Flatten / Invert Curves, Effect on Value of Options

Hi All,

I created the following table but I am missing some fields and I want to run this by you experts to make sure I am understanding things right.

I. If increasing interest rate volatility

Call value: up; Callable bond value: down;

Put value: up, Putable bond value: up

Straight bond value, same

II. if increasing yield curve level

call value: down; callable bond value: down

put value: up; putable bond value: up

straight bond value, down by a lot, more so than a callable bond

III. if flattened or inverted curve

call value: up; callable bond value: up (is this right??? CFAI doesn’t discuss this and this is from my meta-understanding)

put value: down; putable bond value: ??? (what happens to this?)

straight bond value: up by a lot, more so than a callable bond (is this right? I am also not sure about this. Please help me confirm)

Thanks all! Hope my format is not confusing at all

I might have made a mistake above. The value of the putable bond decreases with yield curve level increasing, right?

Yield curve upward → putable bond increase in value since high prob that putable option will ITM

If the yield curve moves up, putable bonds decrease in value, just not by as much as a comparable straight bond would. Putable bonds are composed of 2 parts: the straight bond and the embedded put option. Although it is true that increasing rates would cause the value of the put option to increase, there is still the inverse relationship between interest rates and bond prices, which would cause the straight bond portion of the putable bond to decrease. So, the put option will increase in value, but not by enough to offset the decrease in price of the bond as a whole. The net effect is that as interest rates go up, putable bond prices still go down.