Embedded option value and interest rates

So how are the value of a bond’s call option and interest rates related? i would appreciate answers since i got confused

i think from an investor’s standpoint - 1. call option drops in value when rates are low due to reinvestment risk 2. the put option gains in value when the rates are high since an investor would want to get out of the current lower yielding bond.

Arent call options higher in value when rates are low. The value of a callable bond is low compared to an option free bond at a lower yield bcoz the bond can be called a t a particular price. As the yield increases, the value of the call option reduces.

smeet that is my understanding too

whoops, i goofed up i guess i meant the call option bond’s price / put option bond’s price when i mentioned the relationships i thought. all the various relationships are confusing me now.

A bond call gains in value when interest rates go down. There are a bunch of ways to see that including: a) Interest rates down => bond prices up => call price up b) Interest rates down => cheaper to refinance debt => issuer wants to call debt to refinance => call option value up These relationships hold whether or not the call option is embedded in the bond.

JoeyDVivre, that sounds about right. I also try and remember it by thinking that in a world where there are only two types of investment: T-Bills, or coupon bonds (issued by corporations), investors will value fixed income securities higher when the RFR is low because it provides them with a better rate of return. Whereas, when the RFR is high, investors will pile into T-Bills because not only is the rate of return comparable, but also, there is zero default risk. And yep, as the bond price rises, so does the value to call it at a lower price.