• Risk Management
• Portfolio Optimization
• Forecasting
• Trading Strategy Optimization
• Derivatives Pricing
• Fixed Income Analysis
• Interest Rate Modeling
• Equity Price Modeling and Analysis
• Exchange Rate Analysis

Quantitative analysts are using basic, but vitally necessary algorithms, such as linear algebra, regression, and random number generation all the way up to sophisticated algorithms, such as quadratic programming and nonlinearly constrained optimization.

Below are several applications that demonstrate how quantitative organizations are taking advantage of the reliable and accurate solutions provided by Visual Numerics.

Forecasting
Many finance customers are employing forecasting algorithms such as ARMA and GARCH to forecast in the areas of equities, fixed income, currency and commodities. Quantitative researchers also use Feed Forward Neural Networks, a technique that continuously refines its forecasting model by applying knowledge gained from past results, fine-tuning its forecasting accuracy over time.

Trading
Organizations using the IMSL Libraries for trading systems are obtaining optimal performance in their deployments. These proprietary deployments often leverage quadratic programming and nonlinear programming algorithms, sometimes in distributed computing environments. One JMSL Library trading application with over 100 variables runs in less than half a second with $1 billion worth of trades running through it every week.

Portfolio Optimization
The goal of portfolio optimization is to select a portfolio of assets that yields the highest expected return for a given level of risk; alternatively, the problem can be viewed as one of minimizing the level of risk for a given expected rate of return.

The portfolio optimization problem may be formulated in various ways depending on the selection of the objective function, the definition of the decision variables, and the particular constraints underlying the specific situation. The solution of the portfolio selection problem may therefore involve one or more of the following optimization techniques:

• If the risk of the portfolio can be measured as a ranking of assets or by the linear distance from the target, then the portfolio selection problem can be formulated as a linear programming problem.
• Quadratic programming is applied when the model is a mean variance model.
• Nonlinear programming is applied when the portfolio selection model is characterized by an objective function that seeks to maximize utility as a function of the portfolio composition with the utility function being nonlinear.

Option Pricing
An options contract is characterized by its expiration date, i.e. the date before which the option can be exercised. Options pricing analysts typically value an American call option using the Black-Scholes partial differential equation. Since the asset may be exercised at any time before its expiration date, these analysts usually use algorithms to solve a free boundary problem. Analysts will further set up a linear complementary problem and use a non-negative constrained least-squares (NNLS) algorithm.

Risk Management
Risk management analysts use visual and numerical analysis to develop models and choose portfolios with specified exposure to different risks. Well known risks include: interest rate risks, liquidity risk, credit risk, and volatility risk. Both linear programming and quadratic programming techniques can be used in risk management applications.

Performance Monitoring In this example to the right, developers leveraged a heat map charting capability to allow users to gauge portfolio performance quickly over a selected period of time. To make charts easily, developers use the JMSL Library’s Chart Programmers Guide, which contains a chart description, chart example and code example.
	Above: Example of Heat Map Charting