If the yield curve is upward‐sloping at the time of issue, if a callable bond is issued at par, it implies that the embedded call option is out‐of‐the‐money. It would not be called if the arbitrage‐free forward rates at zero volatility were actually realized.
In this statement what is the significance of upward sloping at the time of issue? and why embedded call option is out‐of‐the‐money. (without knowing the value of straight bond how we can say this?
Please help!
Upward sloping yield curve means that the interest rates of longer maturities are higher than the rates of shorter maturities. For example: 1-year T-bill yield is 4%, the 15-year bond yield is 5% and 30-year bond yield is 6.5%.
A callable bond will be called if its price is above the call price. To that happen interest rates must get lower, so the yield curve must flattern or even invert to a downward sloping yield curve.
If at the time of issuance the yield curve was upward sloping and the bond price was at par, then the callable bond is unlikely to be called because its price is below the call price, hence out of the money.
Thanks not able to undersatnd this “then the callable bond is unlikely to be called because its price is below the call price, hence out of the money.”
what is value of Call price ior exercise price n this case?
The value of the call is from the rearranged formula of Vcallable = Vstraight - Vcall (because the value of the call option is negative to the bond holder, as the firm is the one with the ability to exercise it, not the call holder). Rearranging the above, Vcall = Vstraight - Vcallable.
The bond won’t get called if it is trading below its call price because the company could just go into the market and purchase the bond back for below the call price (i.e. why would it buy it back for more than it needs to if it is cheaper in the market).