With a number of the largest U.S. banks having repaid the capital they received from the Troubled Asset Relief Program, the only real string still attached to them are the warrants issued to the government as part of the bailout.

There’s a lot of money at stake with the warrants, with some estimates of their value ranging between $3.7 billion and $5.1 billion. With getting at the true value of the warrants, banks are loath to shell out too much to buy them back; however, the Treasury Department is already hearing grumbling from Congress and others about selling back the taxpayer’s upside too cheaply. After the Treasury Department released the outline of its process to determine prices for buybacks of the warrants last week, Dealscape spoke with Espen Robak, president of Pluris Valuation Advisors, an expert on the tricky science of determining the value of options and warrants.

The Deal: What are the most important things to take into account when valuing warrants?

Espen Robak: We take into account the usual characteristics that you would apply to any auction. Factors such as volatility and how far into the money the option is. If the warrants are very far into the money, they become worth quite a bit more.

But a critical element here, and the reason why the government shouldn’t expect to get top dollar for these warrants, is that they are illiquid. They are unusual instruments; they’re not tradable immediately; they can be registered, but there is no active market for them. It’s possible to sell them in private transactions; you can’t just call a broker and say, “Sell my warrants.” Especially for the smaller banks. Where there’s going to be even less demand, you do need to consider that [valuation] models — like Black-Scholes are going to give you a value that is significantly higher than what you’re likely to get in an actual transaction.

Even for traded options, people who work with the Black-Scholes model apply a pretty wide “fudge factor” because they know there are all sorts of imperfections in the real market. But for illiquid warrants, the fudge factor will be larger. It’s a liquidity haircut. As with anything that’s illiquid, you’re going to take a haircut on the equivalent value it would command if it was fully liquid. That’s really what makes these warrants worth substantially less than what you would get for fully liquid ones.

The Deal: How will all this play into offer the banks make to Treasury for the warrants?

Espen Robak: If they’re smart, the banks are going to ask for a price that’s substantially below the theoretical value of these things. That could set up some contention between the government and the banks in this process.

The Deal: Is Treasury’s solution a good one for the banks?

Espen Robak: It sounds like the Treasury has found a solution that’s balanced. Their number one concern has got to be to maximize return for the taxpayer, who ultimately made these investments. The banks got money at a time when the idea of investing in a bank was a relatively scary prospect. Considering the significant perceived risk at that point in time for investing in highly levered banks with very substantial losses coming down the pike, they got money that was relatively cheap, and in return the taxpayers got warrants so that they could share in the upside.

The government ultimately wants to sell these warrants. There’s nothing to be gained by sitting on them. It’s better to get out of them now. So if the banks are willing to pay back at a reasonable amount, I think the Treasury is going to be very happy to sell. There’s a balance to be struck. They don’t want to set the price so high that the banks are unwilling to buy them at all. It’s better to get something out of this.

If the Treasury feels a bank is offering something unreasonably low, they can always turn around and sell them on the open market. There are hedge funds, institutions and others more than willing to buy these warrants, if they can get them at a good price.