This is correct.
Stock options are highly affected by the volatility of the stock in the market. The higher the volatility, more valuable is the option.
The strock grants are not options and the price is set at the date they are granted to the employee.
The volatility affects the initial valuation of the stock options granted (e.g., through use of the Black–Scholes model to determine the fair value of the options). The initial valuation of the options determines the expense recognized. Compensation expense for stock grants is based on the fair market value of the stock on the day of the grant and is not affected by the stock’s volatility.