Grant: Discovery Grants Program - Individual

This proposal centres on two related sets of quantitative finance projects i) high-dimensional finance (problems involving three or more stochastic variables); and ii) financial stability and systemic risk. The high-dimensional finance project consists of two subprojects, one focusing on the pricing and risk management of derivative securities with early-exercise features and the other concentrating on public funds management. The valuation of these securities is important to financial institutions for their trading and internal risk management capabilities and for determining the amount of capital needed to satisfy regulatory requirements. Government portfolios are very large and minor improvements in their management can lead to taxpayer savings in the millions. This subproject will investigate alternative strategies for the management of accumulated debt portfolios. Furthermore, performance measures and benchmarks customized to public funds managers will be developed and assessed. In this era of increased government transparency and accountability these measures are required and can lead to improvements in fund performance to the benefit of taxpayers. The taxpayer bailout of financial institutions during the recent financial crisis has highlighted the issues of financial stability and systemic risk. It has been proposed that institutions issue regulatory hybrid securities as part of their capital structure so that firms and not taxpayers fund the cost of recapitalization. The pricing of hybrids will be explored under various paradigms including those of high dimension. The use of network models to assess financial system risk will be investigated, including the implications of hybrid securities and the design of financial markets. These projects are related as the valuation and risk exposure estimation algorithms for derivative securities feed in to the risk assessment of an individual institution which, in turn affects the stability of the financial system.