Pricing and Hedging under Processes with Conditional Independent Increments

有条件独立增量流程下的定价和对冲

• 批准号: RGPIN-2014-03664
• 负责人: Olivares, Pablo
• 金额: $ 0.8万
• 依托单位: Ryerson University
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2014
• 资助国家: 加拿大
• 起止时间: 2014-01-01 至 2015-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=566012
• 关键词: Pricing; Hedging; under; Processes; Conditional

Olivares, Pablo PIN: 346658 The general objective of the proposal is to develop techniques to price multidimensional derivative contracts and methods to obtain adaptive hedging strategies when the dynamic of the underlying assets is described by stochastic processes with conditional independent increments (PCII). The proposal is divided in four interacting components with specific objectives: asset modelling, approximating pricing methods, adaptive hedging strategies and applications to energy and environmental finance. Original contributions to scientific knowledge can be found in five main directions related with these components. Theoretical properties of new models, such as integrated characteristic functions, equivalent martingale measures, subordination, asymptotic behavior, mixed moments and first exit probability distributions will be investigated. Next, existing techniques for pricing will be adapted under the new circumstances. A combination of Fast Fourier methods, Taylor and other polynomial approximations, together with saddlepoint techniques will be taken into account. They are planned to be implemented to most common multidimensional derivatives, starting with European type contracts, and then considering Barriers and Defaultable Bonds, to Credit Derivatives Swaps (CDS), where default is given by PCII models. A novel method for hedging is proposed, where adaptive parameter estimation is studied from an optimal control perspective. Parameter estimation techniques based on approximated characteristic functions and a non parametric point of view will be developed at this stage. Finally, applications to the energy and the emerging environmental financial sectors will be explored, always under the new models in the class of PCIIs. It includes the pricing of real options with oil, heating oil and gasoline as underlying, as well as electricity prices. The relevance of this research proposal lies in the novelty of the mathematics models considered as well as in the original implementation of approximated closed pricing formulas and adaptive hedging strategies derived from them. It may have a potential impact in financial institutions, specifically in the important Canadian energy sector, as it provides practitioners with more accurate tools and faster algorithm to evaluate investment positions based on multidimensional derivative products. Results of the research will be incorporated to the existing programs in Financial Mathematics at Ryerson University, at undergraduate and graduate levels. It will be reflected in the development of our research group, the training of approximately 15 HQP, publication of 10 scientific papers in main stream journals as well as a general improvement in curricular activities. The project viability is supported by author's past experience. The author has an ample base of collaborators at Ryerson University, University of Toronto, University of Montreal, Technical University of Munich, Florida International University, Autonomous Mexican Technological Institute among others. Students will be incorporated at all stages, with special emphasis in applications to energy and environmental finance.

Pablo PIN的Olivares：346658该提案的一般目标是开发技术以进行多维衍生合同和方法，以获取基础资产的动态，以有条件独立增量（PCII）描述了基础资产的动态时。该提案分为具有特定目标的四个相互作用组件：资产建模，近似定价方法，自适应对冲策略以及对能源和环境融资的应用。对科学知识的原始贡献可以在与这些组件相关的五个主要方向上找到。将研究新模型的理论特性，例如综合特征函数，等效的Martingale措施，从属，渐近行为，混合力矩和首次退出概率分布。接下来，在新情况下将改编现有定价技术。将考虑快速傅立叶方法，泰勒和其他多项式近似的组合以及鞍点技术。计划将它们实施到最常见的多维导数，从欧洲类型合同开始，然后考虑障碍和违约债券，向信用衍生品掉期（CDS），其中PCII模型给出了默认值。提出了一种新颖的对冲方法，其中从最佳控制角度研究了自适应参数估计。在此阶段将开发基于近似特征函数的参数估计技术和非参数观点。最后，将始终在PCII类的新模型下探索对能源和新兴环境财务部门的应用。它包括用石油，加热油和汽油作为基础以及电价的真实选择的定价。这项研究建议的相关性在于所考虑的数学模型的新颖性以及近似封闭的定价公式和自适应对冲策略的最初实现。它可能对金融机构，特别是在重要的加拿大能源领域产生潜在影响，因为它为从业者提供了更准确的工具和更快的算法，以根据多维导数产品评估投资头寸。该研究的结果将纳入瑞尔森大学，本科和研究生级的现有金融数学计划。它将反映在我们的研究小组的发展，大约15个HQP的培训，在主流期刊上发表10篇科学论文以及课程活动的总体改进。作者过去的经验支持该项目的可行性。作者在瑞尔森大学，多伦多大学，蒙特利尔大学，佛罗里达州慕尼黑大学，佛罗里达国际大学，自主墨西哥技术学院等人拥有足够的合作者。学生将在各个阶段成立，并特别强调能源和环境融资。