For the periods presented, the following significant instruments are accounted for on a fair value basis:

Periodically, we entered into certain forward natural gas contracts (“natural gas contracts”), which are accounted for on a mark-to-market basis. We are utilizing these natural gas contracts as economic hedges for risk management purposes but are not designated as hedging instruments. At December 31, 2020, our natural gas contracts included 7.3 million MMBtu of natural gas, that extended through December 2021, but these contracts were settled during the first quarter of 2021, primarily due to the weather event discussed in Note 5. At June 30, 2021, we had no outstanding natural gas contracts. The valuations of the natural gas contracts are classified as Level 2. At December 31, 2020, the valuation inputs included the contractual weighted-average cost of $2.65 per MMBtu and the weighted-average market value of $2.49 per MMBtu.

For the six months ended June 30, 2021, we recognized a gain of $2.7 million (including a realized gain of $1.5 million), all of which was recognized in the first quarter. For the three and six months ended June 30, 2020, we recognized a minimal gain and a loss of $0.7, respectively. The gain is classified as a reduction of cost of sales and the loss is classified as cost of sales.

As discussed in Note 8, certain embedded features (“embedded derivative”) relating to the redemption of the Series E Redeemable Preferred, which includes certain contingent redemption features and the participation rights value have been bifurcated from the Series E Redeemable Preferred and recorded as a liability. At June 30, 2021, and December 31, 2020, we estimate that the contingent redemption features have fair value since we estimate that a portion of the shares of this preferred stock would be redeemed prior to October 25, 2023. For certain other embedded features, we estimated no fair value based on our assessment that there is a remote probability that these features will be exercised.

The fair value of the embedded derivative was valued using discounted cash flow models and primarily based on the difference in the present value of estimated future cash flows with no redemptions prior to October 25, 2023, compared to certain estimated redemptions during the same period and applying the effective dividend rate of the Series E Redeemable Preferred. In addition, at June 30, 2021, and December 31, 2020, the fair value of the embedded derivative included the valuation of the participation rights, which was based on the equivalent of 303,646 shares of our common stock at $6.05 and $3.39 per share, respectively.

The valuations of the embedded derivative are classified as Level 3. This derivative is valued using market information, management’s redemption assumptions, the underlying number of shares as defined in the terms of the Series E Redeemable Preferred, and the market price of our common stock.

For the three months ended June 30, 2021, and 2020, we recognized an unrealized loss of approximately $0.7 million and an unrealized gain of approximately $0.1 million, respectively, due to the change in fair value of the embedded derivative. For the six months ended June 30, 2021, and 2020, we recognized an unrealized loss of approximately $1.2 million and an unrealized gain of approximately $0.8 million, respectively, due to the change in fair value of the embedded derivative. The unrealized gain and loss are included in non-operating other income and expense.

The following details our assets and liabilities that are measured at fair value on a recurring basis at June 30, 2021, and December 31, 2020:

			Fair Value Measurements at June 30, 2021 Using
Description	Total Fair Value at June 30, 2021		Quoted Prices in Active Markets for Identical Contracts (Level 1)		Significant Other Observable Inputs (Level 2)		Significant Unobservable Inputs (Level 3)⁽¹⁾		Total Fair Value at December 31, 2020
	(In Thousands)

Assets - Supplies, prepaid items and other:
Natural gas contracts	$	—	$	—	$	—	$	—	$	80
Total	$	—	$	—	$	—	$	—	$	80

Liabilities - Current and noncurrent accrued and other liabilities:
Natural gas contracts	$	—	$	—	$	—	$	—	$	1,285
Embedded derivative	$	2,181	$	—	$	—	$	2,181	$	1,029
Total	$	2,181	$	—	$	—	$	2,181	$	2,314