Financial modelling and derivatives pricing under alternative Stochastic processes

替代随机过程下的金融建模和衍生品定价

• 批准号: 262275-2008
• 负责人: Campolieti, Giuseppe
• 金额: $ 1.17万
• 依托单位: Wilfrid Laurier 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=548019
• 关键词: Financial; modelling; derivatives; pricing; under

The development of realistic stochastic models for risky asset price processes and their implementation to the pricing of generally exotic derivatives is at the heart of modern day financial mathematics. A vast body of research is devoted to this important area which poses computational and theoretical challenges. Current models go well beyond the celebrated Black-Scholes model which does not support commonly observed features such as volatility clustering and fat tail distributions for asset price returns. The observed leverage effect and the market implied volatility smiles are also completely absent in this model and not well replicated in some mathematical extensions of the model. The resolution of these model discrepancies is a fundamental issue and this continues to fuel interest in financial modelling and option pricing with the use of more realistic models. The goal of my research is to make further progress in this and related critical areas of financial mathematics. This proposal focuses on further innovative developments of alternative stochastic processes in the single and multi-asset domain with several applications to derivatives pricing. An underlying component of my research involves the use of our newly developed families of analytically tractable models. Our research to date has shown that our models are rich in their ability to realistically describe option market volatility smiles and skews. My most current work also develops analytically exact spectral expansions for first passage time densities, barrier options and seasoned lookback options for these new models. We have also recently succeeded in developing efficient algorithms for pricing exotic options under subfamilies of our new volatility smile models. This proposal will continue to build on new developments and applications of such alternative stochastic models. The development of efficient numerical algorithms for describing such processes leads to various applications in finance as well as in many other areas of mathematical modelling that involve stochastic processes. The mathematical and computational results that will be generated by this research are expected to significantly impact the field of financial mathematics.

风险资产价格过程的现实随机模型的发展及其对一般奇异衍生品定价的实现是现代金融数学的核心。大量的研究致力于这一重要领域，这带来了计算和理论上的挑战。目前的模型远远超出了著名的布莱克-斯科尔斯模型，该模型不支持通常观察到的特征，如波动率聚集和资产价格收益的厚尾分布。观察到的杠杆效应和市场隐含波动率微笑也完全没有在这个模型中，并没有很好地复制模型的一些数学扩展。这些模型差异的解决方案是一个根本问题，这将继续推动人们对使用更现实的模型进行金融建模和期权定价的兴趣。我的研究目标是在金融数学的这个和相关的关键领域取得进一步的进展。本提案侧重于替代随机过程在单一和多资产领域的进一步创新发展，并在衍生品定价中有几个应用。我的研究的一个基本组成部分涉及使用我们新开发的家庭分析听话的模型。迄今为止，我们的研究表明，我们的模型具有丰富的能力，能够真实地描述期权市场波动率的微笑和偏斜。我目前的工作还为这些新模型的首次通过时间密度、障碍选项和经验丰富的回顾选项开发了分析精确的谱展开。我们最近还成功地开发了有效的算法，我们的新的波动率微笑模型的子族下的异国情调的期权定价。这项建议将继续建立在新的发展和应用这种替代随机模型。描述这种过程的有效数值算法的发展导致了金融以及涉及随机过程的许多其他数学建模领域的各种应用。这项研究所产生的数学和计算结果预计将对金融数学领域产生重大影响。