Hedging strategies and minimal variance portfolios for European and exotic options in a Levy market

This paper presents hedging strategies for European and exotic options in a Levy market. By applying Taylor's Theorem, dynamic hedging portfolios are con- structed under different market assumptions, such as the existence of power jump assets or moment swaps. In the case of European options or baskets of European options, static hedging is implemented. It is shown that perfect hedging can be achieved. Delta and gamma hedging strategies are extended to higher moment hedging by investing in other traded derivatives depending on the same underlying asset. This development is of practical importance as such other derivatives might be readily available. Moment swaps or power jump assets are not typically liquidly traded. It is shown how minimal variance portfolios can be used to hedge the higher order terms in a Taylor expansion of the pricing function, investing only in a risk-free bank account, the underlying asset and potentially variance swaps. The numerical algorithms and performance of the hedging strategies are presented, showing the practical utility of the derived results.Comment: 32 pages, 6 figure

Hedging strategies and minimal variance portfolios for European and exotic options in a Levy market

This paper presents hedging strategies for European and exotic options in a Levy market. By applying Taylor's Theorem, dynamic hedging portfolios are con- structed under different market assumptions, such as the existence of power jump assets or moment swaps. In the case of European options or baskets of European options, static hedging is implemented. It is shown that perfect hedging can be achieved. Delta and gamma hedging strategies are extended to higher moment hedging by investing in other traded derivatives depending on the same underlying asset. This development is of practical importance as such other derivatives might be readily available. Moment swaps or power jump assets are not typically liquidly traded. It is shown how minimal variance portfolios can be used to hedge the higher order terms in a Taylor expansion of the pricing function, investing only in a risk-free bank account, the underlying asset and potentially variance swaps. The numerical algorithms and performance of the hedging strategies are presented, showing the practical utility of the derived results.Hedging Strategies; Levy processes; Variance Gamma; Choatic Representation Property; Power Jump Processs; Variance Swaps; Moment Swaps

Rare Decays of Heavy Baryons using Soft Collinear Effective Theory

In the era of high-luminosity hadronic colliders, the rare heavy-to-light decay Lambda_b to Lambda l+ l- receives increasing research attention in both experimental and theoretical particle phenomenology. This flavour-changing neutral-current decay is a potential window for the discovery of new Physics beyond the Standard Model through its helicity-sensitive nature, complementing past and ongoing searches and calculations related to the B meson. In this work the universal soft form factor in the heavy-quark and large-recoil limits is calculated using light-cone sum rules in the framework of soft-collinear effective theory, as is the O(alpha_s) correction from hard-collinear gluon exchange. Numerical estimates on form-factor ratios and experimental observables are presented. Related issues, including baryonic transition form factors and in particular light-cone distribution amplitudes for the heavy baryon Lambda_b, are also discussed

Lévy processes, representation and models with applications in finance

L????vy processes are becoming increasingly important in Mathematical Finance. This thesis aims to contribute to the development of theoretical representations of L????vy processes and their financial applications. The first part of the thesis presents a computational explicit formula of the chaotic representation property (CRP) for the powers of increments of a L????vy process. The formula can be used to obtain the integrands of the CRP in terms of the orthogonalised compensated power jump processes and the CRP in terms of Poisson random measures. The second part of the thesis presents hedging strategies for European and exotic options in a L????vy market. By applying Taylor s theorem, dynamic hedging portfolios are constructed and in the case of European options, static hedging is also implemented. It is shown that perfect hedging can be achieved by investing in power jump assets, moment swaps or some traded financial derivatives depending on the same underlying asset. Note that variance swaps are special cases of moment swaps and are traded in OTC (Over-The- Counter) markets. We can also hedge by constructing the minimal variance portfolios that invest in the risk-free bank account, the underlying stock and variance swaps. The numerical algorithms and performance of the hedging strategies are presented. The third part of the thesis contributes to the design of an option trading strategy, where the stock price is driven by a L????vy process. The trading strategy is based on comparing the deviations between the density implied by historical time series and that implied by current market prices of the options. The performance of the trading strategy under di????erent market conditions is reported and optimal parameters are obtained using efficient frontier analysis. The analysis compares the expected returns with the Conditional Value at Risks (CVaRs). Simulation results show that the trading strategy has a high earning potential.Imperial Users onl

Lévy Processes, Representations and Models with Application in Finance

Lévy processes are becoming increasingly important in Mathematical Finance. This thesis aims to contribute to the development of theoretical representations of Lévy processes and their financial applications. The first part of the thesis presents a computational explicit formula of the chaotic representation property (CRP) for the powers of increments of a Lévy process. The formula can be used to obtain the integrands of the CRP in terms of the orthogonalised compensated power jump processes and the CRP in terms of Poisson random measures. The second part of the thesis presents hedging strategies for European and exotic options in a Lévy market. By applying Taylor's theorem, dynamic hedging portfolios are constructed and in the case of European options, static hedging is also implemented. It is shown that perfect hedging can be achieved by investing in power jump assets, moment swaps or some traded financial derivatives depending on the same underlying asset. Note that variance swaps are special cases of moment swaps and are traded in OTC (Over-The- Counter) markets. We can also hedge by constructing the minimal variance portfolios that invest in the risk-free bank account, the underlying stock and variance swaps. The numerical algorithms and performance of the hedging strategies are presented. The third part of the thesis contributes to the design of an option trading strategy, where the stock price is driven by a Lévy process. The trading strategy is based on comparing the deviations between the density implied by historical time series and that implied by current market prices of the options. The performance of the trading strategy under di¤erent market conditions is reported and optimal parameters are obtained using efficient frontier analysis. The analysis compares the expected returns with the Conditional Value at Risks (CVaRs). Simulation results show that the trading strategy has a high earning potential

Addressing quality, access and equity in the school direct subsidy scheme in Hong Kong : a study of government strategies and tools

published_or_final_versionPolitics and Public AdministrationMasterMaster of Public Administratio

Environmental change detection in relation to landslide hazard using landsat TM imagery

Landslides are severe environmental hazards in mountainous areas. Nowadays, the threat of landslides to public safety has become more pronounced resulting from the burgeoning development and the increase of deforestation in hilly areas, and the increase of regional precipitation caused by global climate change. Traditional landslide risk assessment requires immense physical power to assemble different in-situ data, such as identification of landslide location and land-cover classification. This traditional data collection technique is very time consuming, and thus impossible to be applied for the large scale assessment. Remote sensing techniques, therefore, are the solutions for providing fast and up-to-date landslide assessments. This thesis focuses on the applications of multispectral Landsat data for landslide recognition. Wollongong of Australia was chosen as a test bed for this analysis. For landslide recognition analysis, three change detection techniques were employed, which were image differencing, bi-temporal linear data transformation and post-classification comparison. For the first two change detection methods, a new landslide identification procedure was developed by integrating surface change information of greenness, brightness and wetness. During the image differencing, the three surface change components were derived from Vegetation Indices (VIs), in which four different surface change composites were generated. Each composite contained three surface change bands which were greenness, brightness and wetness. For bi-temporal linear data transformation, multitemporal Kauth-Thomas (MKT) transformation was adopted for providing the three types of surface change information. In the landslide recognition analysis, the best mapping performance is yielded by the image differencing method using brightness and wetness components of Kauth-Thomas transformation and NDVI. Its omission error (i.e. percentage of actual landslide pixels which were not detected) and commission error (i.e. percentage of change pixels identified which were not landslide) are 14.4% and 3.3%, respectively, with a strong agreement (KHAT = 88.8%)