Convexity of callable bond

[llll]

230 Spring 1999 question #2 asked how interest rate change affect the duration and convexity of a callable bond.

For convexity, I only know it is negative for a callable bond. Can someone tell how it vary with interest rate?

This question is included in JAM Condensed Outline page pp-6 Question #2 part b. (without answer).

Thanks in advance.

[zapped]

my simple attempt:

callable bond price = price of noncallable bond - call option. if interest rate changes (becomes more volatile), the call option price goes up, so the callable bond price goes down. i would think that convexity would decrease (become more negative) if the interest rate becomes more volatile since convexity decreases the price.

putable bond price = price of nonputable bond + put option. if interest rate changes (becomes more volatile), the put option price goes up, so the putable bond price goes up. i would think that convexity would increase (become less negative) if the interest rate becomes more volatile since convexity decreases the price on bonds with embedded options.

but that is my simplistic intuitive first glance....a total guess.

it could be that convexity decreases in both cases & that duration affects the price more....so without a numerical example, i am not sure.

[WWSituation]

Here's what I would say. Good luck on the exam.


% Price Change of a Bond =

-(Duration) * (change in i) + (Convexity) * (Change in i)^2

If interest rates drop, the Duration component adds to the price change.
Negative convexity will offset this change (like when a callable bond stops changing in price when it approaches the call price) and positive convexity will magnify the change further (a putable bond becomes much more valuable when rates drop).

If interest rates rise, the Duration component adds to a negative price change. Negative convexity will add to the negative change (a callable bond is more valuable when rates are rising - the option declines in value) and positive convexity will offset the negative price change (a putable bond stops changing in price when it falls below the put price).

[chucky almendinger]

I think it depends on where you are on the yield curve. My humble opinion.

[zapped]

from the examples in JAM, it seems like the duration ha a much bigger impact than duration. but then again, i don't remember any of those problems having embedded options, so, never mind!