Bonds w/Embedded Options

When the yield curve is upward slopping we know the following:

  1. Call option is unlikely to be exercised and has a low value, while the put option is valuable.

  2. When the yield curve flattens, the call option becomes MORE valuable, while the put option losses value.

With regards to point 1) Isnt that a positive for a callable bond? ie the option is worth less, so the bond is worth more in an upward sloping curve.

with regards to point 2) When the curve flattens, a callable bond will UNDERPERFORM - however which will perform better in a curve flatten environment, a putable or a callable bond? Does anyone have any better logic to understand this?

I’m not sure about #1.

Upward sloping curve…bonds will be discounted at a HIGHER rate in the future, as per the curve…thus, it is unlikely for the callable bond to be called

Regarding point 1, with the call option falling even your straight value should fall.

Point 2, your putable bond has higher effective duration. So even if the put option drops to 0, theres a good chance your straight value will move upwards.