Revised May, 2010

CS 335: Computational Methods in Business and Finance

General Description

An introduction to the use of computational methods for business and finance. Students will learn to apply the basic algorthims and to recognize common pitfalls in their use.

Logistics

Intended for upper-year students interested in the application of numerical computation to business and finance. Expected first offering: Fall 2011.

Related courses (see calendar for official details)

Predecessors: (One of CS 116, 136, 138 145 taken fall 2010 or earlier, 146), MATH 136 or 146, MATH 237 or 247, STAT 231 or 241. Not open to computer science students.
Successors: Normally none.
Conflicts: Other introductory courses in numerical methods, including ECE 204, CS 370 and CS 371/AMATH 242/CM 241.

Software used: MATLAB

Typical Reference(s)

Paolo Brandimarte, Numerical Methods in Finance, A MATLAB-Based Introduction, Wiley, second edition, 2006.

Required preparation

To begin the course, students will need the following.

Programming experience in a high-level procedural programming language (e.g., CS116 or equivalent). This should include the use of control structions such as loops and conditional statements, basic datatypes, and simple data structures such as arrays.
Ability to perform basic computations involving
- calculus derivatives (including finding maxima and minima of multivariate functions),
- matrices,
- discrete and continuous random variables, and
- basic statistical models.

Learning objectives

By the end of the course, students should have the ability to do the following.

Explain the principles of floating-point number systems, including the concepts of chopping, rounding and machine precision; use these principles to analyze error of floating-point arithmetic.
Use the principles of polynomial interpolation to derive and apply splines with various boundary conditions.
Analyze stability and conditioning of numerical problems.
Within the MATLAB programming environment, to
- Use the built-in functions and graphing capabilities for 1D and 2D data, and to implement efficient code using vectorization.
- Solve problems in portfolio optimization using mean-variance criteria, including the construction of efficient frontiers and computation of value-at-risk.
- Implement lattice methods for computing contingent-claims valuation.
- Solve nonlinear equations using iterative methods.
- Implement Monte Carlo methods, generation of normally distributed random numbers, simulation of hedging strategies, and variance-reduction techniques.

Typical syllabus

Introduction to Floating-Point Computation (3 hrs):

Inexact computation, machine epsilon, stability.

Introduction to MATLAB (3 hrs):

Basic data types in MATLAB, use of built-in functions, graphical presentation of data, vectorization of code.

Interpolation (3 hrs):

Linear, Lagrange, splines.

Portfolio Optimization (8 hrs):

Mean variance criteria, the efficient frontier, optimization methods, use of quadratic programming software, stability of results with uncertain data. Value at risk.

Contingent-Claims Valuation (8 hrs):

Lattice methods, implied volatility, the risk-neutral world.

Solution of Nonlinear Equations (3 hrs):

Bisection, fixed-point iteration, Newton iteration.

Monte Carlo Methods (8 hrs):

Stochastic differential equations, timestepping methods, generation of normally distributed random numbers, variance reduction. Applications to contingent claims, simulation of hedging strategies.

David R. Cheriton School of Computer Science
University of Waterloo
Waterloo, Ontario, Canada N2L 3G1

Tel: 519-888-4567 x33293
Fax: 519-885-1208

Contact | Feedback: cs-uops@cs.uwaterloo.ca | David R. Cheriton School of Computer Science | Faculty of Mathematics

Last modified: Wednesday, 15-Feb-2012 10:39:11 EST

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