Applications of Operation Research Techniques

Operation Research is a problem-solving and decision-making technique and it can be applied to a variety of use cases. Some areas of the Financial Market, where the tools and techniques of OR have been successfully utilized are as follows,

The Application of Operations Research Techniques to Financial Markets

OR techniques are applied to nonportfolio problems in financial markets, such as the equity, debt, and foreign exchange markets and the corresponding derivatives markets. Finance problems are an excellent application area for OR researchers. OR techniques are used to value financial instruments, identify market imperfections, design securities, regulate markets, evaluate and control risks, model strategic problems, and understand the functioning of financial markets.

1.  Attractiveness of Finance Problems

An important distinguishing feature of problems in financial markets is that they are generally separable and well defined. The objective is usually to maximize profit or minimize risk, and the relevant variables are amenable to quantification, almost always in monetary terms. The resulting OR model is a good representation of reality, particularly as the role of non-quantitative factors is often small. On the other hand, the investigator is likely to find that much of the requisite historical data has already been collected and is available from company records or recorded market transactions, and that large amounts of real time data are available on prices (traded and quoted) in financial markets which can readily be used in OR models. 

Furthermore, such problems tend to recur, possibly many times per day, spreading the costs of developing an OR solution over a large number of transactions. This scale and repetition makes the development of an OR model more attractive than for small or one-off decisions. Thus, because finance applications (especially applications to financial markets) are largely numerical problems with well defined boundaries and objectives, clear relationships between the variables, large benefits from very small improvements in the quality of decision making and excellent data, they are well suited to OR analysis.

2.  The Valuation of Financial Instruments 

It is very important when trading in financial markets to have a good model for valuing the asset being traded, and OR techniques have made a substantial contribution in this area. Although European style call and put options can be valued using the Black-Scholes model, which provides a good closed form solution, OR techniques have made a substantial contribution to the pricing of more complex derivatives. In 1977, Boyle proposed the use of Monte Carlo simulation as an alternative to the binomial model for pricing options for which a closed form solution is not readily available.

3.  Imperfections in Financial Markets 

As well as accurately pricing financial securities, traders are interested in finding imperfections in financial markets which can be exploited to make profits (Keim and Ziemba, 1999; Ziemba,1994). A fundamental feature of financial markets is the existence of no-arbitrage relationships between prices, and small price discrepancies can be exploited by arbitrage trades to give large riskless profits. Network models have been used to find arbitrage opportunities between sets of currencies(Christofides, Hewins and Salkin, 1979; Kornbluth and Salkin, 1987; Mulvey, 1987; Mulvey and Vladimirou, 1992). This problem can be specified as a maximal flow network, where the aim is to maximize the flow of funds out of the network, or as a shortest path network.

There has been a growing interest in using artificial intelligence based techniques (expert systems, neural networks, genetic algorithms, fuzzy logic and inductive learning) to develop trading strategies for financial markets (e.g. Trippi and Turban, 1993; Refenes, 1995; Goonatilake and Treleaven, 1995; Wong and Selvi, 1998). Such approaches have the advantage that they can pick up non-linear dynamics, and require little prior specification of the relationships involved.

4.  Funding Decisions  

OR techniques have also been used to help firms to determine the most appropriate method by which to raise capital from the financial markets to finance their activities. Brick, Mellon, Surkis and Mohl (1983) put forward a chance constrained linear programming model to compute the values of the debt-equity ratio each period that maximize the value of the firm. Other studies have specified the choice between various types of funding as a linear goal programming problem (Hong, 1981; Lee and Eom , 1989).In this way different people at different time use OR techniques to funding decision.

5.  Strategic Problems

In recent years, some of the decisions facing traders and market makers in financial markets have been analyzed using game theory (O’Hara, 1995; Dutta and Madhavan, 1997). These models typically involve one or more market makers, and traders who may be informed or uninformed, and discretionary or non-discretionary. Traders in stock markets seek to trade at the most attractive prices and large trades are often broken up into a sequence of smaller trades in an effort to minimize the price impact. This can be viewed as a strategic problem with the aim of devising a strategy for trading the block of shares. The initial trades influence the price of subsequent trades, and so executing the large trade at the lowest cost is a dynamic problem.

 6.  Regulatory and Legal Problems 

Financial regulators have become increasingly concerned about financial markets with their very 17 large and rapid international financial flows. OR techniques have proved useful in regulating the capital reserves held by banks and other financial institutions to cover their risk exposure. OR techniques have also been used to ensure compliance with various legal requirements by designing appropriate strategies and to solve other legal problems relating to financial markets.

7.  Economic Understanding

In addition to its traditional role of improving the quality of decision making, OR can also help in trying to understand the economic forces shaping the finance sector. Financial innovation may occur when there is an exogenous change in the constraints or in the costs of meeting existing constraints. Using a linear programming model of a bank, Ben-Horim and Silber (1977) employed annual data to compute movements in the shadow prices of the various constraints. They suggested that a rise in the shadow price of the deposits constraint led to the financial innovation of negotiable CDs.

8.  Conclusions

Mathematical programming is the OR technique that has been most widely applied in financial markets. Most types of mathematical programming have been employed - linear, quadratic, nonlinear, integer, goal, chance constrained, stochastic, fractional, DEA and dynamic. Mathematical programming has been used to solve a considerable range of problems in financial markets -forming portfolios of equities, bonds, loans and currencies, generalized hedging, immunization, equity and bond index tracking, estimating the implied risk neutral probabilities for options, devising a schedule of coupons for municipal bond bids, identifying underpriced bonds, setting the firm’s debt-equity ratio, deciding when to refinance outstanding bonds, estimating the divisional cost of capital, determining the required minimum option margin, structuring MBS and CMO securitizations, creating a trading strategy to execute a block trade, designing leveraged leases, computing the maximum loss sustained by shareholders, spotting insolvent banks, sorting out the failure of a stock exchange and understanding the forces leading to financial innovations.

The main areas of financial markets in which OR techniques have been applied are portfolio problems and pricing complex financial instruments accurately. OR techniques can also be used by financial regulators and financial institutions in setting capital adequacy standards. Some other application areas also exist - devising feasible solutions that meet a complicated set of the legal requirements, making funding decisions, spotting imperfections and arbitrage opportunities in financial markets and solving strategic problems.