Interest Rate Volatility

CFA Level II Fixed Income
#1

The below is taken from one of the FI TTs:

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It makes sense to me that interest rate volatility declining decreases value of options and therefore decreases value of putable and increases value of callable (formulas that help me understand this: straight bond - call option = value of callable and straight bond + put option = value of putable).

HOWEVER, what is confusing me is the statement that i highlighted in bold above. I thought that when the slope moves from flat to upward sloping, the value of the callable bond decreases and value of putable decreases (higher interest rates bring bond prices down).

Could someone please explain this to me? I’m trying to understand how both concepts fit together.

Thank you !!!

#2

the question only asks about the interest rate volatility effect! read carefully!

further explanation on the bold part:

increasing interest rate (upward sloping) affects both callable and straight bonds equally price-wise (assuming both have the same coupons). No issuer in their right mind would like to call a bond when interest rates increase and since call option is really out of the money, the call value is at the minimum of zero.

When it comes to putable, the loss on the bond value is offset by the increase in value of the put option (as the put approaches in the money). Putable bonds still decrease in value but not as much as callable and straight.

#3

thank you so much! makes a lot more sense