If you understand binomial tree pricing, you can conceptualise like this:

YC moves from flat to upward sloping Forward rates go up Binomial tree rates (forward rates) go up as well Discounting at higher rate at each node implies more chance of put as straight bond PV’s are lower. Put option gains value, straight loses value net/net the putable bond should lose value but more slowly than a straight as Putable = Straight + Put option

Thanks! I tried to explain it to myself exactly the same way. I still don’t get then,whey _ “If interest rates increase, the value of a call increases and the value of a put decreases.” _

Or am I mixing up two things here with plain options and embedded options and they just don’t behave the same? (which in my mind would not make a lot of sense…)

if interest rate increases, value of a put increases, because bond price will drop in value and bondholders is more likely to exercise the put as the put option approaches in-the-money

if interest rate decreases, value of a call increases, because the issuer can now refinance their bonds at a lower interest rate and is more likely to exercise the call.