On the Joint Modelling of Financial Assets

在投资界，金融衍生品是从标的资产(如股票、债券、货币)的表现中获得其价值的合同。近年来，他们的数量急剧增加。理论上，这些衍生品或期权的价格包含大量有关金融市场潜在风险的信息。人们可以将这些金融证券的价格与车险保单的保费相提并论。从理论上讲，有可能对汽车保险费进行“逆向工程”，以隔离保险单的潜在风险--例如发生事故的可能性。除了有关实际车祸的信息外，这还可以用来更好地了解潜在风险和保险公司对风险的看法。*金融衍生工具亦可采用同样的理据，以恢复投资者对风险的认知。理想情况下，这两种信息来源--基础资产价格和衍生资产价格--应该结合起来，因为有关资产价格随机属性的信息既包含在价格序列的历史中，也包含在价格序列上所写的任何期权的价格中。这些信息也不是多余的：标的资产价值的时间序列是回溯的，涉及过去的信息，而衍生品是前瞻性的，包含有关市场未来预期的线索。将这两种信息来源结合起来需要灵活的建模和开发新的统计工具。*拟议研究计划的总体目标是开发新的方法，将这些互补数据集的信息联系起来。这些方法将产生精确的参数估计，准确评估不可观察的因素(如瞬时波动、跳跃强度)，从而更好地了解加拿大个人和实体承担的金融风险。*更具体地说，对现有金融信息的全面看法需要设计统一的建模框架，并开发新的统计方法，使用户能够包括各种信息来源，以便更准确地估计金融风险。在接下来的五年里，这项研究计划将侧重于三个短期目标，以评估与(1)股票指数、(2)公司财务健康状况和(3)经济变量有关的风险。*这项工作的预期结果是实用的方法，供自然科学和工程领域的广泛领域的从业者和学者使用；即精算师、金融家、工程师等。事实上，任何需要使用不同来源的补充信息进行参数估计的情况--以及在存在未观察到的因素的情况下--都将受益于本研究计划的结果。

In the investment world, financial derivatives are contracts that derive their values from the performance of an underlying asset (e.g. stock, bond, currency). Their number has increased dramatically in recent years. In theory, the price of these derivatives—or options—contains a great deal of information about the underlying risks in financial markets.******One could draw a parallel between the price of these financial securities and the premium of a car insurance policy. It would be possible, in theory, to “reverse engineer” the car insurance premium to isolate the underlying risk of the insurance policy—the likelihood of having an accident, for instance. This could be used, in addition to the information about the actual car accidents, to gain a better understanding about the underlying risk and the insurer's perception of risk. ******The same rationale could be applied to financial derivatives to recover the investor's perception of risk. Ideally, the two sources of information—both underlying and derivative asset prices—should be combined because information about the stochastic properties of an asset's price is contained both in the history of the price series and the price of any option written on it. This information is also non-redundant: time series of underlying asset values are backward-looking and involve past information, whereas derivatives are forward-looking and contain clues about the market's future expectations. Combining these two sources of information requires flexible modelling and the development of novel statistical tools. ******The overarching goal of the proposed research program is to develop new methodology that bridges the information of these complementary datasets. These methods will yield precise parameter estimates, accurate assessment of the unobservable factors (e.g. instantaneous volatility, jump intensity), and, ergo, a better understanding of the financial risks borne by Canadian individuals and entities.*** ***More specifically, this holistic view of the financial information available requires the design of unified modelling frameworks as well as the development of new statistical methodology that allows the user to include various sources of information to give a more accurate estimation of financial risk. Over the next five years, this research program will focus on three short-term objectives to assess the risks pertaining to (1) stock indexes, (2) firms' financial health and (3) economic variables.******The anticipated outcomes of this work are practical methods to be used by practitioners and academics in a wide range of fields in natural sciences and engineering; i.e. actuaries, financiers, engineers, etc. Indeed, any situations that require parameter estimation using different sources of complementary information—and in the presence of unobserved factors—would benefit from the outcomes of this research program.**