Par value is the face price of a bond. It is also known as “nominal value” or “face value”. If a $1,000 bond trades at $1,000, then it trades “at par”. There are two conditions that may make a bond trade not at par:
First, bonds may trade below par (“discount”) if default risk rises. A junk bond for a company near bankruptcy may trade at pennies on the dollar in order to compensate buyers for taking on the risk of non-repayment.
Second, changing interest rates can affect the demand for a bond. Suppose a $1,000 bond has a 3% annual coupon and is trading at par. Then the Federal Reserve cuts interest rates substantially. Since the 3% return of the bond is now better than what market participants can find elsewhere in the market, the demand for the bond rises. A buyer may then wish to pay more than $1,000 for the bond (“premium”) to get access to the higher interest rate. Conversely, if interest rates rise, sellers of the bond might have to offload the bond for less than $1,000 in order to get people to accept the lower 3% interest rate.