Core Courses

Semester One Core Requirements (Fall)
1. Options and Derivatives Pricing (FIM/ECG/MA/MBA 528)
  • Structure and operation of derivative markets
  • Valuation of derivatives
  • Hedging of derivatives
  • Applications of derivatives in areas of risk management and financial engineering
  • Models and pricing techniques include:
    • Black-Scholes model
    • binomial trees
    • Monte-Carlo simulation.
  • Specific topics include:
    • simple no-arbitrage pricing relations for futures/forward contracts;
    • put-call parity relationship;
    • delta, gamma, and vega hedging;
    • implied volatility and statistical properties;
    • dynamic hedging strategies;
    • interest-rate risk, pricing of fixed-income product;
    • credit risk, pricing of defaultable securities.
2. Fundamentals of Statistical Inference I (ST 501)*
  • First of a two-semester sequence in probability and statistics taught at a calculus-based level.
  • Probability: discrete and continuous distributions, expected values, transformations of random
    variables, sampling distributions.
3. Capital Investment Economic Analysis (ISE 711) (optional)
  • Analysis of economic merits of alternatives including interest and income tax considerations.
  • Risk and sensitivity exploration techniques.
  • Introduction to analytical techniques for multiple objectives or criteria.
  • Use of mathematical programming and computers for capital budgeting.
4. Career Development for Quants, a Seminar (FIM 500)
  • Enhance your professional and career development skills while you are in the Financial Math program with
  • Seminar topics on networking, LinkedIn, resumes, interviews, presentations and business writing tips.
  • Learn about workplace etiquette and business ethics.
  • Gain resources and important industry information from guest speakers and alumni.
  • Become Bloomberg Certified.
  • Gain hands-on experience with these tools by participating in group projects from financial industry.

Semester Two Core Requirements (Spring)
1. Stochastic Calculus for Finance (MA 547)
  • Stochastic models of financial markets.
  • No-arbitrage derivative pricing.
  • From discrete to continuous time models.
  • Brownian motion, stochastic calculus, Feynman-Kac formula.
  • Tools for European options and equivalent martingale measures.
  • Black-Scholes formula.
  • Hedging strategies and management of risk.
  • Optimal stopping and American options.
2. Fundamentals of Statistical Inference II (ST 502)
  • Second of a two-semester sequence in probability and statistics taught at a calculus-based level.
  • Statistical inference: methods of construction and evaluation of estimators, hypothesis tests,
    and interval estimators, including maximum likelihood.
3. Monte Carlo Methods for Financial Mathematics (MA/FIM 548)
  • Monte Carlo [MC] methods for accurate option pricing, hedging and risk management.
  • Modeling using stochastic asset models [e.g. geometric Brownian motion] and parameter estimation.
  • Stochastic models, including use of random number generators, random paths and discretization methods
    [e.g. Euler-Maruyama method], and variance reduction.
  • Implementation using Matlab.
  • Incorporation of the latest developments regarding MC methods and their uses in Finance.
4. Seminar in Financial Mathematics (FIM 601)
  • Presentations and short courses by industry specialists in quantitative fields.
  • Topics varies from semester to semester, and may include portfolio optimization,
    credit risk and market risk, exotic derivatives, high frequency trading, etc.

Summer Semester Requirements
Internship in Financial Mathematics (FIM 650) (1 credit)
  • An opportunity to use quantitative financial mathematics in a workplace under the supervision of a practitioner.
  • Link academic theory to practice.
  • Develop a heightened awareness of workplace issues as they relate to the student’s chosen career path.
  • Clarify and/or confirm professional direction.
Project in Financial Mathematics (FIM 675) (1 credit)
  • An opportunity to apply quantitative financial mathematics to a problem of practical interest
    under the supervision of faculty and/or practitioners.
  • Links academic theory to applications.
  • Examine a practical problem from financial mathematics using marketplace data.
  • Approach solutions to the problem considering aspects of quantitative risk and/or optimal returns.
  • Methods and models will be drawn from academic courses and other sources.

Semester Three Core Requirements (Fall)
1. Computational Methods in Economics and Finance (ECG 766) (optional)
  • Fundamental methods for formulating and solving economic models numerically.
  • Defining the mathematical structure of problems and practical computer methods to model solutions.
  • Solution of systems of equations.
  • Complementarity relationships and optimization.
  • Finite and infinite dimensional problems.
  • Use of finite dimensional approximation techniques.
  • Solving dynamic asset pricing, optimization and equilibrium problems.
2. Seminar in Financial Mathematics (FIM 601)
  • Presentations and short courses by industry specialists in quantitative fields.
  • Topics may include but are not limited to portfolio optimization, exotic derivatives, high frequency trading.

Core classes must be passed with a grade of B or better.