9. Warrants

The following is a summary of activity in the number of warrants outstanding to purchase the Company’s common stock for the nine months ended September 30, 2019 (in thousands):

The following is a summary of activity in the number of warrants outstanding to purchase the Company’s common stock for the nine months ended September 30, 2018 (in thousands):

Warrants consist of equity-classified warrants and warrants with the potential to be settled in cash, which are liability-classified warrants. As of September 30, 2019, and 2018, 159,164 warrants are accounted for as liabilities and 84,211 warrants are accounted for as equity.

Warrants Classified as Equity

Equity-classified warrants consist of stand-alone warrants with rights to buy shares of the Company at a pre-designated price on or before the date of expiration, irrespective of the market price. These purchase warrants are not attached to any debt or equity instruments, thus considered freestanding, and there are no circumstances under ASC 815 that require the warrants to be classified as liabilities or as derivatives. Thus, our May 2018 warrants will be classified as equity, and their value will be carried in the additional paid-in capital account in the stockholders’ equity section of the balance sheet.

These warrants were granted to the underwriters and investment brokers for services provided related to the Company’s May 2018 equity financing, and collectively grant the right to buy 84,211 shares of our stock at $2.09 per share for up to four years until expiration from the commencement date of October 27, 2018.

Warrants Classified as Liabilities

Liability-classified warrants consist of warrants issued by Biozone in connection with equity financings in October 2013 and January 2014, which were assumed by the Company in connection with its merger with Biozone in January 2014. Warrants accounted for as liabilities have the potential to be settled in cash or are not indexed to the Company’s own stock.

The estimated fair value of outstanding warrants accounted for as liabilities is determined at each balance sheet date. Any decrease or increase in the estimated fair value of the warrant liability since the most recent balance sheet date is recorded in the condensed consolidated statement of operations as changes in fair value of derivative liabilities.

The fair value of the warrants classified as liabilities is estimated using the Black-Scholes option-pricing model with the following inputs as of September 30, 2019:

The fair value of the warrants classified as liabilities is estimated using the Black-Scholes option-pricing model with the following inputs as of September 30, 2018:

As of the third quarter in 2019, the Company’s available historical market prices and price volatility exceeded the remaining contractual terms of outstanding warrants accounted for as liabilities. Therefore, as of September 30, 2019, the Company calculated the cumulative volatility percentage used in the Black-Scholes option-pricing model based on its own historical price volatility. In prior periods, including as of September 30, 2018, the Company estimated volatility using a blend of its own historical stock price volatility as well as that of market comparable entities since the Company’s common stock had limited trading history and limited observable volatility of its own. The expected life assumption is based on the remaining contractual terms of the warrants. The risk-free rate is based on the zero-coupon rates in effect at the balance sheet date. The dividend yield used in the pricing model is zero, because the Company has no present intention to pay cash dividends.