November 16, 2012
Speaker: Greg Frank, CIBC
Title: Mathematical Finance: the Applied Mathematician’s Toolkit
Abstract: Options, derivatives and other financial products allow market participants to manage their investment priorities and risk/reward profiles. The financial mathematician’s job is to understand these products and the markets in which they are embedded. In this talk we will examine how tools from applied mathematics are used to build the models that quantify derivatives’ value and risk. Starting with a simple model of random asset prices (random processes) we consider how to model a vanilla derivative on the asset (stochastic calculus, PDE), and how to find its value (integral transforms, ODE). We examine how more complex products can be built, valued (finite difference, Monte Carlo) and calibrated to the market (least squares, SVD). Individual products are combined into portfolios whose risk must be actively managed, and the requirement to measure risk places constraints on each model’s complexity and accuracy. Finally, we will look at how developments over the past few years are driving new financial modeling challenges.