# Binomial pricing model

According to the text.

“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?

Slightly different, yes.

But the point of the statement in the text is that option-free bonds are valued using zero volatility.

In practice, if you used a binomial tree to value an option-free bond, you’d add a constant spread to ensure that you got the same valuation as you would using zero volatility.

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.

Thanks.