“Consider a callable bond. When interest rate volatility increases, the value of the call option increases, the value of the straigth bond is unchanged, and the value of the callable bond decreases.”
I don’t get that part. For a binomial pricing model, more or less volatility at a given point in time will change the one period forward rates and change the calculated market price for a straight bond.
So a change in volatility of interest rates will affect both components, the value of the option, and the value of the bond. Right?
The value of an option-free bond is affected by the level of interest rates, but not by the volatility of interest rates: you use the (zero-volatility) spot curve to calculate the value of an option-free bond.
I was referring to the valuation of an option free bond using a binomial tree.
Let’s say for a given market price of a 3 year T-security, the implicit volatility to make up the binomial tree forward rates is 10%, now if I increase the volatility input, the one period forward rates will spread, giving me a different valuation using backward induction?
That spread should be incorporated in the implicit value of the volatility, given the current market price. I understand the idea that interest rate volatility does not affect the current level of interest rates, of which ulitmately determine price. But I find it strange that the effects of a change in volatlity only affects the OAS spread, when it should also have an effect on the underlying straight bond price in the binomial model. I guess the assumption here is a change in volatility with all else the same (z-spread, price). So a credit risky and a risk free bond, both of which are option free, will always have the same Z-spread independent of changes in interest rate volatility, if we were to draw out both on a bionmial tree.
I need to test this out myself, but maybe after the exam when I have time.