Two years after collateral demands from Goldman Sachs Group Inc. helped spark a cash crunch at American International Group Inc. that led to the insurance giant's near collapse, a mystery remains: How did Goldman come up with the mortgage-securities prices it used to extract cash from AIG?

The Wall Street firm is now trying to convince its critics that it used accurate prices amid a congressional inquiry into the causes of the financial crisis.

Last week, Goldman submitted documents detailing how it established values in 2007 and 2008 for mortgage securities insured by AIG to the Financial Crisis Inquiry Commission, a bipartisan panel probing the crisis, according to people familiar with the matter.

In a nine-page memo, Goldman noted that the securities AIG had insured, known as collateralized-debt obligations, or CDOs, rarely traded, so Goldman instead used prices from trades in other CDOs to "help inform" its valuations on the AIG deals. It also took some cues from valuations of a popular subprime mortgage index known as the ABX. The memo also contained actual prices of trades Goldman conducted in several CDOs, an effort to show how the firm itself bought and sold securities at prices similar to what it provided to AIG as the basis for collateral calls.