Since you took out the loan 2 years ago with less than 20% equity, and prices have decline since then, your absolute best option is A) to request to have it removed when you hit 8o% of the original LTV , noted in the link from IONEGARM above. For example, if it is a 30-year fixed at 90% LTV then it would would take 7-10 years to reach this point if paying no additional principal.
Option B) … If you have other assets or cash you could consider paying it down to about 80% of the home’s current value and refinancing. This would likely require a pile of cash, which you may not have because you chose a less than 20% down in the first place. The only reason I would choose plan B is if the rate on your loan is significantly higher than today’s rates.
