# What happens to undated government stocks when interest rates dip below the coupon rate?

What happens to undated government stocks (debt— known as "bonds" in the US) which pay a coupon and have an embedded call option, when interest rates dip below the coupon rate? Will the market value of the bond exceed its par value, or is the risk that the bond will be redeemed at any time liable to depress the price?

• This is an interesting question, though to answer it, a bit more explanation could be helpful— I take it from the way your question is phrased that these are callable debt securities without any specified term? – dismalscience Aug 14 '15 at 2:28
• Yes, that is what I was trying to say. It think there are slightly different names for the same thing in different countries. – jrrk Aug 14 '15 at 11:16

Consider an example where the government has issued a \$100 bond paying 4% per period and (for whatever reason) chooses not to exercise the option immediately, the prevailing interest rate is 3% per period, and the coupon rate is 4% per period: • Period 1: \$4 payment, discounted present value is \$3.88 • Period 2: \$4 payment, DPV is \$3.77 • Period 3: \$4 payment, DPV is \$3.66 • Period 4: \$4 payment, call option exercised, \$100 principal returned, DPV is \$92.40
Total value: \$103.72 (difference due to rounding). Now consider the case where the bond is outstanding, rates drop to 3%, and the bond is immediately called— the bond pays out \$100, plus whatever interest has accrued.