"Above par" is a term that refers to a situation when the trading price of a bond is above its face value. If a bond trades above par, it means that market interest rates have fallen since its initial issue. Most bonds trade above or below their initial par value.
Coupon rates play a determining role in bonds trading below or above par. Investors will pay a premium for a higher coupon rate, even it that means paying over par value. For example, a $1,000-US Dollar, five-year bond that pays an annual coupon of 10 percent might have an actual value of $1,168 USD if its coupon value beats a market rate of 6 percent. Therefore, investors looking to purchase this bond should expect to pay closer to $1,168 USD than to its $1,000 USD initial value.
One danger in purchasing bonds or securities above par is the risk that the bonds will lose value after their acquisition. When paying $1,168 USD for a $1,000-USD bond, an investor needs that bond to stay at or above its current value before trading. If it falls below $1,168 USD, the investor likely will lose money after trading.
Along these lines, purchasing above par callable bonds can be risky. Issuers of callable bonds can ask that they be redeemed before expected maturation, within their agreed-upon terms. Though normally an issue for discount bonds, above par bonds can also run the risk of defaulting. Paying for the premium bond, the trader must be sure that the bond will be valid in the future when traded.
Bond purchasers who plan for their bonds to fully mature do not need to be concerned about par value. All bonds will be redeemed at maturation for their initial value as long as they do not default. Private bonds normally start at $1,000 USD, and government bonds can be $10,000 USD or more.