Warrants

Warrants outstanding and exercisable are summarized as follows:



	Shares(1)		Weighted Average Exercise Price		Range of Exercise Prices
Outstanding at December 31, 2017	180,894		$	24.96	$2.50-$105.00
Exercised	—		—		—
Expired	(3,988	)	31.25		—
Outstanding at September 30, 2018	176,906		$	24.87	$2.50-$105.00
Exercisable at September 30, 2018	176,906		$	24.87	$2.50-$105.00

(1) Outstanding and exercisable information includes 3,000 equity-classified warrants.

Warrant Liability

The Company's warrant liability is carried at fair value and is classified as Level 3 in the fair value hierarchy because the warrants are valued based on unobservable inputs.

The Company determines the fair value of its warrant liability using the Black-Scholes option-pricing model unless the awards are subject to market conditions, in which case it uses a Monte Carlo simulation model, which utilizes multiple input variables to estimate the probability that market conditions will be achieved. These models are dependent on several variables such as the instrument's expected term, expected strike price, expected risk-free interest rate over the expected term of the instrument, expected dividend yield rate over the expected term and the expected volatility. The expected strike price for warrants with full-ratchet down-round price protection is based on a weighted average probability analysis of the strike price changes expected during the term as a result of the full-ratchet down-round price protection.

The assumptions used in the Black-Scholes option-pricing model to estimate the fair value of the warrant liability as of September 30, 2018 were as follows:




Expected volatility	95.0%-122.5%
Risk-free interest rate	2.6%-2.9%
Dividend yield	—
Expected life in years	1.0-3.2

The assumptions used in the Monte Carlo simulation model to estimate the fair value of the warrant liability as of September 30, 2018 were as follows:




Expected volatility	114.3%
Risk-free interest rate	2.6%
Dividend yield	—
Expected life in years	1.1

The warrant liability, included in accrued expenses and other current liabilities in the accompanying consolidated balance sheets, is re-measured at the end of each reporting period with changes in fair value recognized in other income (expense), net in the consolidated statements of comprehensive loss. Upon the exercise of a warrant that is classified as a liability, the fair value of the warrant exercised is re-measured on the exercise date and reclassified from warrant liability to additional paid-in capital.