What are "bond marks"?

Credit Default Swaps are customized contracts traded on the OTC market between two counterparties. Since they don't trade on exchanges, their valuation is subjective. Since Burry owned many swaps, he wanted accurate pricing or IOW, he wanted "to make sure that their marks on his bonds are fair."

Suppose that you own some asset (for example, a stock, a bond, a house, a work of art, a collectible action figure...)

A lot of times, you're curious to know the "fair" price of your asset, i.e. how much you'd get if you sold it in an orderly market. How can you find this out without actually selling your asset? (Sometimes you also want to know the "prudent" price, i.e. how much you'd get if you sold the asset quickly in distressed markets, also known informally as a "fire sale".) A 300+ page accounting document "Topic 820" discusses what's fair.

Stocks in the secondary market are the easiest because most stocks are traded many times a day. The trades are reported to stock exchange, and everyone can see the prices with a small delay. So you can assume that the fair price of your stock is the price at which it traded. In contrast, the prices of a stocks that trade for the first time (initial public offering) are less certain until they actually begin trading in the market.

Bonds are harder. Although some bonds (for example, U.S. Treasury notes and bonds) trade frequently and their prices are easily observed, most other bonds (for example, most corporate bonds, asset-backed securities, etc) trade seldom.

U.S. regulators require that most bond trades be reported to a database called FINRA TRACE. If you have access to it, then you will know the price at which your bond was last traded, but that might have been literally weeks ago. If you know that a particular bond was sold 3 weeks ago at 95 (% of face value), you don't know whether you'd be able to sell it now for 90 or 100.

Market participants have several databases where they contribute what they think are fair prices of various assets that haven't necessarily traded in a while. Typically, the databases drop the outliers, and publish the median contribution as the "consensus" price. A typical example is Totem.

For assets that don't have an observable traded price and don't have a consensus price (such as real estate, art, collectibles...) you typically pay an expert to assess the asset's value using a "model". For example, your real estate assessor might think along the following lines: "a house 2 blocks away was just sold for $200,000. This house has 10% more square feet, but the location is not as nice, so I'll assess it at $190,000".

This dialogue in The Big Short refers to a time during the 2007-2008 crisis when the market was distressed. There was no orderly market for a while. Some financial instruments were being sold really cheap because their sellers needed cash fast. Some market participants felt that, just because some bond or asset-back was recently sold at 30% of face value under "fire sale" conditions, a similar bond might nevertheless fetch a better price once the markets became more orderly. They were right, but the markets took a long while to come back. Calling the price that you hope to be able to get in a while isn't exactly a "fair" price anymore.

So, for example, asome asset manager could mark some bond at face value and argue that this was still a fair price and the recent trade at 30% should be ignored as a fluke. But some other asset manager might simultaneously mark the same bond at 20%, extrapolating its downward trajectory.