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: 2018
• 资助国家: 加拿大
• 起止时间: 2018-01-01 至 2019-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=661184
• 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.

奥利瓦雷斯，巴勃罗PIN：346658** 该提案的总体目标是开发多维衍生品合约定价技术和方法，以获得自适应对冲策略，当基础资产的动态由具有条件独立增量的随机过程（PCII）描述时。该提案分为四个相互作用的部分，各有具体目标：资产建模、近似定价方法、适应性对冲战略以及对能源和环境融资的应用。对科学知识的原创性贡献可以在与这些组成部分相关的五个主要方向找到。将研究新模型的理论性质，如综合特征函数，等价鞅测度，从属性，渐近行为，混合矩和首次退出概率分布。其次，现有的定价技术将适应新的情况。将考虑快速傅立叶方法、泰勒和其他多项式近似以及鞍点技术的组合。他们计划实施到最常见的多维衍生工具，从欧洲类型的合同开始，然后考虑障碍和可违约债券，信用衍生品掉期（CDS），其中违约由PCII模型给出。 提出了一种新的套期保值方法，从最优控制的角度研究了自适应参数估计。基于近似特征函数和非参数观点的参数估计技术将在这一阶段得到发展。最后，能源和新兴的环境金融部门的应用将被探索，总是在新的模式下的类PCIIs。它包括以石油、取暖油和汽油为基础的真实的期权的定价，以及电力价格。本研究建议的相关性在于所考虑的数学模型的新奇以及近似封闭定价公式和自适应套期保值策略的原始实施。它可能对金融机构产生潜在影响，特别是在重要的加拿大能源部门，因为它为从业者提供了更准确的工具和更快的算法来评估基于多维衍生产品的投资头寸。研究结果将纳入瑞尔森大学现有的本科和研究生金融数学课程。这将反映在我们的研究小组的发展，大约15名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普遍改善。项目的可行性得到了作者过去经验的支持。作者在瑞尔森大学，多伦多大学，蒙特利尔大学，慕尼黑技术大学，佛罗里达国际大学，墨西哥自治技术研究所等有充足的合作者基础。 学生将在各个阶段被纳入，特别强调能源和环境融资的应用。