Chapter 9: The Model Inputs. STOCK AND STRIKE PRICE. The stock price required for the ESO valuation analysis is based on some future grant date’s stock price forecast. | CHAPTj g The Model Inputs STOCK AND STRIKE PRICE The stock price required for the ESO valuation analysis is based on some future grant date s stock price forecast. Typically the strike price is set to the stock price at grant date or issued at-the-money. In an options world the binomial lattice is created based on the evolution of the underlying stock price starting at grant date to forecast the future until the maturity date based on the underlying stock s volatility. The forecast stock price at grant date can be obtained from various sources. The first is from the firm s own finance department and investor relations department where stock price forecasts are usually available. These forecasts tend to be obtained using a straight-line growth approximation and can be used as a baseline. A stock price consensus of Wall Street analysts can be used as well. Sometimes actual prices will be forecasted and in certain other cases we can use the earnings per share EPS price to earnings PE ratio and price to earnings growth PEG ratio to forecast stock prices. For instance if the PE is expected based on historical data to remain flat for the term of the option the EPS projections at the grant date can be multiplied by this PE ratio to obtain the forecast stock price. If the PE ratio is expected to grow . PEG is not zero then the PE at grant date can be computed through the PEG. The same multiplication with the EPS can then be applied and the stock price forecast obtained. Another approach is the use of econometric modeling. A well-prescribed method is to simulate thousands of stock price paths over time using a Brownian Motion process. Based on all the simulated paths a probability distribution can be constructed at each time period of interest. A simple Brownian Motion can be depicted as 119 120 BACKGROUND OF THE BINOMIAL LATTICE AND BLACK-SCHOLES MODELS where a percent change in the variable S or stock price denoted d S is simply a combination of a deterministic part p
