Computational Methods for Management

This article focuses on computational methods for business and financial management. It provides an overview of the wide range of computational methods employed by business and financial managers in the public and private sectors. Computational tools for managerial forecasting and decision-making, including financial econometrics, computational finance, futures, options, and derivatives analysis, capital budgeting analysis, decisional analysis, and financial time series analysis, will be described. The issues associated with using computational methods for financial or corporate risk analysis are addressed.

Keywords Computational Finance; Computational Methods; Decisional Analysis; Econometrics; Financial Management; Financial Time Series Analysis; Forecasting

Economics > Computational Methods for Management

Overview

The financial and business management fields use a wide range of computational methods to solve business and management problems. Computational methods refer to a wide range of numerical and quantifiable approaches to data gathering and analysis. Examples of computational methods common in management include financial econometrics; computational finance; futures, options, and derivatives analysis; capital budgeting analysis; decisional analysis; and financial time series analysis. Computational methods, in contrast to purely theoretical methods, are increasingly used in the field of financial risk management. Financial risk management refers to the effort of financial institutions to protect against the negative outcomes caused by fluctuations in interest rates, exchange rates, commodity prices, and equity prices. Computational methods, financial instruments, and mathematical techniques are used by an increasing number of firms, traders, and financial risk managers across businesses and industries. Financial and business managers use computational methods to develop forecasts of future conditions in areas such as economic cycles, product demand, and market activity. Managers base their financial and business decisions on these forecasts of future conditions.

While business and financial management uses computational methods to forecast future conditions, computational methods, as a general approach to analysis and problem solving, are common practice in multiple fields and industries. According to the "International Journal of Computational Methods" (IJCM), modern computational methods are used across industries and fields of scientific inquiry. Examples of modern computational methods used in multiple fields and industries include the following: “Mathematical formulations and theoretical investigations; interpolations and approximation techniques; error analysis techniques and algorithms; fast algorithms and real-time computation; multi-scale bridging algorithms; and adaptive analysis techniques and algorithms” (About IJCM, 2007, ¶2).

Computational methods, as expressed through theory, algorithm, programming, coding, and numerical simulation, are most common in all fields with quantifiable data such as economics, engineering, science, and computer science. Examples of computational methods used in engineering, science, computer science, and economics include risk management, computational mechanics, computational inverse problem, computational mathematics, quantum methods, advanced finite volume methods, and high-performance computing techniques. Financial and business managers employ subfields of computational methods such as econometrics and computational finance. Econometrics refers to applying statistical theories to economic ones in order to predict future trends. Computational finance refers to the use of advanced computing techniques to study problems in economics and finance. Examples of computational finance include genetic programming, used for financial forecasting, and financial markets models used to facilitate the design of new market mechanisms.

Econometrics and computational finance are just two of a wide range of computational subfields and tools used by financial and business managers. Financial and business managers use computational methods to accomplish the following goals: Forecasts of future conditions and events; financial modeling; value estimation; financial risk analysis; futures, options, and derivatives analysis; capital budgeting analysis; and financial time series analysis. Computational data contributes to the following knowledge base: Explains predictability, persistence, and differences between conditional and unconditional moments; answers questions of asset pricing and financial motivation; simulates financial models on the modern computational environment; and conducts a computational evaluation of derivative instruments (Chaundry, Varano, & Xu, 2000).

This article provides an overview of the wide range of computational methods employed by business and financial managers in the public and private sectors. The following sections provide a discussion and analysis of financial econometrics, computational finance, futures, options, and derivatives analysis, capital budgeting analysis, decisional analysis, and financial time series analysis. This sections serves as a foundation for later discussion of the issues associated with using computational methods for financial or corporate risk analysis.

Applications

Computational methods, while not necessary or applicable for every management problem, are appropriate for computationally intensive management tasks. For example, optimization problems, which tend to be computationally intensive tasks for managers, are well suited to computational analysis (Tsompanakis, Y., & Papadrakakis, M., 2000). In addition, computational methods are appropriate for using rough sets to identify classes, dependencies, and rules in datasets and databases. These findings may be used for managerial operations, forecasting, and problem solving (Bell & Guan, 1998). Computational methods, for both managers and all other users, generally require a foundation in computer modeling, programs, and languages, hypothesis testing, simulation methodology, calculus, probability, and statistics. Managers who use computational methods for forecasting and data analysis often rely on software packages, such as Mathematica, for technical computing tasks. Computational software packages do simple calculations, large-scale computations, complex programming, and data modeling. The following sections describe the main computational methods used in financial and business management.

Financial Econometrics

Financial econometrics, the act of applying statistical theories to economic ones in order to predict future trends, is a form of financial modeling. Financial econometrics combines tools and perspectives from statistics, mathematics, economics, and business. Econometric methods are intended to be actively applied and adapted to financial problems and datasets. The simplest econometric model in financial econometrics is the first-order autoregressive model often referred to as the autoregressive moving average (ARMA). This model helps explain predictability, persistence, and differences between conditional and unconditional moments.

Econometric methods of vector auto-regression (VAR), vector-autoregressive moving average (VARMA), simultaneity, and co-integration are used to answer questions of asset pricing and understand financial motivation. These methods are useful for the creation and maintenance of efficient portfolios. Financial econometrics includes numerous value estimation strategies such as generalized method of moments (GMG). Autoregressive conditionally heteroskedastic (ARCH) and stochastic volatility models connect the volatility of asset prices to risk management. The autoregressive conditionally heteroskedastic model is considered to be a significant breakthrough that helped economists develop empirical evidence contradicting the assumption of the unpredictability of returns.

In addition, asset-pricing models, such as the present value model, dynamic factors model, and derivatives model, are financial econometrics used to analyze financial motivation. Markets can be understood with the financial econometric tools of high-frequency data, market indexes, vale-at-risk (VaR), and extreme-risk modeling. Market indexes refer to approximations to the market portfolio. "Value-at-risk determines the minimum capital required to cover a financial loss with a fixed probability of occurrence" (Kmenta, 2002, p.70). Financial econometrics uses Bayesian analysis to forecast and predict asset returns. Bayesian analysis uses the knowledge of prior events to predict future events (Meyer, 2001). The dynamic linear model (DLM) is one of the most used variations of Bayesian analysis. Applications of the dynamic linear model, including regressions, autoregressions, and exponential trend models, are used for market hypothesis and forecasting (Rossi & Allenby, 2003).

Computational Finance

Computational finance, or the use of advanced computing techniques to studying problems in economics and finance, includes the following methods: Uniform and non-uniform random variate generation; variance reduction techniques; matrix factorizations; finite difference methods; value-at-risk and option pricing computations; stochastic Differential Equations (SDE); and Monte-Carlo analysis. Monte Carlo analysis refers to the use of data obtained by simulating a statistical model in which all parameters are numerically specified. Monte Carlo analysis and simulations may be used to test how an estimation procedure would behave in multiple environments or markets (Meyer, 2001). Managers may use computational finance to complete the following activities and analyses: Imitate financial models in regards to the modern computational environment; conduct a computational evaluation of derivative instruments; and construct partial differential equations necessary to evaluate derivative financial models. Computational finance has almost unlimited applications. That said, managers wishing to use computational finance techniques must have a strong foundation in economics and computer science. Managers using computational finance techniques are generally familiar with portfolio replication, risk-neutral pricing, stochastic calculus, finite difference schemes, binomial decision trees, Monte Carlo simulation, stochastic interest rate models, elasticity models, yield curves, power series expansions, stochastic series expansions, stochastic calculus, ordinary and partial differential equations, and computer programming.

Futures, Options, & Derivatives Analysis

Financial managers are actively involved in business investment decisions and futures, options, and derivatives analysis. Futures, options, and derivatives are an important category of investment used to protect investors from dips in stocks or indexes as well as to create portfolio diversification. Derivatives refer to financial instruments, such as options and futures, which do not signify actual ownership but rather indicate a promise to share ownership rights. Options, such as stock or index options, are a form of derivative that derives its value from something else. Futures refer to an agreement to buy or sell a product at an established price on a certain date. Financial managers use computational methods to analyze advisability of investing in futures, options, and derivatives. Computational methods for futures, options, and derivatives analysis include the following: Determinants of option values; portfolio strategies; put-call parity; spot-futures parity; binomial model; option deltas; elasticities; delta hedging; dynamic hedging; forward rate agreements; interest rate and equity swap methods; and analytic formula for derivative pricing and option pricing.

Capital Budgeting Analysis

Financial mangers are generally directly involved in capital budgeting decisions. Capital budgeting refers to the planning process businesses utilize to identify their long-term investments, including items such as new or replacement machinery, new plants or products, and research and development endeavors. Computational methods for capital budgeting analysis include developing frameworks to conceptualize capital budgeting options, measuring capital budget flexibility, developing both discrete and continuous time models, testing interactions between multiple real options, real options evaluation of projects with high risk potential, and strategic evaluation of options.

Decisional Analysis

Financial and business managers use computational methods to facilitate decisional analysis. Decisional analysis is a step in the problem-solving process during which relevant criteria are reviewed and weighted. Computational methods used for decisional analysis include using judgment probability, Bayesian decision models, decision trees, probabilistic network, influence diagrams, sharing risk and the responsibility for decisions, implementing decision models, and utility theory. Utility theory refers to a measure of the relative satisfaction gained from an event or exchange.

Financial Time Series Analysis

Lastly, financial and business managers use computational methods to facilitate financial time series analysis. Time series analysis refers to calculated prediction where the data for one variable are analyzed for to identify time sensitive trends, seasonality, and cycles. Financial time series analysis is used to forecast product demand, market activity, and economic cycles. Financial and business managers are responsible for forecasting product demand, market activity, and economic cycles and using these forecasts to make time-critical business decisions. Computational methods used for financial time series analysis include volatility models. Volatility models are often used to create a time series of stock prices. Volatility models may reveal patterns such as high variance of returns for extended periods followed by low variance of returns for extended periods (Meyer, 2001). Time series analysis can also be used to understand queueing systems. Queueing systems are most often used by managers for the modeling, analysis, and design of systems such as telecommunication systems, call centers, manufacturing plants, super markets, and traffic patterns (Tripathi & Duda, 1986).

Ultimately, computational methods are an essential tool of financial and business management. Corporate finance involves copious amounts of data that require computational analysis to discover patterns, trends, and rules. Computational methods aid management in forecasting future conditions and making crucial corporate finance decisions about valuing stocks and bonds; investment criteria; optimal capital structure; types of financing; and the timing of initial public offerings (IPOs), mergers, and acquisitions.

Issues

Computational Methods for Financial Risk Analysis

Financial risk managers are responsible for analyzing and mitigating financial risk. Risk management refers to the process of evaluating, classifying, and reducing risks to a level acceptable by stakeholders. Financial risk managers rely on computational methods to analyze large datasets and forecast future financial risk conditions. Financial risk refers to the probability of an investment's actual return. Pure risk refers to a possibility of loss that is unanticipated and beyond control as in, for example, a fire or natural disaster. Insurance companies, in response to events such as the September 11, 2001 attacks on the World Trade Center, the collapse of the Enron Corporation, and growing geopolitical risk, are increasingly unwilling or unable to insure pure risk. Insurance companies are increasingly requiring shared risk scenarios between corporations and governments. The current business and political environment is creating a greater divide between pure risk and speculative risk than ever existed before. While firms face the potential for numerous types of pure risk (within the areas of operational risks, market risks, cultural risks, economic risks, political risks, compliance risk, and credit risks) pure risk managers are possibly most challenged by the need to manage operational risk and market risk. The pure risks associated with operations and market behavior, along with pure risks in general, are characterized by their unpredictability and potential to create devastating losses.

Risk analysis is one of the first and most important steps in the risk management process. Risk analysis involves risk analysis, evaluation, and classification. Risk classification is performed in an effort to create or select effective, efficient, and feasible strategies for risk reduction and mitigation. Risk management works to transform unacceptable risks into acceptable risks within a normal range. Different types of risks require different types of risk management tools such as risk-based, precaution-based, and discourse-based approaches. Once the risk evaluation and risk classification are conducted, the proper risk management tool can be chosen and applied to the problem or situation (Klinke & Renn, 2002). The most common risk management tools include computational methods, enterprise risk management (ERM), alternative risk transfers (ART), and risk differentiation (Coffin, 2007).

Computational methods for financial risk analysis include the following: Economic forecasting; risk prediction; ruin models; credibility premiums and experience rating; operations research techniques in insurance and reinsurance decision making; volatility and correlation modeling; Monte Carlo simulation; stress-testing and scenarios analysis; and events modeling. Common risk measurement tools include the following: developing value-at-risk methods for trading financial instruments in open markets, building analytical value-at-risk models for trading instruments without linear payoffs or normal distributions, simulation methods for conducting risk analysis, and statistical tools in volatility prediction, tail events, and forecasted shortfalls. Computational methods for risk analysis are a crucial component of a firm's overall approach to risk management. Based on the results of computational analysis of risk factors and scenarios, risk managers develop risk management strategies. A risk management strategy is generally a corporate-wide approach to business practice. The main methods and elements of risk management strategy operate to integrate the risk management approach into all levels of operations and the corporate culture itself.

There are six main strategies or principles that characterize corporate risk management strategy: First, management must develop intimate company knowledge. Risk managers require intimate knowledge of corporate operations, goals, and missions to successfully evaluate risk exposures relating to all areas of the company. Second, management must align risk management vision with that of the company: Risk managers are responsible for creating an integrated risk management strategy that reflects and furthers the goals and values of the company. Third, management must identify and analyze the company's areas of risk. Risk managers develop successful risk management strategies by analyzing and planning for potential losses vertically and horizontally across an organization. Four, management must balance financials and objectives. Risk managers are responsible determining how much time, effort, and money is required to achieve a given objective. Risk managers use a balanced scorecard methodology (BSC), a management tool that translates the strategy into operational terms, to connect internal and external processes with corporate cultural and financial objectives. Five, management must close the gaps with strategic initiative. Risk managers should identify the gaps between where the company is in relation to their goals and objectives and their final goals and objectives. Risk managers, along with corporate management, are responsible for finding strategies to close any existing gaps in corporate performance and achievement. Six, management must continually measure and improve after implementation. Risk managers are responsible for creating a risk management system as well as evaluating and improving its performance. Risk managers use data capture and computational analysis to measure the effectiveness of risk management initiatives and forecast future risk conditions (Jorgensen, 2005).

Conclusion

In the final analysis, computational methods for business and financial management are most useful as forecasting tools. Financial and business managers use computational methods to develop forecasts of future conditions in areas such as financial risk, economic cycles, product demand, and market activity. Managers base their financial and business decisions on these forecasts of future conditions. Computational methods by managers include financial econometrics, computational finance, futures, options, and derivatives analysis, capital budgeting analysis, decisional analysis, and financial time series analysis. The computational data gathered from these analytic approaches and methods help managers accomplish the following goals: Explain predictability, persistence, and differences between conditional and unconditional moments; answer questions of asset pricing and understand financial motivation; simulate financial models on the modern computational environment; conduct a computational evaluation of derivative instruments; and construct partial differential equations required for the evaluation of derivative financial models. Ultimately, the lasting importance of computational methods is their ability to help business and financial management analyze large datasets and forecast future conditions.

Terms & Concepts

Capital Budgeting: The planning process businesses utilize to identify their long-term investments, including items such as new or replacement machinery, new plants or products, and research and development endeavors.

Computational Finance: The use of advanced computing techniques to study problems in economics and finance

Computational Methods: Numerical and quantifiable approaches to data gathering and analysis.

Decisional Analysis: A step in the problem-solving process during which relevant criteria are reviewed and weighted.

Decision Trees: A decision-making tool that uses a model of decisions and their potential consequences.

Derivatives: Financial instruments, such as options and futures, that do not constitute ownership but a promise to convey ownership.

Econometrics: The act of applying statistical theories to economic ones in order to predict future trends.

Financial Management: A division of management responsible for both resource management and finance operations.

Forecasting: The process of estimation concerning future conditions and events.

Futures: An agreement to buy or sell a product at an established price on a certain date.

Options: A form of derivative that derives its value from something else.

Stochastic: Involving a random variable or chance.

Time Series Analysis: Calculated prediction where the data for one variable are analyzed for to identify time sensitive trends, seasonality, and cycles.

Bibliography

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Suggested Reading

Brooks, S., Catchpole, E., Morgan, B., & Harris, M. (2002). Bayesian methods for analysing ringing data. Journal of Applied Statistics, 29(1/4), 187-206. Retrieved July 30, 2007, from EBSCO Online Database Business Source Complete. http://search.ebscohost.com/login.aspx?direct=true&db=bth&AN=5911137&site=ehost-live

Harris, C., Brill, P., & Fischer, M. (2000). Internet-type queues with power-tailed interarrival times and computational methods for their analysis. INFORMS Journal on Computing, 12, 261. Retrieved July 30, 2007, from EBSCO Online Database Business Source Complete. http://search.ebscohost.com/login.aspx?direct=true&db=bth&AN=5243848&site=ehost-live

Poe, G., Giraud, K., & Loomis, J. (2005). Computational methods for measuring the difference of empirical distributions. American Journal of Agricultural Economics, 87, 353-365. Retrieved July 30, 2007, from EBSCO Online Database Business Source Complete. http://search.ebscohost.com/login.aspx?direct=true&db=bth&AN=16702013&site=ehost-live