The following table summarizes amounts charged to expense for stock-based compensation related to employee and director stock grants and stock option grants and recorded in connection with stock options granted to non-employee consultants:

 

 

 

. The fair value of each stock option award is estimated on the grant date using the Black-Scholes option-pricing model. The estimated fair value of employee stock options is amortized to expense using the straight-line method over the vesting period. The estimated fair value of the non-employee options is amortized to expense over the period during which a non-employee is required to provide services for the award (usually the vesting period).

 

The Company estimates volatility based on an average of (1) the Company’s historical volatility since its common stock has been publicly traded and (2) review of volatility estimates of publicly held drug development companies with similar market capitalizations.

 

. The risk-free interest rate is based on the U.S. Treasury yield curve in effect at the time of grant commensurate with the expected term assumption.

 

. The expected term of stock options granted is based on an estimate of when options will be exercised in the future. The Company applied the simplified method of estimating the expected term of the options, as described in the SEC’s Staff Accounting Bulletins 107 and 110, as the historical experience is not indicative of the expected behavior in the future. The expected term, calculated under the simplified method, is applied to groups of stock options that have similar contractual terms. Using this method, the expected term is determined using the average of the vesting period and the contractual life of the stock options granted. The Company applied the simplified method to non-employees who have a truncation of term based on termination of service and utilizes the contractual life of the stock options granted for those non-employee grants which do not have a truncation of service.

 

 The Company records stock-based compensation expense only for those awards that are expected to vest. A forfeiture rate is estimated at the time of grant and revised, if necessary, in subsequent periods if actual forfeitures differ from initial estimates. An annual forfeiture rate of 2% was applied to all unvested options for the nine months ended September 30, 2018 and for the year ended December 31, 2017. Ultimately, the actual expense recognized over the vesting period will be for only those shares that vest.

 

The Company has not historically recorded dividends related to stock options.

 

Exercise prices for all grants made during the nine months ended September 30, 2018 and 2017 were equal to the market value of the Company’s common stock on the date of grant.

 

A summary of stock option activity is as follows:

 

 

The aggregate intrinsic value of options outstanding is calculated based on the positive difference between the estimated per-share fair value of common stock at the end of the respective period and the exercise price of the underlying options. There have been no options exercised during 2018. Shares of common stock issued upon the exercise of options are from authorized but unissued shares.

 

As of September 30, 2018, there was approximately $753,000 of total unrecognized compensation cost related to unvested stock-based compensation arrangements. Of this total amount, the Company expects to recognize approximately $170,000, $480,000, $96,000 and $7,000 during 2018, 2019, 2020 and 2021 respectively. The Company’s expense estimates are based upon the expectation that all unvested stock grants and stock options will vest in the future, less the forfeiture rate discussed above. The weighted-average grant-date fair value of vested and unvested stock grants and stock options outstanding at September 30, 2018 was $45.67 and $21.34, respectively.

 

During the nine months ended September 30, 2018, the Company granted a total of 8,000 options.

 

s. During 2017, the Company granted 46,000 shares of restricted common stock with a weighted average grant date fair value of $21.00. The shares vest annually over a three year period. As of December 31, 2017, 38,000 shares of restricted common stock were outstanding. There were no restricted stock grants issued during the nine months ended September 30, 2018. A summary of restricted stock activity is as follows: