Template: Valuation of American Options

Introduction

The binomial model is a popular method for pricing American call and put options, which are types of financial contracts that give the holder the right to sell (put) or buy (call) an asset at a predetermined price before or at a specific date.

How model works

Here’s a simple breakdown of how the binomial model works:

1. Tree Structure: Imagine the future price of the asset (like a stock) can move up or down in discrete steps over time. The model creates a tree-like structure of possible future prices.
2. Steps in Time: The time until the option expires is divided into small intervals. At each interval, the price can either go up or down by specific factors.
3. Up/down movements: Probabilities are assigned to the up and down movements.
4. Option Value Calculation: Starting from the end of the tree (the expiration date), the value of the option is calculated backward to the present day. This is done by looking at the possible values at the next step, applying the probabilities, and discounting to the present value.
5. Early Exercise: American options can be exercised before expiration. At each step, the model checks if it’s more valuable to exercise the option or to keep it. The highest value is chosen. This is different from European options, which can only be exercised at expiration.
6. Result: The model provides the current fair price of the option, taking into account the possibility of early exercise and the various paths the asset price might take.

Weaknesses of the Binomial Model

• Complexity with Many Steps: The more steps added for accuracy, the more complex and time-consuming the calculations become.
• Simplified Assumptions: The model assumes fixed up and down movements and constant probabilities, which is not the case in real markets as pointed out by various empirical studies.

Practical Tool for Accountants

Attached is a template designed for the quick calculation of American option valuations. This tool is specifically tailored for accountants, allowing for a quick check of share options’ fair value and comparison with any more complex models. It incorporates fields for all relevant inputs:

• Underlying share price
• Exercise price
• Periods
• Time until expiration
• Volatility
• Dividend
• Risk-free rate

By inputting these variables, accountants can instantly obtain a fair value estimate. The only thing that may need to be manually adjusted is when changing “Periods” variable. In such a case it is necessary to add or remove the number of columns for periods in all 3 sub-calculations “Share price”, “American Call”, and “American Put”, and correctly update the formulas; (a) update the last period column of the tree, and (b) update separately formula for all other periods, as (a) and (b) have different formulas.

Conclusion

For accountants tasked with the valuation of American share options in financial statements, understanding these financial instruments and mastering their valuation is critical for accurate financial reporting and compliance. The attached template serves as a resource for quick check on the valuation.

Note: The template included is designed only to assist accountants in evaluating reasonableness of the valuation. The actual value should be obtained from more sophisticated valuation techniques.