IOE 623 - Computational Finance
Section: 001
Term: FA 2019
Subject: Industrial and Operations Engineering (IOE)
Department: CoE Industrial and Operations Engineering
Requirements & Distribution:
Waitlist Capacity:
Advisory Prerequisites:
MATH 316 and MATH 425 or 525.
This course counts toward the 60 credits of math/science required for a Bachelor of Science degree.
May not be repeated for credit.
Primary Instructor:

This is a course on computational methods in finance and financial modeling. Using financial mathematics (like many branches of applied mathematics) in practice involves three tasks. First, one needs to develop mathematical models that accurately describe the real-life phenomena that one wishes to study – in the present case, probabilistic models for the evolution of prices, interest rates, and other relevant quantities. Once a model is chosen, the second task is to derive theoretical equations, or formulas, which establish relations between various objects in the financial markets: for example, the prices of derivative securities (options, bonds, etc), and the risk profiles of investment portfolios, as functions of risk factors. Finally, one needs to design and implement numerical methods to perform computations based on these formulas and equations. This course is concerned with the latter task, and it has three components. In the first part, we will study the lattice (or, tree) methods, which correspond to the models based on discrete time Markov chains (e.g. the binomial model). We will discuss the pricing and hedging of financial derivatives in such models, using the arbitrage theory, or, more specifically, the risk-neutral pricing. We will, then, proceed to analyze the diffusion-based models of financial mathematics (including, e.g., the Black-Scholes model) and the associated Partial Differential Equations (PDEs). We will discuss the finite difference methods, which provide numerical approximations for solutions to these PDEs. Both explicit and implicit schemes will be studied, the concepts of stability and convergence will be introduced, and a connection between the finite difference schemes and lattice methods will be established. After that, we will turn to the Monte Carlo simulations – the most general computational method for probabilistic equations. This method is based on generating a large number of paths of the underlying stochastic processes, in order to approximate the expectations of certain functions of these paths (which, e.g., may determine prices, portfolio weights, default probabilities, etc.). In addition to the standard Monte Carlo algorithms, we will study the variance reduction techniques, which are often necessary to obtain accurate results. The computational methods presented in this course will be illustrated using the popular models of equity markets (e.g. Black-Scholes, Heston), fixed income (e.g. Vasicek, CIR, Hull-White, Heath-Jarrow-Morton) and credit risk (e.g. Merton, Black-Cox, reduced-form models).

For more information on this course, please visit the Department of Mathematics webpage

IOE 623 - Computational Finance
Schedule Listing
001 (LEC)
TuTh 10:00AM - 11:30AM
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