Option Pricing with Multivariate GARCH Models

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The ultimate goal of this research program is to 1) develop a multivariate statistical modelling framework, flexible enough to describe the dynamics and to take into account the correlations among financial assets, which can be used for risk management, in general, and option pricing, in particular, in high dimensions, and 2) provide the tools that regulators and supervisors crucially need to increase financial stability and that practitioners in financial institutions need to rapidly evaluate their risk exposures, improving market liquidity, and allow the financial markets to price and bear risk more efficiently. With the proposed model, derivatives on multiple assets can be priced in a theoretically consistent way and the research program develops innovative closed form readily computed expressions or formulas for derivatives pricing in this framework. Currently, the only possible methods for option pricing in such a flexible framework rely on time consuming numerical techniques like Monte Carlo simulation, and pricing securities in a timely manner requires shortcuts which sacrifice realism in the models. Closed form formulas, on the other hand, allow for fast and accurate pricing of the complex derivatives that exist in today's financial markets. The proposed framework also allows derivation of closed form expression for option price sensitivities. These measures are used to assess the risks of these derivative products and necessary for efficient management of the risks associated with such assets. Financial institutions and government regulators frequently perform such calculations to manage the risk of portfolios with thousands of assets. Therefore, closed form solutions are of immense importance because they allow reliable risk management in real time without sacrificing precision. The formulas derived in this research make it possible to incorporate historical option prices in the model estimation, leading to more efficient estimates of model parameters. Incorporating historical option prices in this multivariate framework also allows for calculating innovative measures of the perceived risk in financial markets that take into consideration the complex nature and interdependence of these markets. These innovative measures will lead to better and more consistent assessment of the risks involved in complex products than what is currently available. The flexible framework developed in this project will be of interest to academics, financial industry practitioners, and regulators. The proposed models have implications for how financial derivatives are valued, how their risks are managed, and therefore on how financial policy should be created, implemented, and evaluated. The proposed research program will greatly benefit the Canadian economy by providing tools to improve market liquidity and allow financial markets to efficiently price and bear risk, increasing financial stability and decreasing the likelihood of future financial crises.