A foundation or introduction course in financial engineering will teach about the basics of -- and theoretical framework supporting -- financial instruments and derivatives. Financial instruments are funding media, such as cash or equity securities, which have legally-supported monetary value. Derivatives, in comparison, are specific types of financial instruments whose values fluctuate in response to underlying variables, such as a stock market index. Foundation courses in financial engineering may also cover how statistical models can measure the risk involved with new financial instruments.
Financial computing is the use of computational techniques and methods for solving problems in finance. A financial engineering course that specializes in financial computing will teach students how dynamic programming can be useful for understanding stochastic games, which have random probability outcomes; and Markov chains, which are stochastic models that describe possible outcomes based on past events. Other topics can include solving parabolic partial differential equations for the purpose of option valuation; discrepancy sequences and variance reduction.
A derivatives financial engineering course will take a more in-depth look at derivatives and arbitrage, which is a strategy that employs the simultaneous buying and selling of equivalent derivatives across multiple markets. The discrepancies between market prices can allow for financial benefits. Other topics that a derivatives course could cover include risk valuation, credit derivatives, interest-based derivatives as well as the floors, caps and swaps of interest rates.
Risk management is the use of management practices -- such as diversification, hedging, purchasing insurance and maintaining flexibility and cash reserves -- for reducing the financial risk of conducting business. Students taking advanced course in risk management will need previous experience with financial computing and derivatives. Course objectives include learning how to use financial modeling and mathematics for quantifying risk as well as learning how to develop risk sensitivity reports.
Financial engineering courses that focus on models for corporate finance emphasize how financial theory can help in the conceptualization and solving of multi-faceted problems that arise during risk management strategizing and the designing of financial instruments. Students learn how to use simulation as a tool for modeling markets, risk and credit.