Callable and Putable Bond values with interest rate volatiliy

CFA Level II
#1

Hello,

In the text, I read that value of call and put options themselves increase with interest rate volatility, but the callable bond values decrease while the putable bond values increase. I do not understand why this would be the case if (all else equal) you would expect that call and put bonds themselves would move with the way the options values move. This seems to be the case for putable bonds but not callable bonds and do not understand why.

Thanks,

#2

Value of putable bond = value of straight bond + put option

Value of callable bond = value of straight bond - call option

#3

The reason the callable bond decreases in value while the puttable bond increases in value with volatilitiy is because of the difference between going long or going short on an option. All long positions in options increase in value with increase in volatility. On a callable bond, you actually have a short position in the call (the issuer has the long position) while on a put, you are on the long position.

That’s why in the equation above, the call has the “-” indicating short, while the puttable has the “+” indicating long.