## Financial Engineering

Financial engineering, also refered to as computational finance or quantitative finance, encompasses a range of disciplines used to effectively manage portfolios of often disparate financial instruments. These disciplines include derivatives pricing, asset allocation and econometrics.

Each of these disciplines brings together aspects of financial theory, applied mathematics and software engineering. They are typically used to analyze and/or model the historical performance of potential investments and use them to predict future potential performance. Investment decisions are then made according to which investments are likely to provide the highest portfolio returns for an acceptable level of risk.

These pages contain numerous tutorials and articles that discuss the mathematical fundamentals of financial engineering with an emphasis on how the underlying algorithms may be efficiently implemented in various software languages.

The following links provide more details and tutorials on specific financial engineering disciplines,

Tutorials covering general introductory and advanced usage of leading data analysis, statistics and visualization software such as MATLAB, VBA and C++ are also available.

### Option Pricing

The scope and size of derivatives markets has grown seemingly exponentially over the past 15 to 20 years. This has driven a desire to go beyond the standard Black-Scholes pricing approach to more accurately model price movements of the assets underlying a given derivative and to more accurately model other critical factors such as future interest rates. The overall goal being to more accurately price the derivatives themselves.

The tutorials presented here give examples of the three most commonly applied numerical methods for modeling and pricing derivatives. The tutorials presented discuss both the mathematics behind each of the option pricing methods and give examples showing how to implement the algorithms efficiently in MATLAB.

The tutorials cover,

### Econometrics

Econometrics involves the application of standard mathematical methods and statistical techniques to model and analyse economic data. The typical purpose of this is to understand past relationships between economic variables with a goal of forecasting any future relationship between the same variables.

The tutorials presented here cover a range of econometric techniques. They include,

• Basic statistics and probability distributions.
• Studying cross-sectional and time-series data.
• Ordinary linear regression.
• Testing and compensating for serially correlated data.
• Non-linear and maximum likelihood methods, including ARCH and GARCH.
• Jump diffusion models.
• Time-series modeling, including non-stationary data and co-integrated pairs.
• Using Kalman Filtering techniques.

### Portfolio Optimization

Modern Portfolio Theory provides a rigorous mathematical approach for selecting a portfolio of risky assets such that they minimize the portfolio's risk (measured as the standard deviation of returns) for a given expected portfolio return. Although many of the assumptions underlying MPT are known to not hold in practise, it is still considered a cornerstone of financial engineering.

The tutorials presented here cover the fundamentals of MPT, including,

• Linear programming.