Derivative Financial Instruments — Warrants

Certain warrants issued in connection with the Company’s equity financings are accounted for as derivative liabilities. Accordingly, the warrants are remeasured at each balance sheet date based on their estimated fair value using the Black-Scholes option pricing model. Changes in fair value are recorded within Company’s statements of operations.

The range of assumptions used to determine the fair value of the warrants valued using the Black-Scholes option pricing model during the periods indicated was:



	Year ended December 31,
	2019	2018
Fair value of Trovagene common stock	$1.24 - $3.75	$3.15 - $25.14
Expected warrant term	3.1 - 4.1 years	0 - 5.1 years
Risk-free interest rate	1.56% - 2.49%	1.76% - 2.92%
Expected volatility	102% - 111%	47% - 131%
Dividend yield	—%	—%

Expected volatility is based on the historical volatility of Trovagene’s common stock. The warrants have a transferability provision and based on guidance for instruments issued with such a provision, Trovagene used the remaining contractual term as the expected term of the warrants. The risk-free interest rate is based on the U.S. Treasury security rates consistent with the expected remaining term of the warrants at each balance sheet date.

The following table sets forth the components of changes in the Company’s derivative financial instruments—warrants liability balance, valued using the Black-Scholes option pricing method, for the periods indicated.



Date	Description	Number of Warrants		Derivative Instrument Liability
December 31, 2017	Balance of derivative financial instruments—warrants liability	77,942		$	649,387
	Expiration of derivative financial instruments	(13,446	)	—
	Change in fair value of derivative financial instruments—warrants during the year recognized as a gain in the statement of operations	—		(617,072		)
December 31, 2018	Balance of derivative financial instruments—warrants liability	64,496		32,315
	Change in fair value of derivative financial instruments—warrants during the year recognized as a gain in the statement of operations	—		(28,188		)
December 31, 2019	Balance of derivative financial instruments—warrants liability	64,496		$	4,127

The remaining contractual term of the warrants outstanding at December 31, 2019 and 2018 was approximately 3.1 and 4.1 years, respectively.

At December 31, 2019 and 2018, the total fair value of the above warrants accounted for as derivative financial instruments—warrants, valued using the Black-Scholes option pricing model, was $4,127 and $32,315, respectively, and is classified as derivative financial instruments—warrants liability on the balance sheet.