Other good advice below, especially in drawing the distinction between appraised value and assessed value. However, let me be something of a contrarian.
Let's suppose the home you're considering is truly 15% below current market value. Not some worthless appraisal done for a refi a year ago, and not some worthless assessment. But assume that true comps have sold in the past 3 months for, say, $500,000, and you can buy an identical house for 15% less--or $425,000. And you'll be living there for 3 years, then selling.
Now, you and I don't have a crystal ball, so we don't know what home prices are likely to do in those 3 years. And that's a critical piece of information. However, considering that home prices have been declining...that there are a huge number of homes still likely to go into foreclosure...that the economy in general seems to be cooling...and that investors in some of the harder-hit areas, such as certain parts of California, are bracing for a 5-7 year period of declining, then flat prices...it's entirely possible that home prices in many areas will be the same as, or less than, they are today.
So you buy the house for $425,000. Three years from now, the market is still soft, and prices have slipped another 5%. So the comps are at $475,000. Your total cost of selling is probably going to be around 10%--real estate commission, taxes, fees, and the inevitable (in a flat or buyer's market) price negotiating downward. Hey, right now, even in decent markets, it's considered good if a house sells for 97%-98% of its listing price. So you put your house on the market for $475,000, and after 10% in expenses receive $427,500. You've barely broken even.
And yes, you may have received some tax benefits along the way (I'm not an accountant; check with your own accountant for details), but your monthly payments might have been around $3,000, depending on type of loan, taxes, etc. Compare that with whatever the cost to have rented the same or comparable house would have been, and you may find that you'd have been better off renting.
Now, if you're going to stay there for 5 years, your chances of coming out ahead improve. The market has a better chance of strengthening, and you'll have paid down a bit more on your mortgage (if it's amortized).
Two suggestions: Consider a lease-option. Lease the property for essentially the same monthly cost as rent, but have some of the lease credited toward the purchase price. Lock in a price today. If the market improves sufficiently, you can at some point buy the property, knowing you've got some built-in equity. If the market remains flat, or dips, you have no further obligation when your lease expires.
Second suggestion: Buy at a greater discount than 15%. A questionable investment at 15% under market with only a 3 year holding period becomes more attractive if you're getting that same property at 20% or 25% under market. That will narrow the available properties somewhat, but there are some out there. And you may sleep a lot more comfortably, not having to worry whether the market will decline 5%.
Hope that helps.