Mortgage insurance is insurance that the borrower must purchase for  the lender. Mortgage insurance is sold to borrowers who are a higher  risk for the lender. The insurer agrees to sell insurance to cover the  lender in the case of non-payment by the insured. The home buyer must  pay for the policy and if he/she does not fulfill the mortgage  obligation while the insurance is in effect, the insurance will pay the  lender the principal owed. Eligibility requirements for this insurance  change with the type loan the borrower is qualified for. The borrower  may qualify for government backed loans such as VA or FHA and mortgage  insurance is made available. If the borrower is taking out a loan that  is not backed by the government then a product called Private Mortgage  Insurance (PMI) is made available.
Not only is down payment a factor, but also the condition of the home  purchased. The home has to be livable. That is, there must be adequate  utilities, have a heating unit, have no serious damage to the structure  and the borrower must live in the home. If the home does not meet these  requirements the repairs must be made before the loan is approved and  mortgage insurance will issue a policy on the home.
The lender requires the insurance and will manage the insurance  through payments made on the mortgage. This costs the lender so the  lender will only require the payments through the riskiest part of the  loan repayment plan. This will be up until the borrower has 20% equity  in the house in a lot of cases. If the payment history on the note is  poor then the borrower will have to have at least 22% equity before the  lender will agree to remove the mortgage insurance coverage requirement.  If you want to apply for removal of the insurance at 80% of your loan  then you need to make sure that you pay your mortgage payments on time.  If you are late, don't go past 30 days. The lender will review your  history, especially the prior one or two years and evaluate whether you  can drop the insurance.