Flood Insurance Market Parity and Modernization Act This bill amends the Flood Disaster Protection Act of 1973 to revise requirements for federal and private flood insurance. This bill revises the financial requirements that apply to flood insurance for home loans or loan guarantees by the Federal National Mortgage Association (Fannie Mae) and the Federal Home Loan Mortgage Corporation (Freddie Mac). Private flood insurance must meet any financial strength requirements set forth by Fannie Mae and Freddie Mac. Private flood insurance may include nonadmitted insurers (including surplus lines insurance) as long as the insurer is eligible to provide insurance in the home state of the insured and complies with the laws and regulations of that state. The National Flood Insurance Act of 1968 is amended to direct the Federal Emergency Management Agency (FEMA) to consider any period during which a property was continuously covered by private flood insurance to be a period of continuous insurance coverage, including for the purposes of National Flood Insurance Program subsidies.