Finance Solutions

From asset management to investment banking, quantitative analysts or "quants" at financial organizations around the world utilize the IMSL Numerical Libraries for advanced data analysis and visualization and PyIMSL for prototype to production analytic application development.

Using basic (e.g., linear algebra, regression, random number generation) to extremely advanced algorithms (e.g., neural network forecasting), quantitative analysts can quickly and easily leverage the IMSL Libraries for financial applications.

Financial applications that can be built with the IMSL Libraries include:

Case Studies and White Papers

GFTA - Case Study
PDF | 776.7 KB
Gesellschaft Fuer Trendanalysen (GFTA) - Foreign Exchange Rate Analysis
Case Studies, IMSL Family, PV-WAVE, Finance
IMSL Technology for Neural Network Analysis
PDF | 395.8 KB
Describes IMSL's implementation of Neural Network technology in technical detail.
White Papers, IMSL Family, Finance
Integrating Feynman-Kac Equations Using Hermite Quintic Finite Elements
PDF | 1.4 MB
Describes methods for solving a generalized version of the Feynman-Kac partial differential equation that can be used in many financial modeling applications, including Black-Scholes models.
White Papers, IMSL Family, Finance
Major U.S. Bank - Case Study
PDF | 728.7 KB
Analytical Modeling
Case Studies, IMSL Family, IMSL C Library, Finance
Neural Networks - An Introduction
PDF | 209.6 KB
Describes the fundamental benefits and uses of Neural Network technology.
White Papers, IMSL Family, Finance
Portfolio Optimization via Efficient Frontier with IMSL
PDF | 485.1 KB
Describes how to build a portfolio with the proper proportion of its components that will balance minimum risk and maximum return.
White Papers, IMSL Family, Finance
Risk-Al - Case Study
PDF | 142.9 KB
Embedding IMSL Algorithms for Hedge Fund Management
Case Studies, IMSL Family, Finance
Societe Generale - Case Study
PDF | 805.2 KB
Société Générale - Analysis of Financial Systems
Case Studies, IMSL Family, PV-WAVE, IMSL C Library, Finance

Financial Modeling

Financial models or prototypes helps quants in all areas of the financial services industry make better decisions using prediction, simulation, optimization and other techniques.

PyIMSL Studio is a collection of tested, documented and supported tools for quants to use to create financial models. These tools include both Python open source components and the comprehensive math and statistical algorithms in the IMSL C Library, wrapped in Python for easy access and quick prototype creation.

If a financial model needs to become part of a production application, implementation teams can quickly implement the model into a production C application using the exact same underlying IMSL algorithm.

Risk Management

Risk management represents a broad application area of financial optimization. Risk management models are applied to choose portfolios with specified exposure to different risks. Common risks include:

  • Interest rates
  • Liquidity
  • Credit
  • Volatility

IMSL Library algorithm classes that address risk management include:

  • Monte Carlo techniques to simulate complex systems, do "what-if" analysis and model the effects of volatility. IMSL Libraries provide more than 30 random number generators as well as numerous cumulative distribution and variance/covariance functions.
  • Time series capabilities for cross-correlation and multi-channel cross-correlation to discover relationships between variables and model and predict multiple interrelated time-series values. Specific time series techniques include ARMA, GARCH and Kalman Filters.
  • Data mining algorithms to help users manage the large volumes of financial data. Classification, data conditioning, association, clustering, modeling and prediction algorithms can all help identify and hypothesize relationships within data sets.

IMSL Library functions like Monte Carlo simulation can help analysts manage risk by calculating information about a range of outcomes such as best - and worst-case, the chances of reaching target goals, and the most likely outcomes.

Portfolio Optimization

With portfolio optimization, the basic challenge is to select the portfolio of assets that yields the highest expected return for a given level of risk or minimize the level of risk for a given expected rate of return.

Portfolio optimization can 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 involve one of more of the following optimization techniques available within the IMSL Libraries:

  • 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.
  • The white paper, “Portfolio Optimization via Efficient Frontier with the IMSL Numerical Libraries”, provides more detail on this topic. Charting capabilities in the JMSL Numerical Library help asset managers develop versatile portfolio optimization applications.

Charting capabilities in the JMSL Numerical Library help asset managers develop versatile portfolio optimization applications.


Many finance applications require forecasting algorithms to make calculated future predictions in areas such as equities, fixed income, currency and commodities. Quantitative researchers use forecasting algorithms available within the IMSL Libraries such as:

  • ARMA
  • Auto_ARIMA
  • Feed Forward Neural Networks

Feed Forward Neural Networks is an advanced forecasting technique that continuously refines its forecasting model by applying knowledge gained from past results to fine-tune its forecasting accuracy over time. The “Neural Networks: An Introduction” and “IMSL Technology for Neural Network Analysis” white papers provide more detail on this topic.

This PV-WAVE chart displays the accuracy of Neural Network model prediction compared to historical and actual outcomes.

Fixed Income Analysis

In fixed income analysis, analysts determine whether to buy, sell, hold, hedge or stay out of securities based on analysis of their interest rate risk, credit risk and likely price behavior in hedging portfolios.

Both linear and non-linear optimization functions in IMSL Libraries can help with fixed income analysis while PV-WAVE is a valuable tool for visualizing large quantities of financial data.

Global Advisors, a hedge fund, uses PV-WAVE to visualize commodities information to identify patterns and opportunities for trading.

Trading Strategy Optimization

A key aspect of trading strategy optimization is the ability to quickly process data and provide accurate results. IMSL Library numerical functions and PV-WAVE visual data analysis capabilities deliver superior performance. One JMSL Numerical Library trading application with more than 100 variables runs in less than half a second with $1 billion worth of trades running through it every week.

Another portfolio optimization deployment reduced system execution time from ten hours to ten minutes by moving from a software architecture that wrapped a proprietary analytical package to a clean, pure-Java architecture that utilizes the JMSL Numerical Library for the advanced analytics, all while cutting development time by 20%.

This profit optimization application used the JMSL Numerical Library and cut system execution time from ten hours to ten minutes.

Options and Derivatives Pricing

The IMSL C Library includes a function for numerically solving a generalized version of the Feynman-Kac partial differential equation. The solution is expressed as a linear combination of piece-wise Hermite quintic polynomials. This twice-differentiable representation has the attributes of being a high-order method that allows easy evaluation of the solution and certain of its partial derivatives. The time-dependent solution coefficients are computed by finite element Galerkin procedures. Boundary values and initial conditions are required.

Many significant problems in financial modeling can be expressed as particular choices of coefficients, initial conditions, and boundary values. That fact allows this Feynman-Kac solver to be used in many financial modeling applications. These include the Black-Scholes models with European type or American type exercise opportunities on Calls or Puts. In the case of the Black-Scholes model these functions include many of The Greeks. The white paper, “Integrating Feynman-Kac Equations Using Hermite Qunitic Finite Equations”, provides more detail on this topic.

This PV-WAVE application compares the Black-Scholes price with the actual market price and shows how much a call option is worth at any given time.

Interest Rate Modeling, Exchange Pricing Modeling and Exchange Rate Analysis

Modeling or simulating the behavior of interest rates or foreign exchange pricing and their impact on other financial products is required for analysts in the financial industry that need to value or hedge these products.

IMSL Library function classes provide numerous algorithms that perform interest, bond and other financial calculations, while data mining and other advanced functions are also valuable for analysis and modeling of data.

This simple JMSL Library demo application, using the function, shows how changes in interest rates affect the price of existing treasury bonds.

Performance Monitoring

With increasing amounts of financial data being created and stored, being able to easily visualize the information present in this data is critical for successful financial analysis. In this example, developers leveraged a heat map charting capability available in the JMSL Library to help users easily gauge portfolio performance quickly over a selected period of time.

Example of a Heat Map