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# Using Decision Trees in Finance

Decision trees are major components of finance, philosophy, and decision analysis in college courses. Yet many students and graduates do not understand their purpose, even though these statistical representations play a vital role in corporate finance and economic forecasting.

## Decision Tree Basics

Decision trees are organized as follows: an individual makes a big decision, such as undertaking an investment project or choosing between two competing businesses. These decisions, which are often represented by decision nodes, are based on the expected results of implementing particular action plans. An example of such a result would be something like “revenue should increase by \$5 million”. But since the events indicated by the final nodes are speculative in nature, the random nodes also specify the probability of a specific projection occurring.

As the list of potential outcomes, which depend on past events, becomes more dynamic with complex decisions, Bayesian probability models must be implemented to determine prior probabilities.

## Binomial Option Pricing in Decision Tree Analysis

Decision tree analysis is often applied to option pricing. For example, the binomial option pricing model uses discrete probabilities to determine the value of an option at expiration. The most basic binomial models assume that the value of the underlying asset will rise or fall based on calculated probabilities on the expiration date of the European option.

However, the situation becomes more complex with American options, where the option can be exercised at any time until expiration. The binomial tree would take into account multiple paths that the price of the underlying asset can take over time. As the number of nodes in the binomial decision tree increases, the model eventually converges to the Black-Scholes formula.

Although the Black-Scholes formula offers a simpler alternative to option pricing on decision trees, computer software can create binomial option pricing models with “infinite” nodes. This type of calculation often provides more accurate price information, especially for Bermuda options and dividend-paying stocks.

## Using Decision Trees for Real Options Analysis

The valuation of real options, such as expansion options and exit options, should be done using decision trees because their value cannot be determined via the Black-Scholes formula. Actual options represent actual decisions a business can make, such as expanding or outsourcing operations. For example, an oil and gas company can buy land today, and if drilling operations are successful, it can buy additional land cheaply. If the drilling fails, the company will not exercise the option and it will expire worthless. Because real options add significant value to business projects, they are an integral part of capital budgeting decisions.

Individuals must decide whether or not to purchase the option before the project is launched. Fortunately, once the probabilities of success and failure are determined, decision trees help clarify the expected value of potential capital budgeting decisions. Companies often accept what initially appear to be negative net present value (NPV) projects, but once the true value of the option is factored in, the NPV actually becomes positive.

## Decision Tree Requests for Competing Projects

Similarly, decision trees are also applicable to business operations. Businesses are constantly making decisions about issues such as product development, staffing, operations, and mergers and acquisitions. Organizing all considered alternatives with a decision tree allows simultaneous systematic evaluation of these ideas.

This does not mean that decision trees should be used to consider every micro-decision. But decision trees provide general frameworks for determining solutions to problems and for managing the realized consequences of major decisions. For example, a decision tree can help managers determine the expected financial impact of hiring an employee who does not meet expectations and must be terminated.

## Pricing interest rate instruments with binomial trees

Although not strictly a decision tree, a binomial tree is similarly constructed and is used for the same purpose of determining the impact of a fluctuating/uncertain variable. The upward and downward movement of interest rates has a significant impact on the price of fixed income securities and interest rate derivatives. Binomial trees allow investors to accurately price bonds with built-in buying and selling provisions using uncertainty about future interest rates.

Since the Black-Scholes model does not apply to the valuation of bonds and interest rate options, the binomial model is the ideal alternative. Business projects are often evaluated using decision trees that take into account various possible alternative states of the economy. Similarly, the value of bonds, interest rate floors and caps, interest rate swaps, and other types of investment tools can be determined by analyzing the effects of different interest rate environments. ‘interest.

## Decision trees and business analysis

Decision trees allow individuals to explore line items that could materially impact their decisions. Before running a multimillion-dollar Super Bowl commercial, a company aims to determine the various possible outcomes of its marketing campaign. Various factors can influence the ultimate success or failure of the expenditure, such as the attractiveness of the advertising message, the economic prospects, the quality of the product and the advertisements of competitors. Once the impact of these variables has been determined and the corresponding probabilities assigned, the company can formally decide whether or not to broadcast the ad.

## The essential

These examples provide an overview of a typical assessment, which can benefit from the use of a decision tree. Once all the important variables have been determined, these decision trees become very complex. However, these instruments are often an essential tool in the investment analysis or management decision-making process.