging in an exponential Markov-modulated Lévy model.
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Some Applications of Markov Additive Processes as Models in Insurance and Financial MathematicsBen Salah, Zied 07 1900 (has links)
No description available.
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