11. DERIVATIVE INSTRUMENTS

The warrants issued in connection with the Company’s May 2014 public offering to purchase 1,750,156 shares of the common stock (see Note 10) have anti-dilution protection provisions and, under certain conditions, require the Company to automatically reprice the warrants. Accordingly, these warrants are accounted for as derivative warrant liabilities. Through the date of the warrant exchange (Note 13), the Company used the Binomial Lattice option pricing model and assumptions that consider, among other factors, the fair value of the underlying stock, risk-free interest rate, volatility, expected life, and dividend rates in estimating fair value for the warrants considered to be derivative instruments. As of December 31, 2017 the derivative warrant liability was insignificant. Changes in the fair value of the derivative financial instruments are recognized currently in the Company’s consolidated statement of operations as a derivative gain or loss. The warrant derivative gains or losses are non-cash expenses and for the years ended December 31, 2017, 2016, and 2015, a (gain) loss of $2,267, $(593) and $10,804, respectively, were included in other income (expense) in the Company’s consolidated statement of operations.

The fair value of these derivative instruments at December 31, 2017 and 2016 was $4 and $1,314, respectively, and was included as a derivative warrant liability in current liabilities. The assumptions used principally in determining the fair value of warrants were as follows:


	December 31,
	2017		2016		2015
Risk-free interest rate	1.91	%	1.20	%	0.65	%
Expected dividend yield	0	%	0	%	0	%
Contractual term	1.35	years	2.4	years	3.4	years
Expected volatility	82	%	89	%	100	%

The primary underlying risk exposure pertaining to the warrants is the change in fair value of the underlying common stock for each reporting period.

The table below presents the changes in derivative warrant liability during the years ended December 31, 2017, 2016, and 2015:


	Year Ended December 31,
	2017		2016		2015
Balance at beginning of year	$	1,314	$	1,907	$	7,224
Increase in derivative liability prior to warrant exchange		3,029		—		—
Reduction in derivative liability due to warrant exchange		(3,537)		—		—
Repurchase of warrants		(40)		—		—
Fair value of derivative warrant liability reclassified to additional paid in capital		—		—		(16,121)
Increase (decrease) in the fair value of warrants		(762)		(593)		10,804
Balance at end of year	$	4	$	1,314	$	1,907