How to renegotiate all those bad loans at no cost to the taxpayer.

Earlier this month, President Obama announced a homeowner-relief plan that would offer $75 billion in subsidies to homeowners who have trouble making mortgage payments. The problem with the president's plan is that it does little to address the principal source of the housing crisis—the fact that the bursting of the housing bubble has plunged millions of homeowners into negative equity. Their houses are worth less than their mortgages, or "underwater." What's still needed is an approach to mortgage forgiveness that will give homeowners the right to force mortgage holders to accept terms that both sides can live with. Executed correctly, this could resolve the crisis without costing the taxpayer any money. Really.

The key to understanding our plan is that houses are worth more if kept or sold by their owners than if they are foreclosed on. Bankers tell us that when they foreclose on a house, it typically loses a great deal of value, as much as 30 percent to 50 percent. And this is on top of the loss that the house has already suffered because of the general economic downturn. This means that if you bought a house for $300,000 and today you can sell it for $240,000 but instead lose it to foreclosure, the house will eventually go for only $120,000 to $168,000. The reasons are well-known: Foreclosure can be a time-consuming process, and empty houses are difficult to maintain. Sometimes, they are taken over by squatters and vandalized. And one badly maintained house can bring down the block, leading to more underwater homeowners, more mortgage defaults, and more foreclosures.

If foreclosure is so costly, why don't lenders avoid this cost through renegotiation? Renegotiations aren't happening because so many mortgages are securitized. In the old days, if you wanted to renegotiate your loan, you just called your bank. Now you have to deal with the loan servicer, who acts on behalf of the thousands of mortgage-security holders who have a right to a share of your payment. The loan servicer gains little and loses a lot if it attempts to renegotiate a loan. Securities holders don't trust servicers and threaten to sue them if they renegotiate loans; servicers usually don't lose much money if the mortgage defaults.

The solution to this problem is for the government to force renegotiations to occur. A simple plan could do this. The plan would give all homeowners who live in a ZIP code where house prices have dropped more than 20 percent the option to have their mortgage reduced to the current market value of the house. In exchange, these homeowners would yield to their lenders 50 percent of the future appreciation of the house. To avoid any gaming and future moral hazard, both the current and the future value of the house will be determined by multiplying the purchase price and the variation in the housing price index. So if you bought your house for $300,000, and the average house in your ZIP code has lost 20 percent of its value, then your new house is assumed to have a value of $240,000. If your mortgage was $280,000, now it is $240,000 (the new value of the house). You are no longer underwater.

For the homeowner, this is a very attractive proposition. Suppose he has a $300,000 mortgage on a house he bought for $350,000 but today is worth only $200,000. With the plan, he will receive a $100,000 reduction in his mortgage in exchange for giving up a portion of the future appreciation of the house should that happen. Using the tools of finance theory, we can calculate the value of the "option" that the homeowner gives to the bank. Assuming an 8 percent annual volatility in house prices and an 11-year tenure in the house, the option is worth $36,000. The homeowner loses $36,000 from the lost future appreciation but gains $100,000 in the reduction in mortgage debt: a good deal. The homeowner also has a good incentive to maintain his property. If the homeowner adds a bathroom, he reaps the full benefits of this addition when he sells the house. Although he must pay the bank 50 percent of the increase in the price of the average house in the ZIP code, he keeps any additional return if his own house appreciates more quickly than the average house because of the new bathroom.

For the lender, there is also money to be made. If he were to foreclose, he would get only $100,000 to $140,000, the market value of the house after it has declined 30 percent to 50 percent because of foreclosure. If the mandated renegotiation occurs, he gets $236,000 ($200,000 from the mortgage and $36,000 from the option). This is an excellent deal, even if some homeowners default on the renegotiated mortgage.