Hope everyone is having some fun with the reading so far
I just ran into two concepts dont quite understand. Hope someone can help me with these. Thank you!
For the arbitrade free framework to value the bond with embedded options. The Kaplan book states to use “one period forward rates while using the spot rates for valuing the straight bond.”
Why we need to use forward rate for emebbed bond while using spot rate for straight bond?
page 218 of the fixed income section in Kaplan, it says that “Duration of an option free bond would also decrease as interest rate increases (but not as significantly)”
page 218 of the fixed income section in Kaplan, it says that “Duration of an option free bond would also decrease as interest rate increases (but not as significantly)”
Why the option free bond duration ever changes?
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when rate increases - price of the bond decreases. When price of the bond decreases - the duration of the bond changes (increases) - because it will take longer to pay off the bond. If you look at duration as the price sensitivity of the bond to interest rates. (Price decreases - duration increases)
You use forward rates in a binomial interest rate tree. It doesn’t matter whether you’re valuing a straight bond or a bond with embedded options; binomial interest rate trees are built with 1-period forward rates because we’re discounting back only one period at each step.
For an option free bond, if rates rise bond prices will fall but being a fixed rate bond it is quicker to pay off your bond at a lower rate. Thus duration would fall. From a formula perspective also, the price falls but the rate also increases which reduces cash flows (both the numerator and denominator fall). And as you move forward in time, the price actually should be a bit higher than calculated since it should yield lesser. So actually duration should decrease even as rates rise with time isn’t it (as denominator is actually a bit higher since maturity is closer)?
