On the Joint Modelling of Financial Assets

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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 derivativesor optionscontains 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 policythe 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 informationboth underlying and derivative asset pricesshould 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 informationand in the presence of unobserved factorswould benefit from the outcomes of this research program.