Change in volatility relative shape of yield curve

CFA Level II Fixed Income
#1

Hello,

In a flat yield curve environment, if interest rate volatility declines, the value of callable will rise while the value of putable will fall.

I agree with the second part of the statement '"the value of callable will rise while the value of putable will fall. "

But I dont know does the shape of yield curve will affect this decision rule or not?

Like for example if it will be downward or upward sloping does the relation as stated will vary?

Thanks

#2

When yield curve is upward sloping investor is more likely to exercise the put option, hence putable bond is worth more. When yield curve is downward sloping, issuer is more likely to exercise call option, hence callable bond is worth more less.

#3

Do you mean the call bond or option? Lower vol will reduce the call option value which in turn increases the overall price.

#4

i dont follow this logic, can you please explain?

In a flat yield curve environment, if interest rate volatility declines, the value of callable will rise while the value of putable will fall.

Low IR vol will influence the return on the underlying, no, so low IR vol should reduce a callable’s value (unless its an option on the interest rate), no?

#5

Value of call OPTION will decline. But value of the callable BOND (that is what he/she means by callable) will rise…

#6

^^^

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

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

for the value of the bond itself the shape of the yield curve is inverse to the value of the bond itself. Higher yield s= lower value of a bond vice versa

If the yield curve is upward sloping then the value of the bond will go down lowering the value of the call option since it will be out of the money, but it will increase the value of the put option as it is at or near the money and will be excerceised. If the yield curve is downward sloping then the value of the bond goes up which puts the call option at or near the money raising its value. The put option will lose value as the value of the bond increases.

If the yield curve is flat for example insert 100 into the value of the bond in both equations. More (less) volitility increases (decreases) the value of both a call and put option. Let’s say it raises the value of both to 5. For the value of a callable bond the answer is now 95 and the value of the puttable bond is 105. The call option is seen as in the hands of the short thus the negative sign in front and you the long hold the put thus the plus sign. Hope that helps.

#7

ah! thanks makes sense!