Lattice Model

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To begin with, we will discuss the inputs of the Lattice Model. The Lattice Model will use these user inputs to generate several outputs. In our model, the output being calculated is the Value Per Option, which is multiplied by the number of options to calculate the Total Value of Options. In our Lattice Model, these inputs are:

Current Stock Price
Exercise Price
Contractual Life of the Option
Suboptimal Exercise Factor
Volatility
Risk-Free Interest Rate
Dividend Yield
Number of Shares Granted
The Current Stock Price is the stock price on the grant date. The Exercise Price is the contractual price that the employee must pay to obtain a share. Generally, the exercise price and the current stock price are the same. The contractual life of the option is the period of time from the grant date during which options can be exercised. The Suboptimal Exercise Factor, also called the "Early Exercise Factor", is a multiplier of the exercise price at which the employee would exercise his options. As an example, if the Suboptimal Exercise Factor is 2, the employee is assumed to have exercised his options when the market price is twice the exercise price. Volatility reflects the degree to which the stock tends to change in price. The risk-free interest rate is the rate of a return from an investment with no risk. Since this is only theoretical, it is common for the rate of return on a 90-day US Treasury Bill to be used. The dividend yield in our model is a continuous yield on an annual basis. The number of shares granted is the number of shares the employee can purchase during the contractual life of the option.

The Lattice Model uses a binomial method to calculate the expected price. Our model calculates the expected possible future prices at the end of each year. For this model, we have a maximum contractual life of 4 years. There are two types of calculations that are made. The first is the probability of each instance. Every year, the stock is...
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