interest rate change and option price

On page 171 of Schweser notes (Book 5) they say that “when interest rates increase, the value of a call option increases and the value of a put option decreases.” According to the no-arbitrage relations for puts and calls, this makes sense. However, looking back at bonds, isn’t the opposite true. For bonds with embedded options, an increase in rates decreases call options and increases put options, and vice versa. I am confused…or maybe just wrong. Ahhh…

There are two effects - the rho of the option which is it’s own sensitiity to interest rates and then the moneyness of the option. In a callable bond, they work in opposite directions but moneyness almost always wins.