Topics on discrete-time stochastic volatility models with applications in finance and insurance

离散时间随机波动率模型及其在金融和保险中的应用主题

• 批准号: RGPIN-2018-04746
• 负责人: Badescu, Alexandru
• 金额: $ 1.46万
• 依托单位: University of Calgary
• 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=644428
• 关键词: Topics; discrete; time; stochastic; volatility

The pricing and hedging of financial and insurance products have been key objects of study in over two decades. Although tremendous research efforts have addressed important aspects, there are still 'puzzles' yet to be solved. This research project focuses on topics selected from the financial econometrics and mathematical finance literature.******Volatility trading has recently become almost as important as option trading, as daily volumes of volatility trading have recently become larger than daily volumes of S&P 500 option trading. Variance swap contracts are the building blocks of volatility derivatives. Although a vast majority of the mathematical finance literature examines the modelling of financial assets and pricing of volatility derivatives in continuous-time (mainly due to the tractability offered by this setup) variance swaps are in practice sampled at fixed dates and therefore, a discrete-time setting might be more appropriate. The following summarizes my future research directions. ******In the first part of this proposal, I plan to study the relationship between discrete and continuous time pricing models, by investigating the weak convergence of several popular affine and non-affine models such as the Generalized Autoregressive Conditional Heteroskedastic (GARCH) family and autoregressive Stochastic Volatility (SV) models. These results will be derived in both a univariate and multivariate setting, and applications to pricing European and American options will be discussed. One of the goals of this exercise, is to identify new pricing models and strategies which make use of the advantages of the non-affine structure, when fitting financial asset data, and the affine properties when pricing derivatives. ******In the second part of the proposal, I intend to look at novel pricing methodologies for variance swaps when the sampling is performed at discrete time points. Using the convergence results computed in the first part, I aim to derive new formulas for the discretely sampled variance swaps, when the underlying asset is modelled in continuous time, which is not possible following a direct calculation. Using real market quotes for variance swaps, I plan to construct models which fit well their term structure. For example, in the option pricing theory it is a well-known fact that adding jumps to a stochastic volatility models only helps in fitting the short-term out-of-money contracts, and therefore it will be interesting to test if that is also the case for variance swaps. I believe the proposed research plan will bring several important contributions to the modelling and pricing and hedging of financial derivatives, in particular volatility derivatives.

金融和保险产品的定价和对冲一直是二十年来研究的关键对象。尽管巨大的研究工作已经解决了重要方面，但仍有“难题”尚未解决。该研究项目的重点是从金融计量经济学和数学金融文献中选择的主题。******波动性交易最近几乎与期权交易一样重要，因为最近每天的波动性交易量最近变得比每日的每日标准普尔500期期权期权。差异交换合同是波动衍生物的基础。尽管绝大多数数学金融文献都研究了金融资产的建模和连续时间的波动性导数的定价（主要是由于本设置提供的障碍性）在固定日期下进行样品差异，因此，离散的时间设置可能更合适。以下总结了我未来的研究方向。 ******在该提案的第一部分中，我计划通过研究几种流行的仿期和非植入模型的弱收敛性，例如广义自动回归有条件的异性恋（Garch）家族和自动恢复性的随机挥发性（SV）模型来研究离散和连续定价模型之间的关系。这些结果将在单变量和多变量环境中得出，并将讨论定价和美国选择的应用。这项练习的目标之一是确定新的定价模型和策略，这些模型和策略在拟合金融资产数据时利用非承包结构的优势以及定价衍生产品时的仿射特性。 ******在提案的第二部分中，我打算在离散时间点执行采样时研究新颖的定价方法，以进行方差互换。使用第一部分中计算的收敛结果，我旨在在连续时间建模基础资产时为离散采样的方差掉期提供新公式，这是在直接计算后不可能的。我计划使用差异掉期的真实市场报价，我计划构建适合其期限结构的模型。例如，在期权定价理论中，众所周知的事实是，在随机波动率模型中增加跳跃仅有助于适合短期损失的合同，因此测试是否也是差异掉期的情况会很有趣。我相信拟议的研究计划将为建模，定价和对冲的金融衍生品（特别是波动性衍生品）带来一些重要的贡献。