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1	Option pricing under exponential jump diffusion processes Bu, Tianren January 2018 (has links) The main contribution of this thesis is to derive the properties and present a closed from solution of the exotic options under some specific types of Levy processes, such as American put options, American call options, British put options, British call options and American knock-out put options under either double exponential jump-diffusion processes or one-sided exponential jump-diffusion processes. Compared to the geometric Brownian motion, exponential jump-diffusion processes can better incorporate the asymmetric leptokurtic features and the volatility smile observed from the market. Pricing the option with early exercise feature is the optimal stopping problem to determine the optimal stopping time to maximize the expected options payoff. Due to the Markovian structure of the underlying process, the optimal stopping problem is related to the free-boundary problem consisting of an integral differential equation and suitable boundary conditions. By the local time-space formula for semi-martingales, the closed form solution for the options value can be derived from the free-boundary problem and we characterize the optimal stopping boundary as the unique solution to a nonlinear integral equation arising from the early exercise premium (EEP) representation. Chapter 2 and Chapter 3 discuss American put options and American call options respectively. When pricing options with early exercise feature under the double exponential jump-diffusion processes, a non-local integral term will be found in the infinitesimal generator of the underlying process. By the local time-space formula for semi-martingales, we show that the value function and the optimal stopping boundary are the unique solution pair to the system of two integral equations. The significant contributions of these two chapters are to prove the uniqueness of the value function and the optimal stopping boundary under less restrictive assumptions compared to previous literatures. In the degenerate case with only one-sided jumps, we find that the results are in line with the geometric Brownian motion models, which extends the analytical tractability of the Black-Scholes analysis to alternative models with jumps. In Chapter 4 and Chapter 5, we examine the British payoff mechanism under one-sided exponential jump-diffusion processes, which is the first analysis of British options for process with jumps. We show that the optimal stopping boundaries of British put options with only negative jumps or British call options with only positive jumps can also be characterized as the unique solution to a nonlinear integral equation arising from the early exercise premium representation. Chapter 6 provides the study of American knock-out put options under negative exponential jump-diffusion processes. The conditional memoryless property of the exponential distribution enables us to obtain an analytical form of the arbitrage-free price for American knock-out put options, which is usually more difficult for many other jump-diffusion models. 510
2	Testing for jumps in face of the financial crisis : Application of Barndorff-Nielsen - Shephard test and the Kou model Pszczola, Agnieszka, Walachowski, Grzegorz January 2009 (has links) <p>The purpose of this study is to identify an impact on an option pricing within NASDAQ OMX Stockholm Market, if the underlying</p><p>asset prices include jumps. The current financial crisis, when jumps are much more evident than ever, makes this issue very actual and important in the global sense for the portfolio hedging and other risk management applications for example for the banking sector. Therefore, an investigation is based on OMXS30 Index and SEB A Bank. To detect jumps the Barndorff-Nielsen and Shephard non-parametric bipower variation test is used. First it is examined on simulations, to be finally implemented on the real data. An affirmation of a jumps occurrence requires to apply an appropriate model for the option pricing. For this purpose the Kou model, a double exponential jump-diffusion one, is proposed, as it incorporates essential stylized facts not available for another models. Th parameters in the model are estimated by a new approach - a combined cumulant matching with lambda taken from the Barrndorff-Nielsen and Shephard test. To evaluate how the Kou model manages on the option pricing, it is compared to the Black-Scholes model and to the real prices of European call options from the Stockholm Stock Exchange. The results show that the Kou model outperforms the latter.</p> Bipower variation Barndorff-Nielsen and Shephard test Stylized facts Double exponential jump-diffusion model Kou model Options pricing Cumulant matching
3	Testing for jumps in face of the financial crisis : Application of Barndorff-Nielsen - Shephard test and the Kou model Pszczola, Agnieszka, Walachowski, Grzegorz January 2009 (has links) The purpose of this study is to identify an impact on an option pricing within NASDAQ OMX Stockholm Market, if the underlying asset prices include jumps. The current financial crisis, when jumps are much more evident than ever, makes this issue very actual and important in the global sense for the portfolio hedging and other risk management applications for example for the banking sector. Therefore, an investigation is based on OMXS30 Index and SEB A Bank. To detect jumps the Barndorff-Nielsen and Shephard non-parametric bipower variation test is used. First it is examined on simulations, to be finally implemented on the real data. An affirmation of a jumps occurrence requires to apply an appropriate model for the option pricing. For this purpose the Kou model, a double exponential jump-diffusion one, is proposed, as it incorporates essential stylized facts not available for another models. Th parameters in the model are estimated by a new approach - a combined cumulant matching with lambda taken from the Barrndorff-Nielsen and Shephard test. To evaluate how the Kou model manages on the option pricing, it is compared to the Black-Scholes model and to the real prices of European call options from the Stockholm Stock Exchange. The results show that the Kou model outperforms the latter. Bipower variation Barndorff-Nielsen and Shephard test Stylized facts Double exponential jump-diffusion model Kou model Options pricing Cumulant matching
4	Option pricing under the double exponential jump-diffusion model by using the Laplace transform : Application to the Nordic market Nadratowska, Natalia Beata, Prochna, Damian January 2010 (has links) <p>In this thesis the double exponential jump-diffusion model is considered and the Laplace transform is used as a method for pricing both plain vanilla and path-dependent options. The evolution of the underlying stock prices are assumed to follow a double exponential jump-diffusion model. To invert the Laplace transform, the Euler algorithm is used. The thesis includes the programme code for European options and the application to the real data. The results show how the Kou model performs on the NASDAQ OMX Stockholm Market in the case of the SEB stock.</p> Financial Mathematics Laplace transform Kou model Double Exponential Jump-Diffusion option pricing MATHEMATICS MATEMATIK Other mathematics Övrig matematik Applied mathematics Tillämpad matematik
5	Option pricing under the double exponential jump-diffusion model by using the Laplace transform : Application to the Nordic market Nadratowska, Natalia Beata, Prochna, Damian January 2010 (has links) In this thesis the double exponential jump-diffusion model is considered and the Laplace transform is used as a method for pricing both plain vanilla and path-dependent options. The evolution of the underlying stock prices are assumed to follow a double exponential jump-diffusion model. To invert the Laplace transform, the Euler algorithm is used. The thesis includes the programme code for European options and the application to the real data. The results show how the Kou model performs on the NASDAQ OMX Stockholm Market in the case of the SEB stock. Financial Mathematics Laplace transform Kou model Double Exponential Jump-Diffusion option pricing MATHEMATICS MATEMATIK Other mathematics Övrig matematik Applied mathematics Tillämpad matematik
6	Régulation du marché des matières premières / Regulation in commodities markets Huang, Xiaoying 11 April 2016 (has links) Cette thèse se structure en 2 parties, le marché physique et le marché financier des matières premières agricoles et prend 3 thèmes intéressants à étudier. D'une part, si les interventions sur les marchés des matières premières sont limitées, une autre option toujours ouverte est de tenter d'atténuer les impacts négatifs des comportements extrêmes des prix. Ce thème fait le point sur la gestion efficace des risques. D'autre part, à ce jour aucun consensus n'a pu être trouvé concernant l'impact des nouveaux produits dérivés (ex : fonds indiciels). Cette question peut en fait être abordée directement dans l'impact des fonds indiciels sur le stockage des matières premières. Enfin, parmi les régulateurs sur les marchés des matières premières, le rôle des banques centrales est souvent ignoré. Pourtant, elles peuvent aussi être un régulateur efficace sur ces marchés. / This thesis provides an overview on the evolution of commodity markets and focuses on the price behaviour in both the commodity physical and the financial derivatives markets. Instead of directly analysing regulation in the commodity markets, this thesis highlights the market changes and specific market behaviour, which gives potential implications for market regulation.Main results of thesis. This research on regulation of commodity markets has been conducted within two different markets: commodity physical markets and commodity derivatives markets. Results in physical markets confirm the evidence of jump in agricultural commodity prices. Price volatility varies with time and is not constant. Commodity markets’ –at least agricultural markets’- prices oscillated during the period 2007/2008, which coincided with financial crisis. Relatively high frequent and small jumps in commodity prices are probably due to financial market factors instead of market fundamentals.The implication of these results in risk management of agricultural cooperatives is that, although taking into account jump in risk measure, such as VaR does not out-perform traditional VaR with normal distribution. Considering this kind of extreme price variation can be complementary for risk managers when facing a highly volatile commodity market. Findings for financial derivatives markets lead to two conclusions.Firstly, commodity index funds are confirmed again as having a short-term impact on futures prices in most products. Based on the theoretical conclusion about the intermediary role of inventory on the impact of speculation on the commodity market, we have found that commodity index can influence commodity futures prices without necessarily passing through inventory changes, which is probably due to price-inelasticity. Secondly, in relation to the impact of central bank announcements on commodity prices, the study shows that the central bank can be an alternative regulator to influence the commodity market. Additionally, it shows that commodity prices include the information from macroeconomic factors, such as currency rate and inflation rate. Prix spot du blé Double sauts exponentiels Fonds indiciels des matières premières Stockage Structure par terme Value at risk Double-exponential jump Storage 650
7	Pricing of exotic options under the Kou model by using the Laplace transform Dzharayan, Gayk, Voronova, Elena January 2011 (has links) In this thesis we present the Laplace transform method of option pricing and it's realization, also compare it with another methods. We consider vanilla and exotic options, but more attention we pay to the two-asset correlation options. We chose the one of the modifications of Black-Scholes model, the Kou double exponential jump-diffusion model with the double exponential distribution of jumps, as model of the underlying stock prices development. The computations was done by the Laplace transform and it's inversion by the Euler method. We will present in details proof of finding Laplace transforms of put and call two-asset correlation options, the calculations of the moment generation function of the jump-diffusion by Levy-Khintchine formulae in cases without jumps and with independent jumps, and direct calculation of the risk-neutral expectation by solving double integral. Our work also contains the programme code for two-asset correlation call and put options. We will show the realization of our programme in the real data. As a result we see how our model complies on the NASDAQ OMX Stock-holm Market, considering the two-asset correlation options on three cases by stock prices of Handelsbanken, Ericsson and index OMXS30. Financial Mathematics Double exponential jump-diusion model Kou model Laplace transform Laplace transform inversion two-dimensional Euler algorithm two-asset correlation options. Applied mathematics Tillämpad matematik Mathematical statistics Matematisk statistik
8	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
9	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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